The force of approximately 16.9 N is needed to hold the load stationary on the ramp.
What is friction?Friction is the force that prevents two solid objects from rolling or sliding over one another.
Although frictional forces, such the traction required to walk without slipping, may be advantageous, they can provide a significant amount of resistance to motion.
Since the ramp is frictionless, the only forces acting on the load are its weight (mg) and the normal force (N) exerted by the ramp perpendicular to the surface.
We can break the weight into two components: one parallel to the ramp (mg sin θ) and one perpendicular to the ramp (mg cos θ).
To keep the load stationary on the ramp, the force applied parallel to the ramp (call it F) must balance the component of the weight parallel to the ramp:
F = mg sin θ
Substituting the given values, we get:
F = (5.00 kg) * (9.81 [tex]m/s^2[/tex]) * sin 20.0° ≈ 16.9 N
Therefore, a force of approximately 16.9 N is needed to hold the load stationary on the ramp.
The ideal mechanical advantage (IMA) of the ramp is the ratio of the length of the ramp (L) to its height (h):
IMA = L/h
Let's say the ramp has a height of h and a base of b. Then:
h = b sin θ
L = b cos θ
Substituting the given angle, we get:
h = b sin 20.0°
L = b cos 20.0°
Dividing L by h, we get:
IMA = L/h = (b cos 20.0°) / (b sin 20.0°) = cos 20.0° / sin 20.0° ≈ 1.16
Thus, the ideal mechanical advantage of the ramp is approximately 1.16.
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If air resistance exerts a constant force of 200 N on a car, what amount of forward force from the engine is
needed to make a 1000 kg car accelerate at 10 m/s² forward? Is this force constant or increasing?
The forward force is 10200 N.
What is the forward force?The term "forward force" is not commonly used as a specific term, but it could refer to any force that acts in the direction of motion of an object. For example, the force generated by a car's engine that propels it forward is commonly referred to as the "driving force," which could be considered a type of forward force.
We have to note that the Fnet = ma
= 1000 * 10 = 10000 N
Thus;
Fnet = Force force - Resistance force
Forward force = Fnet + Resistance force
= 10000 + 200
= 10200 N
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The amount of forward force from the engine needed to make the 1000 Kg car accelerate 10 m/s² forward is 10200 N
How do I determine the forward force needed to accelerate the car?First, we shall obtain the net force acting on the 1000 Kg car. Details below:
Mass of car (m) = 1000 KgAcceleration of car (a) = 10 m/s²Net force (F) =?Net force = mass × acceleration
Net force = 1000 × 10
Net force = 10000 N
Finally, we shall obtain the forward force needed to accelerate the car. This is illustrated below:
Net force = 10000 NResistant force = 200 NForward force = ?Net force = Forward force - resistant force
10000 = Forward force - 200
Collect like terma
Forward force = 10000 + 200
Forward force = 10200 N
Thus, the forward force needed is 10200 N
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Let E =3i^+1j^ and F =1i^−3j^.
A. Find the magnitude of E.
B. Find the magnitude of F.
C. Find the magnitude of G =E +F.
D. Find the magnitude of H =−E −2F.
The given vectors E and F are in Cartesian form. To find their magnitudes, we can use the formula:
|v| = √(vx² + vy²)
where vx and vy are the x and y components of the vector.
What is the Cartesian algebra?Cartesian algebra, also known as coordinate algebra or analytic geometry, is a branch of mathematics that deals with the use of algebraic equations to describe geometric shapes and their properties. It is named after the French philosopher and mathematician René Descartes, who developed the Cartesian coordinate system, which provides a way to describe the position of points in space using numbers.
A. Magnitude of E:
|E| = √((3i)² + (1j)²)
= √(9i² + 1j²)
= √(9 + 1)
= √(10)
Therefore, the magnitude of E is √(10).
B. Magnitude of F:
|F| = √((1i)² + (-3j)²)
= √(1 + 9)
=√(10)
Therefore, the magnitude of F is √(10).
C. Magnitude of G = E + F:
G = E + F = (3i + 1i) + (1j - 3j)
= 4i - 2j
|G| = √((4i)² + (-2j)²)
=√(16 + 4)
= √(20)
= 2√(5)
Therefore, the magnitude of G is 2√(5).
D. Magnitude of H = -E - 2F:
H = -E - 2F = (-3i - 2i) + (-1j + 6j)
= -5i + 5j
|H| = √(-5i)² + (5j)²)
= √(25 + 25)
= √(50)
= 5√(2)
Therefore, the magnitude of H is 5√(2).
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The mass of Jupiter is 1/1047 of the Sun's mass (that's 0.000955). We want to confirm this using Newton's version of Kepler's Third Law, following the examples in Lecture 7. We'll use the approximate data for two different moons of Jupiter to see how close the results are. Pick the closest answer in each case: (a) Ganymede is the third moon from the inside. It has an orbital period around Jupiter of approximately 0.0194 Earth years. Its semimajor axis is 0.0071 AU. Which of these comes closest to the mass of Jupiter (in solar masses) when using these data → [Select ] 0.000951 (b) Europa is the second moon from the inside. It has an ork 0.000989 approximately 0.0096 Earth years. Its semimajor axis is 0.0045 AU. Which of these comes closest to the mass of Jupiter (in solar masses) when using these data? [Select] Hint: See also example 3.4 in the textbook.
These come closest to the mass of Jupiter as (a) 0.000951; (b) 0.000955.
what is Kepler's law?Kepler's laws describe the motion of planets in their orbits around the sun.
This question involves using Newton's version of Kepler's Third Law to calculate the mass of Jupiter. Kepler's Third Law states that the square of the period of revolution of a planet/moon around a central object is proportional to the cube of the semimajor axis of the orbit. Newton's version of the law introduces the masses of the two objects in the equation, allowing us to solve for the mass of the central object (in this case, Jupiter) if we know the period and semimajor axis of a moon's orbit around it.
For part (a), we are given the period and semimajor axis of Ganymede's orbit and asked to select the closest answer for the mass of Jupiter when using this data. By plugging the values into Newton's version of Kepler's Third Law and solving for Jupiter's mass, we get an answer of 0.000951 solar masses.
For part (b), we are given the period and semimajor axis of Europa's orbit and asked to select the closest answer for the mass of Jupiter when using this data. Again, by plugging the values into the equation and solving for Jupiter's mass, we get an answer of 0.000989 solar masses.
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Learning Goal:
To understand the role of the internal resistance of various devices and the use of the ammeter and the voltmeter.
Consider the circuit shown.(Figure 1) All wires are considered ideal; that is, they have zero resistance. We will assume for now that all other elements of the circuit are ideal, too: The value of resistance R is a constant, the internal resistances of the battery (r) and the ammeter (RA) are zero, and the internal resistance of the voltmeter (RV) is infinitely large.
The internal resistance of devices like batteries, ammeters, and voltmeters can affect the overall current and voltage in a circuit.
To accurately measure these values, it's important to take into account the internal resistance of these devices and to use them correctly in the circuit. It's important to note that the internal resistance of devices can affect the overall performance of a circuit.
For example, the internal resistance of a battery can affect the voltage available to the circuit and the internal resistance of a speaker can affect its efficiency. Therefore, it's important to take into account the internal resistance of devices when designing and analyzing circuits.
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A 1500 kg car traveling east at 20 m/s collides with a moving 2500 kg truck moving 30 m/s west.. After they collide, the two interlock and move together. What was the final velocity of the truck? (Hint-momentum is a vector and direction matters, use + or - values as appropriate)*
A. 11.25 m/s west
B. 11.25 m/s east
C. 32.6 m/s east
D. 32.6 m/s west
The final velocity of the truck after collision, given that the car and the truck interlock and move together is 11.25 m/s west (Option A)
How do I determine the final velocity of the truck?The final velocity of the truck after the collision can be obtained as illustrated below:
Mass of car (m₁) = 1500 KgInitial velocity of car (u₁) = 20 m/sMass of truck (m₂) = 2500 KgInitial velocity of truck (u₂) = 11 m/sEast = Positvie directionWest = Negative directionFinal velocity (v) = ?Momentum before = momentum after
m₁u₁ + m₂u₂ = v(m₁ + m₂)
(1500 × 20) - (2500 × 30) = v(1500 + 2500)
30000 - 75000 = v × 4000
-45000 = v × 4000
Divide both sides by 4000
v = -45000 / 4000
v = -11.25 m/s
Recall => West is negative
v = 11.25 m/s west
Thus, the final velocity is 11.25 m/s west (Option A)
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Without having the help of the moving pad, you and a friend have to move the very heavy
entertainment center. The kinetic friction opposing the motion is equal to 1600 N and your
maximum applied force is 1000N. How much force does your friend need to apply to make the
entertainment center move at a constant velocity?
The force needed by my friend to make the entertainment center move at a constant velocity is 600 N
How to find force application?To find the force application in a specific situation, one needs to consider the forces that are acting on an object and the net force (the vector sum of all forces acting on an object) which determines the motion of the object.
In order to make the entertainment center move at a constant velocity, the sum of the applied forces must equal the force of kinetic friction. If the maximum applied force you can provide is 1000 N, then your friend needs to apply a force of 1600 N - 1000 N = 600 N.
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When a local house was on fire, the firefighters were able to save most of it by dousing the house with water. What will happen when forensic scientists investigate this fire?.
Forensic scientists will investigate the fire by looking for clues as to what caused it and how it spread. They will collect evidence such as burn patterns and debris, and analyze the scene to determine the origin of the fire.
What is debris?
Debris is any loose material (solid or liquid) that is scattered or discarded, such as the remains of a wrecked or destroyed structure or object. Common examples of debris include rubble, broken glass, fallen tree branches, discarded plastic, scrap metal, and other discarded materials. Debris can also include materials that are the by-product of a process, such as the dust created by grinding or sawing. Debris can also be the result of natural disasters or human activities. Debris can be found in any environment and can cause environmental or safety hazards if left unchecked.
Therefore, Forensic scientists will investigate the fire by looking for clues as to what caused it and how it spread. They will collect evidence such as burn patterns and debris, and analyze the scene to determine the origin of the fire.
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A car moving with an initial velocity of 25 m/s north has a constant acceleration of 5.5 m/s2 south. After 10 seconds its velocity will be
Answer:
80 m/s
Explanation:
v = v₀ + at
v = 25 m/s + (5.5 m/s²)(10 s) = 80 m/s
the perception that seemingly infertile couples who adopt a child are subsequently more likely to conceive a child themselves best illustrates
The perception that seems infertile couples who adopt a child are generally more likely to conceive a progeny themselves best describes an illusory correlation.
What is an illusory correlation?Illusory correlation when we overexcite to one outcome and ignore the other. In psychology, it states that the relationship between the variables, even such a relation does not exist.
In the given passage couples who adopt a child are subsequently more likely to conceive a child themselves best explains, suggesting the illusory correlation.
Therefore, this passage suggests an illusory correlation.
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(17%) Problem 2: The drawing shows a small sphere of mass m=0.26 g that carries a charge of q = 85 x 10-10 C. The sphere is attached to one end of a very thin silk string of length L = 6.25 cm. The other end of the string is attached to a large vertical conducting plate that has a charge density of o = 30 x 10-6C/m². + + + + + + L m, A 25% Part (a) Write an expression for the magnitude of the electric field due to the charge distribution on the conductive plate. E = 0 Grade Summary Deductions 0% Potential 100% €0 B 0 Y b 0 Submissions Attempts remaining: 20 (% per attempt) detailed view d h ( 789 HOME 1456 1 23 + 0 END VO BACKSPACE GEL CLEAR g k j m n P S Submit Hline Feedback I give up! Hints: for a 0% deduction. Hints remaining: 0 Feedback: 0% deduction per feedback. Date Submission History All Date times are displayed in Eastern Standard Time Red submission date times indicate late work. Time Answer Hints Feedback 24 25% Part (b) Write an expression for the horizontal component of the net force acting on the charged sphere in terms of the tension T in the string, the electric field, and the given variables. A 25% Part (c) Write an expression for the vertical component of the net force acting on the charged sphere in terms of the tension T in the string and the given variables. 425% Part (d) What is the angle in degrees that the string makes with respect to the vertical?
θ = 39.7º is the angle in degrees that the string makes with respect to the vertical using Newtons law.
In each exercise, we construct the equations at the equilibrium point using Newton's second law for the sphere. We'll assume that plate 1 is on the left for this exercise.
Y Axis
Y= -W = 0 = W
X axis
X= - F_{e2} + Tₓ = 0
Let's utilize trigonometry to determine the tension's component parts. We gauge the angle in relation to the vertical
sin θ = Tₓ / T
cos θ = T_{y} / t
Tₓ = T sin θ
T_{y} = T cos θ
Gauss's law can be used to determine the electric field of each leaf. Since a cylinder forms a Gaussian surface, the component of the field perpendicular to the cylinder's base is the one containing electric flow.
F = ∫ E. dA
The flow is towards both sides of the plate in this instance, and the scalar product is reduced to the algebraic product.
F = 2E A = q_{int} / ε₀
let's use the concept of surface charge density
σ = q_{int} / A
we substitute
2E A = σ A /ε₀
E = σ / 2ε₀
T cos θ = mg
- q σ₁ / 2ε₀ - q σ₂ /2ε₀ + T sinθ = 0
we introduce t in the second equations
- q /2 ε₀ (σ₁ + σ₂) + (mg / cos θ) sin θ = 0
mg tan θ = q /2ε₀ (σ₁ + σ₂)
θ = tan -1 (q / 2ε₀ mg (σ₁ + σ₂)
data indicates the mass of 0.26 g = 0.26 10⁻³ kg
give the charge density on plate 2, suppose ab = 10 10⁻⁶ C / m²
let's calculate
θ = tan⁻¹ (9.0 10⁻¹⁰ (30 + 10) 10⁻⁶ / (2 (6.25 10⁻¹² *0.26 10⁻³ 9.8))
θ = tan⁻¹ 8.3 10⁻¹)
θ = 39.7º
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If two bowling balls were to collide head on stick to one another, with some loss in kinetic energy, the collision would be considered a(n) ___________ collision.*
A. Cushy
B.Perfectly Inelastic
C.Reversable
D.Elastic
Answer: D
Explanation:An inelastic collision is one in which objects stick together after impact, and kinetic energy is not conserved. This lack of conservation means that the forces between colliding objects may convert kinetic energy to other forms of energy, such as potential energy or thermal energy.
A glider of length 12.4 cm moves on an air track with
constant acceleration (Fig P2.31). A time interval of 0.628 s
elapses between the moment when its front end passes a
fixed point A along the track and the moment when its
back end passes this point. Next, a time interval of 1.39 s
elapses between the moment when the back end of the
glider passes the point A and the moment when the front
end of the glider passes a second point B farther down the
track. After that, an additional 0.431 s elapses until the
back end of the glider passes point B. (a) Find the average
speed of the glider as it passes point A. (b) Find the acceleration
of the glider. (c) Explain how you can compute the
acceleration without knowing
the distance between points A
and B.
[tex]19.7cm/s and 4.70 cm/s^2[/tex] are the average speed and acceleration of the glider.
(a) As the glider's front end crosses point A, start a timer at t=0. The instantaneous speed at t=0.314s, halfway through the time interval, is [tex]12.4cm/(0.628s)=19.7cm/s[/tex], which equals the glider's average speed for the interval between t=0 and t=0.628s.
(b) The instantaneous speed at the point [tex]t=(2.02+2.45)/2=2.23s[/tex]. is equal to [tex]12.4cm/(0.431s)=28.8cm/s[/tex], which is the average speed of the glider for the time span between [tex]0.628+1.39=2.02s[/tex] and [tex]0.628+1.39+0.431=2.45s[/tex].
Now that we are aware of the velocities at two points, we can calculate the acceleration using the formula [tex][(28.8-19.7)cm/s]/[(2.23-0.314)s]=4.70cm/s2[/tex].
(c) The average velocity over a predetermined period of time is determined using the glider's length rather than the distance between points A and B.
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Lab: Newton's Laws of Motion
Newton's law of motion
Three newton's law of motion:-
1. An object will not change its motion unless a force acts on it.
2. The force of an object is equal to its mass time its acceleration.
3. When two objects interact , they apply forces to each other of equal magnitude and opposite direction.
Newton's law of motion are three basic laws of classical mechanics that describes the relationship between the motion of an object and the forces acting on it.
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How much of the total energy in Problem 3 and 4 has been transformed to kinetic energy?
Answer:
Explanation:To find the change in kinetic energy, we subtract the initial energy from the final energy. This answer in positive because the car gains energy when it increases its velocity.
The energy of the flower pot is potential energy. The potential energy of the flower pot when it weighs 3 N in a height of 300 m is 900 J.
What is potential energy ?Potential energy of an object is the energy generated by virtue of its position whereas, kinetic energy is the energy generated by virtue of its motion.
Potential energy = mass x gravity x height
Given the weight of the flower pot is 3N. That is the force by gravity. Then displacement = 300 m.
Thus, P = 3 m × 300 m = 900 J.
If the flower pot is placed at a height of 10 m, the potential energy reduces as follows:
Potential energy = 3 x 10 m = 30 J.
Remaining energy is converted to the kinetic energy
ie. 900 J - 30 J = 870 J
Therefore, 870 J is transformed to kinetic energy.
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Your question is incomplete. But your complete question probably was:
A flower pot weighing 3 newtons is sitting on a windowsill 300 meters from the ground is the energy of the flower pot potential of kinetic? How many joules is this?
When the flower pot in problem 3 is only 10 meters from the ground, what is its potential energy?
How much of the total energy in problems 3 and 4 has been transformed to kinetic energy?
An asteroid is travelling through the solar system at a constant velocity. Which of the following
choices correctly models the forces acting on the asteroid?
Answer:
The forces acting on an asteroid include gravity from the Sun and other celestial bodies, radiation pressure from the Sun, and the pressure from interplanetary gas and dust. The gravitational forces will act to pull the asteroid towards the Sun, while the radiation pressure and interplanetary gas and dust will act to push it away. The net force acting on the asteroid will determine its path and velocity through the solar system.
Explanation:
The cart is given an initial push up the ramp. After this push, as the car moves up the ramp, the direction of the acceleration of the cart is_________the ramp. After ther turns around, and begins moving down the ramp, the direction of the acceleration of the cart is__________ eaches its highest point, the ramp. At the highest point the cart reaches on the ramp, when the cart momentarily comes to rest, the magnitude of the acceleration of the cart is_________O down, down, zeroO up, down, nonzeroO down, down, nonzeroO up, down, zero
The correct answers to the blanks are 1. UP ,2. UP and 3. ZERO
When the cart is initially given a push up the ramp, the direction of the acceleration of the cart is up the ramp. This is because the net force acting on the cart is directed up the ramp, in the same direction as the component of the gravitational force that is parallel to the ramp. As a result, the cart accelerates up the ramp in the same direction as the net force.
When the cart turns around and begins moving down the ramp, the direction of the acceleration of the cart is still up the ramp. This is because the component of the gravitational force that is parallel to the ramp is still directed down the ramp, but the net force acting on the cart is directed up the ramp due to the normal force exerted by the ramp on the cart. As a result, the cart accelerates down the ramp in the opposite direction to the net force, which is up the ramp.
At the highest point that the cart reaches on the ramp, when the cart momentarily comes to rest, the magnitude of the acceleration of the cart is zero. This is because at this point, the cart is at the highest point on the ramp and has stopped moving. As a result, the velocity of the cart is zero, and therefore the acceleration of the cart is also zero.
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You perform an experiment to measure the speed of a car over time. The
results are shown in the graph below.
Speed (m/s)
30
25-
20
15
10
5
0+
O
5
10
A. 24 m/s
B. 22 m/s
15
Time (s)
What was the speed of the car after 20 seconds?
C. 20 m/s
D. 30 m/s
20
25
The speed of the car after 20 seconds are 20 m/s.
What is the speed ?The speed of an object is a measure of how quickly the object is moving in a particular direction. It is typically measured in units such as meters per second (m/s). Speed is a scalar quantity, which means it is only concerned with the magnitude of the velocity (or speed) and not the direction
The graph shows that the speed of the car was 20 m/s after 20 seconds.
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1. A car moves at 10m/s
a. Net Force on the car is zero
b. Force of friction is equal to the forward force applied by the engine
c. Both a and b are correct
d. a is correct but b is wrong
Answer:
d. a is correct but b is wrong.
Explanation:
A car that is moving at a constant speed of 10m/s is experiencing a net force of zero, meaning that the sum of all forces acting on the car is equal to zero. This means that the forward force applied by the engine is equal in magnitude but opposite in direction to the force of friction acting on the car.
The force of friction acts to slow down the car, but it does not equal the forward force applied by the engine. Instead, it is determined by factors such as the weight of the car, the road surface, and the tire traction. If the forward force applied by the engine is greater than the force of friction, the car will accelerate. Conversely, if the force of friction is greater than the forward force applied by the engine, the car will decelerate.
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A 3.0 kg object swings back and forth as a simple pendulum with a small amplitude. The potential energy U of the object as a function of distance x from its equilibrium position is shown above. This particular object has a total energy E of 0.4 J.
b) What is the farthest the object moves along the x-axis in the positive direction? Explain your reasoning.
c) Determine the object’s kinetic energy when its displacement is -8 cm.
d) What is the object’s speed at x = 0?
10cm is the farthest the object moves along the x-axis in the positive direction .0.15J is the object’s kinetic energy when its displacement is -8 cm. 0.316m/s is the object’s speed at x = 0.
Define kinetic energy.
Kinetic energy, which may be seen in the movement of an item or subatomic particle, is the energy of motion. Kinetic energy is present in every particle and moving object. Examples of kinetic energy in action include a person walking, a baseball soaring through the air, a piece of food falling from a table, and a charged particle in an electric field.
Given,
Total energy is 0.4J
m is 3kg
The farthest the object moves along the x-axis in the positive direction would be as potential energy is 0.4J. So from given diagram, displacement will be 10cm
If displacement is -8cm , P.E from diagram will be 0.25J
According to energy conservation formula ,
ME ⇒ U+KE
KE ⇒ ME-U ⇒ 0.4-0.25 ⇒ 0.15J
At x ⇒ 0,
KE ⇒ 1/2 mv^2
0.15 ⇒ 0.5*3*v^2
v ⇒ 0.316m/s
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Below are free-body diagrams for three electric charges that lie in the same plane. Their relative positions are unknown.
Below are free-body diagrams for three electric ch
Along which of the lines (A to H) in the figure(Figure 1)should charge 2 be placed so that the free-body diagrams of charge 1 and charge 2 are consistent?
Figure 2:
Below are free-body diagrams for three electric ch
Along which of the lines (A to H) in the figure(Figure 2)should charge 2 be placed so that the free-body diagrams of charge 1 and charge 2 are consistent?
In Figure 1, charge 2 should be placed along line D to make the free-body diagrams of charge 1 and charge 2 consistent.
The electric field lines produced by charge 2 should point towards charge 1 to provide the attractive force between them. As shown in the free-body diagram of charge 1, the electric field lines point towards the left, which means that charge 2 should be placed on the left side of charge 1. Similarly, in Figure 2, charge 2 should be placed along line F to make the free-body diagrams of charge 1 and charge 2 consistent. The electric field lines produced by charge 2 should point towards the left to provide the attractive force between them. In Figure 1, charge 2 should be placed along line D to make the free-body diagrams of charge 1 and charge 2 consistent.
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A particle moves in a straight line such that its displacement, x meters, from a fixed point 0 on the line at time t seconds is given by x = (t — 1)^3 -2t^2 +1 .
(a) Find the time when the particle is instantaneously at rest.
(b) Find the displacement of the particle from O when t=6 s.
(c) Find the total distance travelled during the first 6 seconds of its motion.
(a) The particle is instantaneously at rest at time, t = 3/2 seconds.
(b) The displacement of the particle is 54 meters from the fixed point O at t = 6 seconds.
(c) The total distance travelled by the particle during the first 6 seconds of its motion is 52 meters.
What is the time when the particle is instantaneously at rest?To find the time when the particle is instantaneously at rest, we need to find the time when its velocity is zero. The velocity of the particle can be found by taking the derivative of its displacement with respect to time, which gives us the velocity function, v(t) = d(x)/dt.
Taking the derivative of x = (t — 1)^3 -2t^2 +1 with respect to time t, we get:
v(t) = 3(t - 1)^2 - 4t
To find when the velocity is zero, we set v(t) = 0 and solve for t:
0 = 3(t - 1)^2 - 4t
3(t - 1)^2 = 4t
t = (3(t - 1)^2)/4
t = (3(t - 1)^2)/4
Solving this equation, we find t = 3/2 seconds. So, the particle is instantaneously at rest at t = 3/2 seconds.
To find the displacement of the particle from O when t=6 s, we simply substitute t = 6 into the displacement function:
x = (6 - 1)^3 - 2 * 6^2 + 1
x = 125 - 72 + 1
x = 54 meters
To find the total distance travelled during the first 6 seconds of its motion, we need to find the definite integral of the velocity function over the interval [0, 6].
x(t) = ∫v(t) dt
x(t) = ∫(3(t - 1)^2 - 4t) dt
x(t) = (t - 1)^3 - 2t^2 + C
where C is the constant of integration. We can determine the value of C by using the initial condition that x(0) = 0:
0 = 0 - 2 * 0^2 + C
C = 0
So, x(t) = (t - 1)^3 - 2t^2.
Finally, to find the total distance travelled during the first 6 seconds of its motion, we evaluate the definite integral of x(t) from 0 to 6:
d = x(6) - x(0)
d = [(6 - 1)^3 - 2 * 6^2] - [(0 - 1)^3 - 2 * 0^2]
d = 125 - 72 - 1
d = 52 meters
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I need help figuring this question out?
The momentum of the driver is 1,750 kgm/s.
What is the momentum of the driver?Momentum refers to an object's tendency to maintain its velocity (or speed) in a straight line unless acted upon by an external force.
The magnitude of momentum is determined from the product of mass and velocity of the object.
The momentum of the driver is calculated as follows;
P = mv
where;
m is the mass of the driverv is the speed of the driverP = 70 kg x 25 m/s
P = 1,750 kgm/s
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A battery is connected to an electrical circuit. During each second, 2.3 coulombs of charge pass through the battery when the switch is closed. The battery supplies energy to each coulomb of charge at a rate of 4.2J C^-1. Take 1 C = 6.24 x 10^18 electrons
State the potential difference across the battery
Answer:
The potential difference across the battery can be calculated using the equation:
Potential difference (V) = Energy supplied (J) / Charge (C)
Energy supplied during each second = 2.3 coulombs * 4.2 J/C = 9.66 J
Therefore, the potential difference across the battery would be:
Potential difference (V) = 9.66 J / 2.3 C = 4.2 V
So the potential difference across the battery is 4.2 volts.
To pick up a few staples from the table, a student wrapped copper wire around a nail and connected it to a battery. She was able use this device to pick up all staples. How was this possible?
A. The current moving through the wire made the nail into an electromagnet.
B. The staples are responding to the wire because it was made of copper.
C. The electricity from the wire was arcing to the staples.
D. The protons in the staples and are attracted to the electrons in the wire.
Answer:
The correct answer is A. The current moving through the wire made the nail into an electromagnet.
An electromagnet is created when a current is passed through a wire. The flow of electrons creates a magnetic field, which can attract or repel other magnetic objects. In this case, when the student wrapped the copper wire around the nail and connected it to a battery, the flow of electrons created a magnetic field around the nail. This magnetic field allowed the student to pick up the staples because they were attracted to the nail, which was now acting as an electromagnet.
What is the case of hose pipe in Newton's third law of motion?
Newton's third law of motion states that "for every action, there is an equal and opposite reaction." In the case of a hose pipe, this law applies to the forces involved in the flow of water through the hose.
When water is flowing through the hose, it is being accelerated by the pressure difference between the inlet and outlet of the hose. As the water moves through the hose, it exerts a force on the walls of the hose, pushing them outwards. This is the "action" described in Newton's third law.
According to the law, there must be an equal and opposite "reaction" force. In this case, the reaction force is the force that the hose exerts on the water. The force of the hose pushing outwards is equal and opposite to the force of the water pushing inwards.
This reaction force is what allows the water to flow through the hose. Without it, the water would not be able to move through the hose and would instead remain stationary.
So, in summary, in the case of a hose pipe, Newton's third law of motion applies to the forces involved in the flow of water through the hose. The force that the water exerts on the hose is equal and opposite to the force that the hose exerts on the water, and this allows the water to flow through the hose.
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A is thrown up into the air with initial vem/s. How fast is the ball moving when it first reachemeters?
Once the ball is thrown, the only force acting on it is gravity, which means that it's acceleration is -9.81 m/s² (negative means downward).
List the known and unknown quantities from the question.
u = initial velocity = 20 m/s
v = final velocity = ? m/s
g = acceleration due to gravity = -9.81 m/s²
t = time interval = ? s
s displacement = 11 m
Before calculating the time it takes for the ball to reach 11 m, the final velocity needs to be calculated using the following kinematic equation.
v² = u² + 2gs
v = √(u² + 2gs)
= √((20 m/s)² + (2x-9.81 m/s² x 11 m)) = 13.57 m/s V=
Calculate the time it takes the ball to reach 11 m using the following kinematic equation.
V = u + gt
Solve for t.
t = (v-u)/g
t (13 57 m/s - 20 m/s)/(-981 m/s²) = 0.655 s
A child is riding on a merry go round. As the speed of the merry go round is doubled, the magnitude of the centripetal force acting on the childa. Remains the sameb. Is quadrupledc. Is doubledd. Is halved
A youngster is on a merry-go-round. The centripetal force acting on the toddler is quadrupled as the merry-go-speed round's is doubled. So, option B is correct.
What is centripetal force?
Centripetal force is a term used to describe a force that moves a body along a curved path. The centripetal force is always applied in the general direction of the path's instantaneous center of curvature and against the motion of the subject. According to Isaac Newton, it is "a force by which bodies are dragged or forced, or in any other way gravitate, towards a point as to a center." Gravity is the centripetal force that generates astronomical orbits, according to Newtonian mechanics theory.
As, the formula of Centripetal force,
[tex]F=\frac{mv^2}{r}[/tex],
We can see that, F is directly proportional to [tex]v^{2}[/tex], When the speed of the merry-go-round is doubled, the centripetal force acting on the child is multiplied by four.
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TRUE OR FALSE: Increasing the time of impact during a collision increases the force experienced by the object. * True False
Answer:
False
Explanation:
I'm pretty sure increasing the time of impact actually decreases the force because it is being spread out.
A 400Hz tuning fork is vibrating, producing a sound wave in the
air.
What is the wavelength of the sound wave (in given units)? In centimeters ?
The wavelength of the sound wave that has a frequency of 400Hz is 7.5 × 10⁵m.
How to calculate wavelength?Wavelength is the length of a single cycle of a wave, as measured by the distance between one peak or trough of a wave and the next.
It is often designated in physics as λ, and corresponds to the velocity of the wave divided by its frequency.
According to this question, a 400Hz tuning fork is vibrating, producing a sound wave in the air. The wavelength is calculated as follows:
λ = 3 × 10⁸ ÷ 400
λ = 7.5 × 10⁵m
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c. i) A block of mass of 2 kg with constant velocity is pushed along a table by a
force of 5N, what is the magnitude of the force opposing its motion?
Answer:
The Force of Friction:
Friction is a self-adjusting force. The block in the question is moving with constant velocity under the force of 5 N. This implies that the force of kinetic friction acting on the block is also 5 N, acting opposite to the applied force and net force on the block is
