The cylinder rolls on the plane without slipping, and the string is parallel to the plane. Assume the cylinder has a radius of R and an inertia moment about its center of mass of I.
Tension in the string (T), the gravitational force on mass m (mg), and the frictional force on the cylinder from the plane are the forces acting on the system (f).
The tension in the string (T) is balanced by the gravitational force on mass m because the string is parallel to the plane (mg). As a result, we can write:
T = mg
To find the acceleration of mass m, we can use Newton's second law for the vertical motion of mass m:
mg - T = ma
Substituting T with mg, we get:
a = g - g(M/m)
where M/m is the ratio of the masses of the cylinder and the mass, respectively.
To find the condition on the ratio M/m for which the cylinder accelerates down the plane, we need to apply Newton's second law for the rotational motion of the cylinder. The torque acting on the cylinder is due to the frictional force f, which is given by:
f = μN
where μ is the coefficient of static friction, and N is the normal force on the cylinder from the plane. Since the cylinder rolls without slipping, the frictional force f is equal to the force due to the tension in the string, which is mg.
Therefore, we can write:
mg = f = μN
The normal force N is equal to the weight of the cylinder, which is Mg. Therefore, we can write:
mg = μMg
Simplifying, we get:
μ = m/M
For the cylinder to accelerate down the plane, the frictional force must be less than or equal to the maximum static frictional force, which is given by:
f_max = μ_s N
where μ_s is the coefficient of static friction. Therefore, we need to have:
f <= f_max
Substituting f and f_max, we get:
mg <= μ_s Mg
Substituting μ = m/M, we get:
mg <= μ_s Mg
Simplifying, we get:
m/M <= μ_s
Therefore, the condition on the ratio M/m for which the cylinder accelerates down the plane is:
M/m > μ_s
where μ_s is the coefficient of static friction between the cylinder and the plane.
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The first active volcano observed outside the Earth was discovered in 1979 on Io, one of the moons of Jupiter. The volcano was observed to be ejecting material to a height of about 3.00×105m
Given that the acceleration of gravity on Io is 1.80m/s2 find the initial velocity of the ejected material.
The material that was thrown out had an approximate initial velocity of 1.50-10⁵ m/s.
How can the ejected material's initial velocity be determined?The following equation can be used to determine the ejected material's initial velocity under gravity's constant acceleration:
y is equal to v₀ x t x (1/2) a x t₂, where:
The values for y, a, and t are as follows: y is the vertical displacement (height) of the ejected material (3.00 10⁵ m); a is the acceleration caused by gravity on Io (1.80 m/s²); t is the time it takes for the ejected material to reach its maximum height (let's assume it is equal to 2 seconds for simplicity).
3.00×10⁵ m = v₀ ×2 s + (1/2) × 1.80 m/s² × (2 s)²
3.00×10⁵ m = v₀ × 2 s + 1.80 m/s² × 4 s²
3.00×10⁵ m = v₀× 2 s + 7.2 m/s²
v₀ = (3.00×105 m - 7.2 m/s²) / 2 s
v₀ = (3.00×105 m - 7.2 m/s²) / 2 s
v₀ = 1.50×10⁵ m/s
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Prove that AxB = B.A
Unless A=B or unless either A or B is the empty set, AxB does not equal BxA. Students typically have no trouble understanding this because we define a cartesian product as an ordered pair, which implies that order would be important.
What is the parameter for solving cartesian product?A plane's cartesian form is denoted by the formula ax + by + cz = d, where a, b, and c are the direction cosines normal to the plane and d is the distance from the origin to the plane.
If and only if the matching initial elements in both ordered pairs are the same, two ordered pairs are said to be equivalent. (ii) There will be mn elements in A B if there are m elements in A and n elements in B. This means that n(A B) if n(A) = m and n(B) = n.
Therefore, When the inner inverse fulfils P R (B ) B (A B) = 0 and (A B) B P R (B) = 0, it is implied that is closed and is the general solution.
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1.2 Determine the total displacement of the diagram in FIGURE 1. 123 m 20⁰ (3) 72 m
The total displacement of the diagram in the velocity-time graph is 55 m.
What is the total displacement?To find total displacement from a velocity-time graph, the area under the curve of the graph is calculated.
Considering the given figure:
The area under the velocity-time graph is composed of two triangles ABF & DCE having area A₁ & A₂ respectively, and a rectangle BEIF having area A3.
The area of A₁ = (2- 0) × (5 - 0)/2 = 5 m
The area of A₂ = (10 - 5) × (10 - 6)/2 = 10 m
The area of A₃ = (5 - 0) * (10 - 2) = 40 m
The total area under the curve = A₁ + A₂ + A₃
The total area under the curve = 5 + 10 + 40 =
The total area under the curve = 55 m
Therefore, the total displacement is 55 m.
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Car A is driving 21.4 m/s in the positive x-direction according to an observer standing stationary on the side of the road. Car B is driving on the same road with a velocity of 27.4 m/s, as observed by a passenger in Car A. What is Car B's velocity as observed by the person on the side of the road?
Car B's velocity as observed by the person on the side of the road is -6.0 m/s, which means that it is moving in the negative x-direction.
explain about velocity ?
Velocity is a physical quantity that describes the rate of change of an object's position with respect to time. In other words, it is the speed and direction of an object's motion. Velocity is a vector quantity, which means that it has both a magnitude (or size) and a direction.
the relative velocity formula, which gives the velocity of one object as observed by another object or observer:
velocity of B with respect to observer = velocity of B with respect to A + velocity of A with respect to observer
In this problem, we have:
velocity of A with respect to observer = +21.4 m/s (positive because it is in the positive x-direction)
velocity of B with respect to A = -27.4 m/s (negative because it is in the opposite direction to A's velocity)
(Note that we use a negative sign for the velocity of B with respect to A because they are moving in opposite directions.)
Using the formula, we get:
velocity of B with respect to observer = -27.4 m/s + 21.4 m/s = -6.0 m/s
Therefore, Car B's velocity as observed by the person on the side of the road is -6.0 m/s, which means that it is moving in the negative x-direction.
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The figure showed a thin rod of length L and charge Q.
Find an expression for the electric potential a distance z away from the center of rod on the line that bisects the rod.
Give your answer in terms of L, Q, z and appropriate constants.
Expression for the electric potential a distance z away from the center of rod on the line that bisects the rod is [tex]V = k * Q / L * \int\limits {cos\theta / z \sqrt{(1 + L^2/4z^2 * tan^2\theta)} d\theta} \, dx[/tex].
The electric potential at a distance z from a point charge Q is given by:
V = k * Q / r
here
k is Coulomb constant and
r is distance from the point charge to the point.
For a thin rod of length L and charge Q, we can model it as a line of charge with linear charge density λ = Q/L. The electric potential at a distance z away from the center of the rod on the line that bisects the rod can be found by breaking the rod into infinitesimal charge elements and integrating the electric potential due to each element over the length of the rod.
Let's consider a small element of length dx located at a distance x from the center of the rod:-
[tex]dQ = \lambda * dx = Q/L * dx[/tex]
The displacement element to pt.:-
[tex]r = \sqrt{(x^2 + z^2)}[/tex]
The electric potential due to this element is:
[tex]dV = k * dQ / r = k * Q/L * dx / \sqrt{(x^2 + z^2)}[/tex]
Integrating this expression over the length of the rod, we get the total electric potential at a distance z away from the center of the rod on the line that bisects the rod:
[tex]V = \int\limits^(^-^L^/^2^)_L_/_2 {k * Q/L * dx / √\sqrt{(x^2 + z^2)}} \, dx[/tex]
To evaluate this integral,
[tex]u = x^2 + z^2, du/dx = 2x dx[/tex],
This can be further simplified:-
[tex]u = z^2 * tan^2\theta + L^2/4 * sec^2\theta[/tex]
[tex]V = k * Q / L * \int\limits {cos\theta / z \sqrt{(1 + L^2/4z^2 * tan^2\theta)} d\theta} \, dx[/tex]
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____help the body change food into energy and repair and replace old and damaged parts.
Answer: Vitamins
Explanation:
When Marcus goes to play golf, he steps up to his ball and swings the club without thinking at all about his technique. Due to years of practice and repetition Marcus has most likely begun to use __________ processes when swinging his golf club.
Due to years of practice and repetition, Marcus has most likely begun to use unconscious processes when swinging his golf club.
What are unconscious processes?The unconscious is the process that proceeds outside the person's awareness and plays a major role in directing thoughts, feelings, behavior, and mental illness.
When Marcus goes to play golf, he steps up to his ball and swings the club without thinking at all about his technique, so the signs about the unconscious process.
Therefore, Marcus has most likely begun to use unconscious processes when swinging his golf club.
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Two box of the masses 5 kg and 40 kg are in contact with each other on a frictionless surface. What is the acceleration of the more massive box?
Answer:ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd
Explanation:
Two balls are dropped to the ground from different heights. One is dropped 1.5 s after the other, but they
both strike the ground at the same time, 5.0 s after the first was dropped. (a) What is the difference in the
heights from which they were dropped? (b) From what height was the first ball dropped? Ans. (a) 63 m;
(b) 0.12 km
Answer:
Height difference: approximately [tex]63\; {\rm m}[/tex].
The first ball was dropped from a height of approximately [tex]123\; {\rm m}[/tex].
(Assumptions: both balls were released from rest, air friction is negligible, and that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex].)
Explanation:
Under the assumptions, both ball would accelerate at a constant [tex]a = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}[/tex].
Let [tex]t[/tex] denote the time since the first ball was released.
Height of the first ball at time [tex]t[/tex] can be modelled with the SUVAT equation [tex]h(t) = (1/2)\, a\, t^{2} + u\, t + h_{0}[/tex], where [tex]u[/tex] is the initial velocity. However, since [tex]u = 0\; {\rm m\cdot s^{-1}}[/tex] by assumption, this equation simplifies to [tex]h(t) = (1/2)\, a\, t^{2} + h_{0}[/tex].
Since this ball reached the ground after [tex]t = 5.0\; {\rm s}[/tex], [tex]h(5.0) = 0\; {\rm m}[/tex]. In other words:
[tex]\begin{aligned}\frac{1}{2}\, (-9.81)\, (5.0)^{2} + h_{0} = 0\end{aligned}[/tex].
Simplify and solve for the initial height of this ball, [tex]h_{0}[/tex]:
[tex]\begin{aligned}h_{0} &= -\frac{1}{2}\, (-9.81)\, (5.0)^{2} \\ &\approx 123\; {\rm m}\end{aligned}[/tex].
In other words, the first ball was dropped from a height of approximately [tex]123\; {\rm m}[/tex].
Similarly, the height of the second ball may be modelled as [tex]h(t) = (1/2)\, a\, t^{2} + h_{0}[/tex].
Since this ball reached the ground [tex]t = (5.0 - 1.5)\; {\rm s} = 3.5\; {\rm s}[/tex] after being released, [tex]h(3.5) = 0\; {\rm m}[/tex]. The initial height of this ball would be:
[tex]\begin{aligned}h_{0} &= -\frac{1}{2}\, (-9.81)\, (3.5)^{2} \\ &\approx (-60)\; {\rm m}\end{aligned}[/tex].
Subtract the initial height of the second ball from that of the first ball to find the difference in initial height:
[tex](123 - 60) \; {\rm m} \approx 63\; {\rm m}[/tex].
An old-fashioned single-play vinyl record rotates on a turntable at 45.0 rpm. What are (a) the angular velocity in rad/s and (b) the period of the motion? nand (h the period of the
The angular velocity in rad/s are 4.7124 rad/s and the period of the motion is 1.333s.
a) Find angular velocity
Given
45 rpm that is rotations per min converting it in to rad/s
we know that the angular displacement for one rotation is 2pi rad
45 rpm = 45*2pi/60
= 4.7124 rad/s
So,the angular velocity is W = 4.7124 rad/s
b) We have relation between the angular velocity and time period is
W = 2pi /T
T = 2pi/W
T = 2pi/4.7124 s
T = 1.333 s
Angular velocity is a physical quantity that describes the rate of change of the angular displacement of an object with respect to time. It is a vector quantity, and its direction is perpendicular to the plane in which the object is rotating. The magnitude of the angular velocity is given by the ratio of the angular displacement of the object to the time taken to complete the displacement. It is measured in radians per second (rad/s).
Angular velocity is an important concept in physics and is used in the study of rotational motion. It is used to calculate the centripetal force required to maintain circular motion and is also used to describe the motion of planets and other celestial bodies. In addition, angular velocity is used in engineering and mechanics to design and analyze rotating machines and devices.
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Quick someone please help this was already due and I need to go to bed plssssssss
The number of amino acids different between sequence 1 and sequence 2 is 2.
The translations of sequence 1 and sequence 2 are different because:
Sequence 1 and 2 have different nucleotide sequencesWhat are nucleotides?Nucleotides are the building blocks of nucleic acids, such as DNA and RNA. They consist of a nitrogenous base, a sugar molecule (ribose or deoxyribose), and a phosphate group. The nitrogenous bases in nucleotides can be adenine, guanine, cytosine, or thymine (in DNA) or adenine, guanine, cytosine, and uracil (in RNA).
Nucleotides are linked together to form long chains, which make up the backbone of nucleic acids. The sequence of nitrogenous bases in nucleotides determines the genetic information stored in DNA.
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How could you use creative thinking to show the relationship between velocity and kinetic energy?.
Kinetic energy depends οn the velocity of the object squared. This means that when the velocity of an οbject doubles, its kinetic energy quadruples.
What is Kinetic energy ?The energy an οbject has as a result of motion is referred to as kinetic energy. If we want tο accelerate an object, we must exert force. To apply a force, we must wοrk hard. When the work is done, energy will have been transferred tο the item, causing it to move at a new, constant speed.
This equation demοnstrates the direct relationship between an object's kinetic energy and the square οf its speed. Therefore, for every twofold increase in speed, the kinetic energy will increase by a factοr of four. A threefold increase in speed will result in a nine-fοld increase in kinetic energy.
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8. In which of the following situations is the kinetic energy of the object decreasing?
A. A sphere is dropped from a building.
B. A satellite moving is a circular motion around the earth.
C. A baseball is heading upward after being thrown at an angle.
D. An elevator is moving upward at a constant velocity
The answer is option C. A baseball is heading upward after being thrown at an angle.
What is kinetic energy?Kinetic energy is a type of energy associated with motion. It is defined as the energy an object possesses due to its motion, and is dependent on both the object's mass and its velocity. The formula for kinetic energy is KE = 1/2 mv^2, where m is the mass of the object and v is its velocity.
Kinetic energy can be transferred between objects, and is often involved in collisions and other interactions. For example, when a moving object collides with another object, some of its kinetic energy may be transferred to the second object. Kinetic energy is an important concept in physics and is used in many real-world applications, such as in the design of vehicles, machines, and athletic equipment.
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fill in the balance equation below with the name of missing compuod. The answer the question that follow in the space provided
____ ____ sunlight ____ ___ ____
The answer to the question that follows in the space provided is
carbon dioxide + water + sunlight = glucose + oxygen.
What is photosynthesis?Green plants produce their food in the presence of sunlight during photosynthesis. The process is only done by autotrophs.
They use carbon dioxide and water, which are inorganic components from the environment, to create glucose, and oxygen gas is released into the atmosphere.
Carbon dioxide + water → Glucose + Oxygen
Therefore, the correct option is
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The bottom cube has mass m2 = 4.8kg and sits on a surface without friction. The top cube has mass m1 = 2.2kg. The friction between the two cubes is μ = 0.5. What is the maximum force that can be applied on the upper cube so that the two cubes move together?
The maximum force that can be applied on the upper cube is 26.29N.
Solving for the the maximum force that can be applied on the upper cube, we have:The maximum force that can be applied on the upper cube so that the two cubes move together is given by the equation:
F_max = μ(m1 + m2)g
where,
μ = the coefficient of friction
m1 and m2 = the masses of the top and bottom cube
g = the acceleration due to gravity.
Substituting in the values, we get:
F_max = 0.5(2.2kg + 4.8kg)(9.81m/s²)
F_max = 26.29N
Therefore, the maximum force that can be applied on the upper cube is 26.29N.
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A bowling ball with a mass of 7.0 kg strikes a pin that has a mass of 2.0 kg. The pin flies forward with a velocity of 7.0 m/s, and the ball continues forward at 4.0 m/s. What was the original velocity of the ball?
The original velocity of the ball was -4.0 m/s, which means it was moving in the opposite direction of the final velocity (4.0 m/s).
How to find the original velocity of the ball?
The original velocity of the ball can be found using the principle of conservation of momentum. The principle of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act upon it. In this case, the closed system is the ball and the pin. Before the collision, the total momentum of the system was zero (since the ball was at rest). After the collision, the momentum of the system is given by the ball's momentum plus the pin's momentum.
The momentum of an object is given by the product of its mass and velocity:
p = m * v
where:
p is the momentum of the object
m is the mass of the object
v is the velocity of the object
First, let's find the total momentum of the system after the collision:
p_total = p_ball + p_pin
p_total = (m_ball * v_ball) + (m_pin * v_pin)
p_total = (7.0 kg * v_ball) + (2.0 kg * 7.0 m/s)
Now, we'll use the principle of conservation of momentum to set the total momentum of the system before the collision equal to the total momentum of the system after the collision:
p_total_before = p_total_after
0 = p_total
0 = (7.0 kg * v_ball) + (2.0 kg * 7.0 m/s)
Solving for v_ball:
v_ball = (-2.0 kg * 7.0 m/s) / 7.0 kg
v_ball = -4.0 m/s
So, the original velocity of the ball was -4.0 m/s, which means it was moving in the opposite direction of the final velocity (4.0 m/s).
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What are the magnitude Δ and angle of the change in velocity if the initial velocity is 65.0 m/s south and the final velocity is 20.0 m/s west? Let the angle be measured relative to the east direction (e.g., =90∘ means Δ⃗ points north, =180∘ means Δ⃗ points west, etc.).
Answer:
∆ = 68.0∠ = 107.1°Explanation:
You want the magnitude and direction of the change in velocity from 65.0 m/s south to 20.0 m/s west.
ChangeThe change in velocity can be represented by a vector from the initial velocity to the final velocity as shown in the attachment. The magnitude and direction of it can be found using the usual tools for solving triangles.
MagnitudeThe magnitude of the change is the hypotenuse of a right triangle with legs 20 and 65. Its value is ...
∆ = √(20² +65²) = √4625 ≈ 68.007 . . . . m/s
The magnitude of the velocity change is ∆ = 68.0 m/s.
DirectionAs the diagram shows, the direction of the change is west of north by an angle θ that satisfies ...
tan(θ) = 20/65
θ = arctan(20/65) ≈ 17.1027°
The direction of the change measured from east is 90° +17.1° = 107.1°.
The angle of the velocity change is about 107.1°.
__
Additional comment
These calculations are handled neatly by a vector calculator, as shown in the second attachment.
A rock is thrown upward with a velocity of 14
meters per second from the top of a 50
meter high cliff, and it misses the cliff on the way back down. When will the rock be 2
meters from ground level? Round your answer to two decimal places.
Answer:
The rock will be 2 meters from the ground after 1.29 seconds.
Explanation:
The motion of the rock can be described by the following kinematic equation:
h = vi * t + 0.5 * a * t^2
where h is the height of the rock above the ground, vi is the initial velocity (14 m/s), t is time, and a is the acceleration due to gravity (-9.8 m/s^2).
Setting h = 2 m and solving for t, we get:
2 = 14 * t + 0.5 * (-9.8) * t^2
Expanding and solving for t, we get:
t = 1.29 seconds
So, the rock will be 2 meters from the ground after approximately 1.29 seconds.
A box with weight of 10000 pounds is held 25 miles above the Earth. What is the box's potential
energy in kip-feet? one kip = 1000 pounds (Remember that weight in pounds already accounts for
acceleration due to gravity.)
The potential energy of the box is 4180 kip-ft.
What is potential energy?Potential energy is described as the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
The potential energy of an object can be calculated using the formula:
PE = mgh
In the scenario,
the mass of the box is m = 10000 pounds and
the height above the ground is h = 25 miles = 25 * 5280 feet = 132000 feet.
The acceleration due to gravity is g = 32.2 ft/s^2.
Substituting these values into the formula, wehave:
PE = mgh = 10000 * 32.2 * 132000 = 4.18 x 10^8 ft-lb
Converting this to kip-ft,
PE = 4.18 x 10^8 ft-lb / 1000 = 4180 kip-ft
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A ball is thrown toward a cliff of height h with a speed of 33 m/s and an angle of 60∘ above horizontal. It lands on the edge of the cliff 4.0 s later.
Answer: I am assuming you're asking for the cliff height, which is 24M
We can use the kinematic equations to find the horizontal and vertical components of the ball's velocity and its final position.
The initial velocity components are:
v_x = 33 m/s * cos(60∘) = 28.6 m/s
v_y = 33 m/s * sin(60∘) = 33 * √3/2 m/s
The displacement components can be found using the kinematic equation:
x = v_x * t = 28.6 m/s * 4.0 s = 114.4 m
y = v_y * t - 0.5 * g * t^2 = 33 * √3/2 m/s * 4.0 s - 0.5 * 9.8 m/s^2 * (4.0 s)^2 = 102.4 m - 78.4 m = 24.0 m
The ball lands on the edge of the cliff, so its height must be equal to h, or:
y = h
24.0 m = h
So, the height of the cliff is 24.0 m.
Two opposite charges of the same magnitude Q = 2x10^-7c are separated by a distance of 15.0cm. What is the magnitude and direction of the force acting on an electron placed at the midpoint
The direction of the force is along the line joining the two charges, and its magnitude is approximately 1.44 x 10^-12 N.
What is magnitude?Magnitude can be defined as the maximum extent of size and the direction of an object.
The force on the electron can be found using Coulomb's law:
F = k * (q1 * q2) / r^2
where
k is Coulomb's constant (k = 9 x 10^9 N*m^2/C^2)q1 and q2 are the magnitudes of the two charges r is the distance between themF is the magnitude of the forceIn this case, the two charges have the same magnitude Q = 2 x 10^-7 C, so we can write:
F = k * [(Q * -Q) / (0.15 m)^2]
where the negative sign for one of the charges indicates that it has the opposite charge to the other. Simplifying this expression, we get:
F = k * (Q^2 / 0.0225)
F = (9 x 10^9 N*m^2/C^2) * (2 x 10^-7 C)^2 / 0.0225
F ≈ 1.44 x 10^-12 N
Therefore, the direction of the force is along the line joining the two charges, and its magnitude is approximately 1.44 x 10^-12 N.
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A ball strikes the floor for 0.0105 s and experiences a change in momentum of 1.52 kg·m/s. What is the force experienced by the ball?
A.) 1.60N
B.)144.76N
C.)23.82N
D.)0.016N
Pic is attached below
The force experienced by an object is 144.76 N.
O\ption B is correct.
What is force?A force is described as an influence that can change the motion of an object or that can cause an object with mass to change its velocity
The force can be calculated using the equation of force = change in momentum / time.
So, force = 1.52 kg·m/s / 0.0105 s = 145 N
Therefore, the answer is 144.76 N.
Some types of force available includes the following:
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12. A truck travelling at 110 km/h has to cover a distance of 640 km in the next 6 hours. Will the driver be on time if he can hold his current speed? (4 marks)
Answer:
calculate the expected time of arrival, we need to divide the total distance by the speed of the truck.
In this case, the expected time of arrival would be:
640 km ÷ 110 km/h = 5.82 hours
So the driver should be able to arrive at the destination within 6 hours if he can hold his current speed.
20. You accidentally throw your car keys horizontally at 6.0 m/s from a cliff 42 m high. How far from the base of the cliff should you look for your keys?
The keys will land 19.32 meters away from the base of the cliff.
How the solution was obtainedAssuming that there is no air resistance, the motion of the keys can be described using the equations of motion for constant acceleration.
The initial horizontal velocity of the keys is 6.0 m/s, and the vertical velocity is zero. The acceleration due to gravity is 9.8 m/s^2, and it acts vertically downwards.
The time taken for the keys to fall from the top of the cliff to the ground can be found using the equation:
h = 1/2 * g * t^2
where h is the height of the cliff (42 m), g is the acceleration due to gravity (9.8 m/s^2), and t is the time taken.
Rearranging this equation to solve for t, we get:
t =√(2h/g)
t =√(2*42/9.8)
t = 3.22 s
During this time, the keys will have travelled a horizontal distance equal to their initial velocity multiplied by the time taken:
d = v * t
d = 6.0 * 3.22
d = 19.32 m
Therefore, the keys will land 19.32 meters away from the base of the cliff.
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POSSIBLE POINTS: 1
Based on what you have learned from this project so far, describe the relationship between mass and gravitational force (the size of the gravity force
vectors). You should use directly proportional or inversely proportional in your answer. Use at least three complete sentences to justify your answer
(explain why you think what you think).
Answer:
F = G * (m1 * m2) / r^2
Explanation:
The relationship between mass and gravitational force is directly proportional. This means that as the mass of an object increases, the magnitude of the gravitational force acting on it also increases. The exact relationship can be described using Newton's law of universal gravitation, which states that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.
This relationship can be expressed mathematically as:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
This relationship makes intuitive sense: larger objects have a greater ability to pull other objects towards them, so the gravitational force they exert is stronger. On the other hand, as the distance between two objects increases, the gravitational force between them decreases, because the pull is spread out over a larger area.
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
A simple circuit contains a 9 V battery connected with wires to a small light bulb. If the current through the bulb is 0.025 A, what is the resistance of the bulb?
Group of answer choices
360 ohms
15 ohms
127 ohms
0.225 ohms
Answer:
[tex]\huge\boxed{\sf R = 360\ ohms}[/tex]
Explanation:
Given data:Potential Difference = V = 9 V
Current = I = 0.025 A
Required:Resistance = R = ?
Formula:V = IR (Ohm's Law)
Solution:V = IR
Divide I to both sides
[tex]\displaystyle \frac{V}{I} = R[/tex]
Put the given data
9/0.025 = R
360 ohms = R
OR
R = 360 ohms[tex]\rule[225]{225}{2}[/tex]
QUESTION 3 Consider a block of mass 6 kg on a rough plane inclined at 25° to the horizontall A force, F of magnitude 37,173 N is applied to this block to keep it moving at a constant velocity 6 kg 25 what is the normal force
The normal force is 53.3 N.
What is the normal force on an object?We have to note that the force that is acting on the object may be a single force or a system of forces. In this case, the force that is acting on the object would have many components including the normal force.
You must note that the normal force is the force that in a direction that is opposite to the weight of the object but does have the same magnitude as the weight of the object.
Thus we can see that the normal force is obtained from;
R = mgcosθ
m = mass
g = acceleration due to gravity
θ = angle
R = 6 * 9.8 * cos 25
R = 53.3 N
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1. Which of the resistors are in parallel connection? Which of the resistors are in series connection?
Answer:
Explanation: In a series circuit, the output current of the first resistor flows into the input of the second resistor; therefore, the current is the same in each resistor. In a parallel circuit, all of the resistor leads on one side of the resistors are connected together and all the leads on the other side are connected together.
When a transverse wave travels through a medium, which of the following is TRUE?
A. the medium determines the wavelength
B. the medium determines the amplitude of the wave vibrations.
C. vibrations are parallel to the direction the wave travels.
D. the medium determines the wave frequency
E. vibrations are perpendicular to the direction the wave travels
The medium determines the amplitude of the wave vibrations is the correct option (B) .
What is wave ?
Laminar and transverse waves are the two types of waves. Longitudinal waves are similar to those of sound in that they alternate between compressions and rarefactions in a medium, much like transverse waves in that the surface of the medium rises and falls.
What is transverse wave ?
The term "transverse wave" refers to motion in which all wave points oscillate along trajectories that are perpendicular to the wave's forward velocity. Transverse waves include electromagnetic (such as radio and light) and seismic S (secondary) waves. Surface ripples on water are another example.
In a transverse wave, the medium's particles vibrate up and down perpendicular to the wave's direction. In a longitudinal wave, the medium's particles vibrate back and forth parallel to the wave's direction.
Therefore, medium determines the amplitude of the wave vibrations is the correct option (B) .
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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 the collision is -11.25 m/s.
A. 11.25 m/s west How to find the final velocity?In this collision, the total momentum of the system before the collision is equal to the total momentum of the system after the collision, since momentum is conserved. The total momentum of the system before the collision can be found by adding up the momenta of the car and truck.
The momentum of the car is given by:
= mass of car * velocity of car
= 1500 kg * 20 m/s = 30000 kg m/s (east)
The momentum of the truck is given by:
= mass of truck * velocity of truck
= 2500 kg * -30 m/s
= -75000 kg m/s (west)
The total momentum of the system before the collision is given by:
30000 kg m/s + (-75000 kg m/s) = -45000 kg m/s
The total mass of the system is given by:
total mass = mass of car + mass of truck = 1500 kg + 2500 kg = 4000 kg
The final velocity of the system is given by:
final velocity = -45000 kg m/s / 4000 kg = -11.25 m/s
Since the final velocity is negative, it means that the system is moving west, which is the direction of the truck's initial velocity.
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