The dimensional relation of the time period bob with its length is shown below.
what is meant by "dimensional analysis"?a method of analysis that represents physical quantities in terms of their fundamental dimensions in the absence of enough data to create precise equations.
What is the purpose of dimensional analysis?Dimensional analysis is a method used in engineering and the physical sciences to reduce physical quantities like acceleration, viscosity, and energy to their three basic dimensions of length, mass, and time (T).
[T]=[M^0 L^0 T^1]
[L]=[M^0 L^1 T^0]
[g]=[M^0 L^1 T^-2]
SQUARE ROOT OF (L/g)=[m0l1t0]/[m0l1t-2]
=[m0l0t1]
= R.H.S.
Hence it's dimensionally correct.
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Why are dams on rivers thicker at the bottom than the top?
Dams on rivers are thicker at the bottom than the top because the majority of the force exerted on the dam is from the weight of the water pushing down on it. The water exerts more pressure on the lower part of the dam than the upper part, so the bottom of the dam must be stronger and thicker to withstand this pressure. Additionally, the bottom of the dam is also more susceptible to erosion from the water flow, so it also needs to be thicker to resist erosion. The thicker bottom also helps to counterbalance the hydrostatic pressure and provide stability to the dam.
Dams on the rivers are thicker at the bottom than that of the top because of the pressure which is exerted by liquids increases with depth. The walls are made thicker at the bottom, so that they can handle the pressure exerted by water.
What are dams?A dam is a barrier which stops or restricts the flow of surface water or underground streams on the planet. Reservoirs are created by dams not only to suppress floods but also to provide water for activities such as irrigation, human consumption, industrial use, aquaculture, and for the navigability.
Dams made on the rivers are generally thicker at the bottom than at the top because the pressure at a point inside a liquid depends on the depth from the free surface, therefore, the pressure is very high at the bottom of the dam. To tolerate this pressure, the walls of a dam are made thicker at the bottom. As we move upwards in the river, the pressure goes on decreasing, so the thickness of wall is made smaller and smaller. That is why, the walls of a dam are made thinner at the bottom .
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Where are you likely to find a cooling coil located in the ductwork?
A. A medium-sized office
B. A large apartment building
C. A single-family home
D. A large factory
Cooling coil is a part of air conditioner and you are likely to find it located in the ductwork of a large apartment building. Hence, option (B) is correct.
What is cooling coil?The cooling coils are a part made up of tubes made of various materials that allow a fluid to move through them. These tubes also have an exterior contact with air or another gas, which enables a heat exchange.
In the fluid that flows through the cooling coils, either water or a refrigerant may be present.
The cooling coils are elements that cool or warm the air in a cooling system intended for comfort.
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Which word identifies the shaking that results from movement under Earth’s surface? earthquake fault plate stress
Answer: Earthquake
Explanation:
An earthquake is the ground shaking caused by a sudden slip on a fault. Stresses in the earth's outer layer push the sides of the fault together. Stress builds up and the rocks slip suddenly, releasing energy in waves that travel through the earth's crust and cause the shaking that we feel during an earthquake.
Answer:The word earthquake identifies the shaking that results from movement under Earth's surface.
explanation: What is earthquake?
An earthquake is an intense shaking of Earth’s surface. The shaking is caused by movements in Earth’s outermost layer.When tectonic plates move, it also causes movements at the faults. An earthquake is the sudden movement of Earth’s crust at a fault line.
A car, initially traveling 18.0m/s speeds up at a rate of 2.00m/s2 for 3.80s. Determine all unknowns and answer the following questions.
What was the car's final speed?
How far did the car travel during this time?
The final speed of the car is 25.6 m/s.
The distance travelled by the car is 82.84 m.
What is the final speed of the car?The final speed of the car is calculated by applying the first equation of motion as shown below.
v = u + at
where;
u is the initial speed of the cara is the acceleration of the cart is time of motionv = ( 18 m/s ) + ( 2 m/s² ) x ( 3.8 s )
v = 25.6 m/s
The distance travelled by the car is calculated as follows;
s = ut + ¹/₂at²
s = ( 18 x 3.8 ) + ¹/₂ ( 2 )(3.8²)
s = 82.84 m
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13. John needs to figure out the heat change in watts of a circuit with 20 ohms of resistance and that's carrying a current of 5 amps. What's his result?
A. 250
OB. 100
OC. 500
OD. 125
Explain how a person who weighs 500 N and is wearing high heels can exert a force of 45,000 N on the floor.
Pressure on ground is inversely proportional to the surface area in contact, more the surface area in contact, less will be the exrted pressure and vice versa.
even if small force of 500N is applied, due to extremely less surface area, the force acts as 45000 N.
Charlotte is deep water diving with a spear gun, hoping to find a tasty meal. She spots a delicious fish and fires a 2 kg spear from her spear gun toward the fish at a speed of 20 m/s . The 12 kg fish attempts to swim away at a speed of 6 m/s . After the fish is speared, how fast will it be moving through the water?
After the fish is speared, it will be moving through the water at a velocity of 9.3 m/s.
What is conservation of momentum principle?
The conservation of momentum principle states that the total momentum of a system remains constant if no external forces act on it.
Before the spear is fired, the total momentum of the system is zero (Charlotte and her spear gun are at rest). After the spear is fired, the total momentum of the system is given by the momentum of the spear (2 kg * 20 m/s = 40 kg m/s)
After the fish is speared, the total momentum of the system will be the sum of the momentum of the spear and the fish. The momentum of the fish is (12 kg * 6 m/s = 72 kg m/s). Therefore the total momentum of the system is (40 kg m/s + 72 kg m/s = 112 kg m/s)
Since the total momentum of the system remains constant, we can use the conservation of momentum principle to find the final velocity of the fish.
The final velocity of the fish is (total momentum of the system / mass of the fish) = (112 kg m/s / 12 kg) = 9.3 m/s
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a rectangle has a length of (2.8+-0.2) m and a width of (1.2+-0.2) m. calculate the area and perimeter of the rectangle, and give the uncertainty in each value
Answer:
AREA = 3.6
PERIMETER = 7.2
UNCERTAINTY of Area = 3.0m
UNCERTAINTY of Perimeter = 7.0m
Explanation:
Formula for Area = length • width
(2.8 + -0.2)m • (1.2 + -0.2)m
= 2.6m^2
Formula for Perimeter:
2 • (length + width)
= 7.2m
UNCERTAINTY: round numbers to their correct significant figures.
A boy of weight 300n climbs to the top of a hill of height 20 m. The work done by the boy against the force of gravity is
Given,
W = 300N
S = 20 m
Work = force x Displacement.
= 300 x 20
= 6000 Joules.
P.S
Many people get fonfused as to why i took the goven weight as the force. Its because weight is also a force exerted by objects on earth.
ALL THE BEST
Formula for work:
[tex]w=Fd[/tex]
work(measured in joules) = force(measured in newtons) * distance(measured in meters)
__________________________________________________________
Given:
[tex]F=300N[/tex]
[tex]d=20m[/tex]
[tex]w=?[/tex]
__________________________________________________________
Finding work:
[tex]w=Fd[/tex]
[tex]w=300\times20[/tex]
__________________________________________________________
Answer:
[tex]\fbox{w = 6000 Joules}[/tex]
The front 1.20 m of a 1,350-kg car is designed as a "crumple zone" that collapses to absorb the shock of a collision. (a) If a car traveling 27.0 m/s stops uniformly in 1.20 m, how long does the collision last?
Answer:
Explanation:(a) If a car traveling 22.0 ms stops uniformly in 1.20 m, how long does the collision last?(b) What is the magnitude of the average force on the car?(c) What is the magnitude of the acceleration of the car? Express the acceleration as a multiple of the acceleration of gravity.
what is the physics behind why electric parallel plates move from positive to negative
The physics behind the movement of electric charges between parallel plates is based on the principles of electrostatics. Electric charges are either positive or negative, and they are affected by electric fields.
Electric fields are created by a difference in electric potential, which is measured in volts. When a voltage is applied to a set of parallel plates, the charges within the plates will be affected by the electric field, and will move in response to it.
What are electric parallel plates?When a voltage is applied to a set of parallel plates, the positive charges in the plate connected to the positive voltage will be attracted to the negative voltage, while the negative charges in the plate connected to the negative voltage will be attracted to the positive voltage.
The movement of charges between the plates is also affected by the presence of any obstacles or resistances in the electric field, such as resistance in the wire. This can slow down the movement of charges and result in a decrease in the current flowing through the circuit.
In all, the movement of charges between electric parallel plates is the result of the electric field created by a difference in electric potential, and the movement of charges is called drift velocity. The movement is also affected by the presence of resistance.
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9. A block of mass m 10kg is pulled up at an angle of 600 incline as shown in Figure below with a force of 80N. (Take: Cos 60° = Sin30º = 0.5, Cos 30° = Sin 60⁰ = 0.9) b. Find the acceleration of the block if the incline is frictionless. Find the acceleration of the block if the coefficient of kinetic friction is 0.2
teds res ers tere wsed tezf
A brass rod is 2m long at a certain temperature. what is its length for a temperature rise of 100k, if the expansivity of brass 18x10
The length of brass rod with a thermal expansion of 100k temperature will be 2.0036m.
What is the length of brass rod?Thermal expansion refers to the tendency of matter to change shape, volume, and area in response to temperature changes. Temperature is a monotonic function of a substance's average molecular kinetic energy.
The formula to find the gain length will be:
ΔL = αL₀ ΔT
Here,
α is the expansivity = 18 x 10⁻⁶ K⁻¹
L₀ is the initial length = 2m
ΔT is the change in temperature = 100K
Therefore,
ΔL = 18 x 10⁻⁶ x 2 x 100
= 3.6 x 10⁻³
= 0.0036m
Therefore the final length is adding both lengths that is initial length and change in length,
L = L₀ + ΔL
By substituting,
L = 2m + 0.0036m
L = 2.0036m
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A student wants to investigate the motion of a ball by conducting two different experiments, as shown in Figure 1 and Figure 2 above. In Experiment 1, the student releases a ball from rest and uses a slow-motion camera to film the ball as it falls to the ground. Using video analysis, the student is able to plot the ball’s horizontal position x and vertical position y as a function of time t . In Experiment 2, the student horizontally rolls the same ball off a table, and uses video analysis to plot the ball’s horizontal position x and vertical position y as a function of time t starting from the instant the ball leaves the table. The graphs from each experiment are shown above along with each graph’s best-fit curve line.
The student can conclude that in Experiment 1, the ball is following a parabolic path, demonstrated by the best-fit curve line. In Experiment 2, the ball is following a linear path, demonstrated by the best-fit curve line.
What is curve?
A curve is a line in a two-dimensional plane that is bent or curved. It is often used to describe the shape of objects or mathematical functions. It is often used to study changes in data over time and to understand the behavior of functions and equations. Curves can be described using a variety of mathematical equations and equations can be used to predict the behavior of a curve. Additionally, curves can be used to describe the motion of physical objects and to help visualize the relationships between the objects.
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The three of us are going to Lake Balaton. The starting meeting point is the M1-M7 MOL gas station in Budaörs.
Connor is there on time at 8 in the morning with his electric van. He hums along peacefully at 90 km/h
average speed.
You and Steve are driving an old Suzuki, you are 5 minutes late, but the average speed is 120 km/h, so
even Steve is not worried that there will be a lot of consumption.
Teacher Watson is late with the sport Seat, after a quarter of an hour he sees that there is no one at the gas station,
he's running after us. According to the km clock, its speed is 140 km/h, but it is an 8% climb.
The destination is the exit of the highway 65 in Siófok, the roundabout, right after the Sió canal bridge.
Steve and I stop at the gas station at km 83 to refuel for 10 minutes.
1. Who meets who when?
2. Who drove how long time until the meeting?
3. Who gets to Siófok first?
Distance 1: Budaörs-MOL 73.3 km
Distance 2: MOL-Siófok 22.3 km
The answer of speed are:
1. Connor meets You and Steve at the M1-M7 MOL gas station in Budaörs. Teacher Watson is running after them.
2. Connor drove 73.3 km, You and Steve drove 78.3 km, and Teacher Watson drove 95.3 km.
3. Teacher Watson gets to Siófok first due to his higher speed.
What is speed?
Speed is the rate of motion, or the rate of change in position, of an object relative to a frame of reference. It is a scalar quantity that is measured in terms of distance traveled per unit of time. It is the magnitude of the velocity vector and is thus a scalar quantity. The average speed of an object over a certain period is the total distance traveled divided by the total time taken. Speed is also known as velocity, and it is a vector quantity that includes both the magnitude and direction of motion.
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Where does the force come from to make a windmill turn?
Answer:
When wind flows across the blade, the air pressure on one side of the blade decreases. The difference in air pressure across the two sides of the blade creates both lift and drag. The force of the lift is stronger than the drag and this causes the rotor to spin.
Explanation:
) The graph in the figure shows the position of a particle as a function of time as it travels along the x-axis.
What is the average velocity of the particle between t = 2.0 s and t = 4.0 s?
The average velocity of the particle between t = 2.0 s and t = 4.0 s is 4 m/2.0 s = 2.0 m/s.
What is average velocity?Average velocity is the rate of change of an object's position, expressed as a vector quantity that tells both the speed and direction of the object's motion.
The average velocity of the particle between t = 2.0 s and t = 4.0 s can be calculated by taking the difference in the x-position of the particle at t = 4.0 s and t = 2.0 s, and dividing it by the difference in the time.
The x-position of the particle at t = 2.0 s is 4 m and the x-position of the particle at t = 4.0 s is 8 m.
Therefore, the difference in the x-position is 8 m - 4 m = 4 m.
The difference in time is 4.0 s - 2.0 s = 2.0 s. Therefore, the average velocity of the particle between t = 2.0 s and t = 4.0 s is 4 m/2.0 s = 2.0 m/s.
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A Crew Dragon with a mass of 12,519 kg is launched from the Kennedy Space Center. It is accelerating from rest to an orbital velocity to 7,800 m/s. Which of the following would be equal to the pull of Earth on the capsule?
A. The gravitational pull of the sun on the capsule
B. The gravitational pull of the capsule on Earth
C. The push of air resistance on the capsule
D. The push of air resistance on Earth
B. The gravitational pull of the capsule on Earth
The gravitational pull of the capsule on Earth is equal to the weight of the capsule, which is calculated by multiplying the mass of the capsule (12,519 kg) by the acceleration due to gravity on Earth (approximately 9.8 m/s^2). The gravitational pull of the sun and air resistance are not related to the gravitational pull of Earth on the capsule. The push of air resistance on the capsule and the push of air resistance on Earth are not related either to the gravitational pull of Earth on the capsule and they're not relevant in this scenario.
Let to the right be the positive direction.
A 25.8 g marble sliding to the right at 21.0
cm/s overtakes and collides with a 12.4 g
marble moving in the same direction at 13.8
cm/s. After the collision, the 12.4 g marble
moves to the right at 23.9 cm/s.
Find the velocity of the 25.8 g marble after
the collision.
Answer in units of cm/s. Answer in units
of cm/s.
The final velocity of the 25.8 g marble after the collision is 16.15 cm/s.
What is the velocity of the 25.8 g marble after the collision?
The velocity of the 25.8 g marble after the collision is calculated as follows;
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where;
m₁ is the mass of 25.8 g marblem₂ is the mass of 12.4 g marbleu is their initial speedsv is their final speedsThe final velocity of the 25.8 g marble after the collision is calculated as;
( 25.8 x 21 ) + ( 12.4 x 13.8 ) = ( 12.4 x 23.9 ) + ( 25.8v )
712.92 = 296.36 + 25.8v
25.8v = 416.56
v = 416.56 / 25.8
v = 16.15 cm/s
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There is a +1.0 mC charge at the origin and a +3.0 mC charge at (x, y) =(2.0 m, 0), a. Find the force on the +3.0 mC charge. b. Calculate the electric field at (x, y) = (1.00 m, 0.50 m). c. Find a point where the electric field is zero (other than at infinity). d. What is the potential at the point found in part c?
a. The force on the +3.0 mC charge is 1.35 x 10^-6 N.
b. The electric field at (x, y) = (1.00 m, 0.50 m) is 5.49 x 10^5 N/C
c. The point where the bc is zero (other than at infinity) is located on the line that connects the two charges and at the midpoint of the line segment connecting them.
d. The potential at the point found in part c is at point zero
What is electric field?An electric field is described as the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them.
a. we need to use Coulomb's law, which states that the force between two charges is given by:
F = k * (q1 * q2) / r^2
F = k * (q1 * q2) / r^2 = 8.99 x 10^9 Nm^2/C^2 * (1.0 x 10^-3 C * 3.0 x 10^-3 C) / (2.0 m)^2 = 1.35 x 10^-6 N
b. To calculate the electric field at (x, y) = (1.00 m, 0.50 m), we use the equation for the electric field due to a point charge:
E = k * q / r^2
The distance from the point charge is:
r = sqrt((1.00 m - 2.0 m)^2 + (0.50 m - 0 m)^2) = sqrt(3.25 m^2) = 1.8 m
Therefore, the electric field at (x, y) = (1.00 m, 0.50 m) is:
E = k * q / r^2 = 8.99 x 10^9 Nm^2/C^2 * (3.0 x 10^-3 C) / (1.8 m)^2 = 5.49 x 10^5 N/C
c. This point is located on the line that connects the two charges and at the midpoint of the line segment connecting them.
d. At the point found in c, the electric field is zero, so the work done to move a test charge from infinity to that point is also zero.
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Two smooth round objects of equal density are kicked with the same amount of force. One accelerates faster and travels further than the other. Explain why and list a real-life explains of this scenario. (No, one object does not hit a wall or anything…but good try)
Answer:
The object that accelerates faster and travels further is likely to have a smaller mass or a larger surface area.
A real-life example of this scenario could be a soccer ball and a bowling ball. Both are smooth, round objects of equal density, but the soccer ball has a smaller mass and larger surface area, which allows it to accelerate faster and travel further when kicked with the same amount of force.
Help, I have no clue what the answer is
Answer:
A. 1
B. n
C. 0
Explanation:
The numbers to the right of the symbols represent the [tex]\frac{mass\ number}{atomic\ number}[/tex]. Recall that the mass number is the sum of the number of neutrons and the number of protons in an atom's nucleus. The atomic number is the number of protons in an atom's nucleus. For this equation to be true, both sides must agree on the total number of subatomic particles. So, for the mass number:
[tex](1+235)=(99+133+4A)\\236=232+4A\\4=4A\\1=A[/tex]
This means the sum of the protons and neutrons in the particle is 1.
For the atomic number:
[tex](0+92)=(41+51+4C)\\92=92+4C\\0=4C\\0=C[/tex]
This means there are 0 protons in the particle.
The two derived values indicate that the particle is a lone neutron. So, the answer to B is n.
What is the resultant of two displacement vectors having the same direction? Question 16 options: The resultant is the sum of the two displacements having the same direction as the original vectors. The resultant is the difference of the two displacements having the same direction as the original vectors. The resultant is the sum of the two displacements having the direction opposite to the direction of the original vectors. The resultant is the sum of the two displacements having the direction perpendicular to the direction of the original vectors.
The resultant is the sum of the two displacements having the same direction as the original vectors.
What is displacement?A displacement is described as a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion.
Vectors in the same direction can be simply added to obtain the resultant vector.
We can describe vector as a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.
In conclusion, If we want to sum two vectors that are collinear and have the same sense, we can make that adding such as an algebraic sum.
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The resultant is the sum of the two displacements having the same direction as the original vectors. Option A
What are vectors?We know that there are generally two kinds of variables that we can be able to have in Physics, we have the scalars and the vectors. In the vectors we have the quantities that have both magnitude and direction while in the scalars we have the quantities that have only magnitude.
We know that when two vectors do have the same direction, we can be able to obtain the resultant vector by addition of the vectors together.
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How does the total momentum of two objects before a collision compare with the total momentum after the collision?
The world’s tallest lighthouse is located in Japan and is 106 m tall. A winch that provides 3.00 × 10^2 W of power is used to raise 14.0 kg of equipment to the lighthouse top at a constant velocity. How long does it take the equipment to reach the lighthouse top?
To find out how long it takes for the equipment to reach the lighthouse top, we can use the work-energy principle which states that the work done on an object is equal to the change in its kinetic energy. Since the velocity is constant, the change in kinetic energy is zero.
Therefore, the work done on the object is equal to the force required to lift it multiplied by the distance it is lifted. We can use the formula:
Work = force x distance
We know that the work done is equal to the power multiplied by the time, so we can use this formula as well:
Work = Power x time
We can use these two formulas to find the time it takes to raise the equipment to the lighthouse top:
force = mg = (14.0 kg)(9.8 m/s^2) = 137.2 N
distance = 106 m
Work = force x distance = 137.2 N x 106 m = 14,532.8 J
Power = 3.00 x 10^2 W
We can now substitute these values into the second formula:
Work = Power x time
14,532.8 J = 3.00 x 10^2 W x time
time = Work / Power = (14,532.8 J) / (3.00 x 10^2 W) = 484.4 seconds
So, it takes the equipment approximately 484.4 seconds (8 minutes and 4.4 seconds) to reach the lighthouse top.
I hope this helps :)
Refers to electricity that is produced at large power plants and transmitted great
distances through power lines to the end user.
When connecting asynchronous grids together or transferring significant amounts of electricity across long distances, high-voltage direct current (HVDC) is employed.
Why is electricity transported in this way over such distances, and how is it transmitted?Order to be transported across great distances via high-voltage transmission power lines, a transformer at a power plant raises the voltage of generated power by thousands of volts. Transmission lines, often called conductor bundles, are used to transport electric electricity from power plants to far-off substations.
Transmission lines use what kind of power?In an electric power system, transmission lines move electric energy from one location to another. They can transport direct current, alternating current, or a system that combines both. Also, overhead or subsurface wires can both carry electric current.
Which kind of electricity is most suitable for long-distance transmission?When opposed to alternating current transmission systems, high-voltage direct current (HVDC) technology has several benefits. For instance, it enables longer-distance bulk power transfer that is more effective.
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The tape in a videotape cassette has a total
length 200 m and can play for 2.4 h. As the
tape starts to play, the full reel has an outer
radius of 41 mm and an inner radius of 11 mm.
At some point during the play, both reels will
have the same angular speed.
What is this common angular speed?
Answer in units of rad/s.
At some point during the play, both reels will have the same angular speed. The common angular speed is 0.001389 rad/s.
What is angular speed ?
Angular speed is the rate at which an object rotates or revolves around a point, or the rate at which the angular position or orientation of an object changes with time. It is measured in radians per second or in revolutions per minute, and it is usually symbolized by the Greek letter omega (ω).
Angular speed is closely related to linear speed, or the distance an object travels in a given amount of time, because the linear speed of an object can be calculated by multiplying the angular speed by its distance from the centre of rotation.
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A basketball and a ballon are kicked with the same amount of force. However, the ball travels faster and further. Is Newtons 2nd law inaccurate? Explain
Answer:
No, Newton's second law is not inaccurate in this scenario. The second law states that the acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass.
Explanation:
In this scenario, the basketball and the balloon are kicked with the same amount of force, but the basketball has a greater mass than the balloon. Therefore, the basketball will experience a greater acceleration than the balloon and will travel faster and further.
In addition, the air resistance is much greater on the balloon than on the basketball, the air resistance makes the balloon to slow down faster than the basketball, so the acceleration and the final speed of the basketball will be greater than the balloon.
In summary, Newton's second law is still accurate, but it is also necessary to take into account other factors such as air resistance, friction, and mass that can affect the motion of an object.
A 3kg book is resting high on a book shelf. If the book has 73.5 J of potential energy, how high is the shelf?
_____ m
If this book slipped off the shelf and fell all the way to the ground, how much kinetic energy would it have the instant it hit the ground (if we ignore air resistance)?
____
Answer:
below
Explanation:
Potential Energy = mgh
73.5 = 3 kg * 9.81 m/s^2 * h
h = 2.5 m
when the book hits it will have the PE all converted to KE = 73.5 J
A bullet of mass 0.02kg traveling at a speed of 100 m/s comes to rest when it has gone 0.4m into sand. Find the resisting force exerted by the sand.
Answer:
[tex]250\; {\rm N}[/tex], assuming that the sand exerts a constant force.
Explanation:
If the sand exerts a constant force, acceleration (deceleration) would be constant. Let [tex]a[/tex] denote this acceleration.
It is given that:
displacement is [tex]x = 0.4\; {\rm m}[/tex]. initial velocity is [tex]u = 100\; {\rm m\cdot s^{-1}}[/tex].Additionally, final velocity is [tex]v = 0\; {\rm m\cdot s^{-1}}[/tex] when the object is at rest.
Rearrange the SUVAT equation [tex]v^{2} - u^{2} = 2\, a\, x[/tex] to find acceleration [tex]a[/tex]:
[tex]\begin{aligned}a &= \frac{v^{2} - u^{2}}{2\, x} \\ &= \frac{{(0\; {\rm m\cdot s^{-1}})}^{2} - {(100\; {\rm m\cdot s^{-1}})}^{2}}{2\, (0.4\; {\rm m})} \\ &= (-12500)\; {\rm m\cdot s^{-2}}\end{aligned}[/tex].
Multiply acceleration by mass to find the net force:
[tex]\begin{aligned}(\text{net force}) &= m\, a \\ &= (0.02\; {\rm kg})\, (-12500\; {\rm m\cdot s^{-2}}) \\ &= (-250)\; {\rm {N}}\end{aligned}[/tex].
(Negative since velocity is decreasing.)
Assuming that all other forces are negligible. The force that the sand exerted would be equal to the net force, [tex](-250)\; {\rm N}[/tex] (negative since this force opposes the motion.)
