Question 1

An ideal spring is used to fire a 15.0-g block horizontally.The spring has a spring constant of 20 N/m and is initially compressed by 7.0 cm.The kinetic energy of the block as it leaves the spring is:

Accepted Answer

The potential energy stored in the spring is given by:
$U_s = \frac{1}{2}kx^2$, where $k$ is the spring constant and $x$ is the displacement from equilibrium.
Thus, $U_s = \frac{1}{2}(20	ext{ N/m})(0.07	ext{ m})^2 = 0.049	ext{ J}$.
Since energy is conserved, the kinetic energy of the block when it leaves the spring is equal to the potential energy stored in the spring:
$K = U_s = 0.049	ext{ J}$
However, since the answer choices are given in different units, we need to convert Joules to the appropriate unit:
$K = 0.049	ext{ J} = 4.9	imes10^{-2}	ext{ J} = \boxed{C) 4.9	imes10^{-2}	ext{ Nm}}$

Question 2

A small object of mass m, on the end of a light cord, is held horizontally at a distance r from a fixed support as shown.The object is then released.What is the tension in the cord when the object is at the lowest point of its swing?

Accepted Answer

The answer of A small object of mass m, on...

Question 3

A simple pendulum consists of a 2.0 kg mass attached to a string.It is released from rest at X as shown.Its speed at the lowest point Y is:

Accepted Answer

The answer of A simple pendulum consists of a 2.0...

Question 4

A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface.When the spring is 4.0 cm longer than its equilibrium length, the speed of the block is 0.50 m/s.The greatest speed of the block is:

Accepted Answer

We can use the conservation of energy to solve this problem.
The potential energy stored in the spring when it is stretched by 4.0 cm is:
$$U_s=\frac{1}{2}kx^2=\frac{1}{2}(80	ext{ N/m})(0.04	ext{ m})^2=0.064	ext{ J}$$
At this point, all the potential energy is converted to kinetic energy:
$$\frac{1}{2}mv^2=0.064	ext{ J}$$
$$v=\sqrt{\frac{2(0.064	ext{ J})}{0.50	ext{ kg}}}=0.71	ext{ m/s}$$
Therefore, the greatest speed of the block is 0.71 m/s, which is choice C.

Question 5

The potential energy of a body of mass m is given by U = -mgx + 1/2kx².The corresponding force is:

Accepted Answer

The answer of The potential energy of a body of...

Question 6

A particle moves along the x axis under the influence of a stationary object.The net force on the particle, which is conservative, is given by F = (8N/m³)x³.If the potential energy is taken to be zero for x = 0 then the potential energy is given by:

Accepted Answer

The potential energy (U) associated with a conservative force is given by U = -∫F dx. Given F = (8N/m)x, integrating with respect to x gives U = -(8/2)x^2 = -4x^2. The correct unit for potential energy is Joules (J), so the answer is (-2 J/m^2)x^2, which corresponds to choice B.

Question 7

A 700-N man jumps out of a window into a fire net 10 m below.The net stretches 2 m before bringing the man to rest and tossing him back into the air.The maximum potential energy of the net, compared to its unstretched potential energy, is:

Accepted Answer

The answer of A 700-N man jumps out of a...

Question 8

A 0.5-kg block slides along a horizontal frictionless surface at 2 m/s.It is brought to rest by compressing a very long spring of spring constant 800 N/m.The maximum spring compression is:

Accepted Answer

The initial kinetic energy of the block is given by:
Kinitial = (1/2)mv^2 = (1/2)(0.5 kg)(2 m/s)^2 = 1 J

The final potential energy stored in the compressed spring is given by:
Ufinal = (1/2)kx^2
where x is the maximum compression of the spring.

Since energy is conserved, we have:
Kinitial = Ufinal

Substituting the values, we get:
1 J = (1/2)(800 N/m)x^2
x^2 = 0.0025 m^2 = (0.05 m)^2

Taking the square root, we get:
x = 0.05 m = 5 cm

Therefore, the maximum spring compression is 5 cm.

Question 9

A toy cork gun contains a spring whose spring constant is 10.0 N/m.The spring is compressed 5.00 cm and then used to propel a 6.00-g cork.The cork, however, sticks to the spring for 1.00 cm beyond its unstretched length before separation occurs.The muzzle velocity of this cork is:

Accepted Answer

The answer of A toy cork gun contains a spring...

Question 10

A small object of mass m starts at rest at the position shown and slides along the frictionless loop-the-loop track of radius R.What is the smallest value of y such that the object will slide without losing contact with the track?

Accepted Answer

The answer of A small object of mass m starts...

Question 11

A small object slides along the frictionless loop-the-loop with a diameter of 3 m.What minimum speed must it have at the top of the loop in order to remain in contact with the loop?

Accepted Answer

The answer of A small object slides along the frictionless...

Question 12

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x)= (8.0 J/m²)x²− (2.0 J/m⁴)x⁴.When the particle is at x = 1.0 m the magnitude of its acceleration is:

Accepted Answer

The magnitude of acceleration can be found by taking the derivative of the potential energy with respect to position twice and multiplying by the mass of the particle:

a = -m(d^2U/dx^2)

Taking the second derivative of U(x), we get:

d^2U/dx^2 = -16 J/m^3x + 6 J/m^4x^3

Plugging in x = 1.0 m and m = 0.20 kg, we get:

a = -(0.20 kg)(-16 J/m^3(1.0 m) + 6 J/m^4(1.0 m)^3)
  = -40 m/s^2

Therefore, the magnitude of the particle's acceleration is 40 m/s^2 in the negative direction, so the answer is D).

Question 13

Which of the five graphs correctly shows the potential energy of a spring as a function of its elongation x?

Accepted Answer

The answer of Which of the five graphs correctly shows...

Question 14

The string in the figure is 50 cm long.When the ball is released from rest, it swings along the dotted arc.How fast is it going at the lowest point in its swing?

Accepted Answer

The answer of The string in the figure is 50...

Question 15

A projectile of mass 0.50 kg is fired with an initial speed of 10 m/s at an angle of 60$\degree$ above the horizontal.The potential energy of the projectile-Earth system when the projectile is at its highest point (relative to the potential energy when the projectile is at ground level)is:

Accepted Answer

At the highest point, the projectile has zero kinetic energy as its velocity becomes zero. Therefore, the total energy of the system is equal to its potential energy at that point. Using the formula for gravitational potential energy, we have:
PE = mgh
where m = 0.50 kg, g = 9.81 m/s^2 (acceleration due to gravity), and h is the maximum height reached by the projectile. We can find h using the vertical component of the initial velocity:
v0y = 10 m/s × sin(60°) = 8.66 m/s
At the highest point, v = 0 m/s. We can use the kinematic equation:
v^2 = v0^2 - 2gh
to find h:
h = (v0y^2)/(2g) = (8.66 m/s)^2/(2×9.81 m/s^2) ≈ 3.75 m
Substituting into the formula for potential energy, we get:
PE = (0.50 kg)(9.81 m/s^2)(3.75 m) ≈ 18.75 J
Therefore, the best answer is B.

Question 16

The long pendulum shown is drawn aside until the ball has risen 0.5 m.It is then given an initial speed of 3.0 m/s.The speed of the ball at its lowest position is:

Accepted Answer

The answer of The long pendulum shown is drawn aside...

Question 17

For a block of mass m to slide without friction up the rise of height h shown, it must have a minimum initial kinetic energy of:

Accepted Answer

The answer of For a block of mass m to...

Question 18

A rectangular block is moving along a frictionless path when it encounters the circular loop as shown.The block passes points 1,2,3,4,1 before returning to the horizontal track.At point 3:

Accepted Answer

The answer of A rectangular block is moving along a...

Question 19

The graphs below show the magnitude of the force on a particle as the particle moves along the positive x axis from the origin to x = x₁.The force is parallel to the x axis and is conservative.The maximum magnitude F₁ has the same value for all graphs.Rank the situations according to the change in the potential energy associated with the force, least (or most negative)to greatest (or most positive).

Accepted Answer

The answer of The graphs below show the magnitude of...

Question 20

A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface.The total mechanical energy is 0.12 J.The greatest speed of the block is:

Accepted Answer

The answer of A 0.50-kg block attached to an ideal...

Quiz 8: Potential Energy and Conservation of Energy

An ideal spring is used to fire a 15.0-g block horizontally.The spring has a spring constant of 20 N/m and is initially compressed by 7.0 cm.The kinetic energy of the block as it leaves the spring is:

A small object of mass m, on the end of a light cord, is held horizontally at a distance r from a fixed support as shown.The object is then released.What is the tension in the cord when the object is at the lowest point of its swing?

A simple pendulum consists of a 2.0 kg mass attached to a string.It is released from rest at X as shown.Its speed at the lowest point Y is:

A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface.When the spring is 4.0 cm longer than its equilibrium length, the speed of the block is 0.50 m/s.The greatest speed of the block is:

The potential energy of a body of mass m is given by U = -mgx + 1/2kx².The corresponding force is:

A particle moves along the x axis under the influence of a stationary object.The net force on the particle, which is conservative, is given by F = (8N/m³) x³.If the potential energy is taken to be zero for x = 0 then the potential energy is given by:

A 700-N man jumps out of a window into a fire net 10 m below.The net stretches 2 m before bringing the man to rest and tossing him back into the air.The maximum potential energy of the net, compared to its unstretched potential energy, is:

A 0.5-kg block slides along a horizontal frictionless surface at 2 m/s.It is brought to rest by compressing a very long spring of spring constant 800 N/m.The maximum spring compression is:

A toy cork gun contains a spring whose spring constant is 10.0 N/m.The spring is compressed 5.00 cm and then used to propel a 6.00-g cork.The cork, however, sticks to the spring for 1.00 cm beyond its unstretched length before separation occurs.The muzzle velocity of this cork is:

A small object of mass m starts at rest at the position shown and slides along the frictionless loop-the-loop track of radius R.What is the smallest value of y such that the object will slide without losing contact with the track?

A small object slides along the frictionless loop-the-loop with a diameter of 3 m.What minimum speed must it have at the top of the loop in order to remain in contact with the loop?

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) = (8.0 J/m²) x²− (2.0 J/m⁴) x⁴.When the particle is at x = 1.0 m the magnitude of its acceleration is:

Which of the five graphs correctly shows the potential energy of a spring as a function of its elongation x?

The string in the figure is 50 cm long.When the ball is released from rest, it swings along the dotted arc.How fast is it going at the lowest point in its swing?

A projectile of mass 0.50 kg is fired with an initial speed of 10 m/s at an angle of 60 $\degree$ above the horizontal.The potential energy of the projectile-Earth system when the projectile is at its highest point (relative to the potential energy when the projectile is at ground level) is:

The long pendulum shown is drawn aside until the ball has risen 0.5 m.It is then given an initial speed of 3.0 m/s.The speed of the ball at its lowest position is:

For a block of mass m to slide without friction up the rise of height h shown, it must have a minimum initial kinetic energy of:

A rectangular block is moving along a frictionless path when it encounters the circular loop as shown.The block passes points 1,2,3,4,1 before returning to the horizontal track.At point 3:

A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface.The total mechanical energy is 0.12 J.The greatest speed of the block is:

Quiz 8: Potential Energy and Conservation of Energy

An ideal spring is used to fire a 15.0-g block horizontally.The spring has a spring constant of 20 N/m and is initially compressed by 7.0 cm.The kinetic energy of the block as it leaves the spring is:

A small object of mass m, on the end of a light cord, is held horizontally at a distance r from a fixed support as shown.The object is then released.What is the tension in the cord when the object is at the lowest point of its swing?

A simple pendulum consists of a 2.0 kg mass attached to a string.It is released from rest at X as shown.Its speed at the lowest point Y is:

A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface.When the spring is 4.0 cm longer than its equilibrium length, the speed of the block is 0.50 m/s.The greatest speed of the block is:

The potential energy of a body of mass m is given by U = -mgx + 1/2kx2.The corresponding force is:

A particle moves along the x axis under the influence of a stationary object.The net force on the particle, which is conservative, is given by F = (8N/m3) x3.If the potential energy is taken to be zero for x = 0 then the potential energy is given by:

A 700-N man jumps out of a window into a fire net 10 m below.The net stretches 2 m before bringing the man to rest and tossing him back into the air.The maximum potential energy of the net, compared to its unstretched potential energy, is:

A 0.5-kg block slides along a horizontal frictionless surface at 2 m/s.It is brought to rest by compressing a very long spring of spring constant 800 N/m.The maximum spring compression is:

A toy cork gun contains a spring whose spring constant is 10.0 N/m.The spring is compressed 5.00 cm and then used to propel a 6.00-g cork.The cork, however, sticks to the spring for 1.00 cm beyond its unstretched length before separation occurs.The muzzle velocity of this cork is:

A small object of mass m starts at rest at the position shown and slides along the frictionless loop-the-loop track of radius R.What is the smallest value of y such that the object will slide without losing contact with the track?

A small object slides along the frictionless loop-the-loop with a diameter of 3 m.What minimum speed must it have at the top of the loop in order to remain in contact with the loop?

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) = (8.0 J/m2) x2 − (2.0 J/m4) x4.When the particle is at x = 1.0 m the magnitude of its acceleration is:

Which of the five graphs correctly shows the potential energy of a spring as a function of its elongation x?

The string in the figure is 50 cm long.When the ball is released from rest, it swings along the dotted arc.How fast is it going at the lowest point in its swing?

A projectile of mass 0.50 kg is fired with an initial speed of 10 m/s at an angle of 60 °\degree° above the horizontal.The potential energy of the projectile-Earth system when the projectile is at its highest point (relative to the potential energy when the projectile is at ground level) is:

The long pendulum shown is drawn aside until the ball has risen 0.5 m.It is then given an initial speed of 3.0 m/s.The speed of the ball at its lowest position is:

For a block of mass m to slide without friction up the rise of height h shown, it must have a minimum initial kinetic energy of:

A rectangular block is moving along a frictionless path when it encounters the circular loop as shown.The block passes points 1,2,3,4,1 before returning to the horizontal track.At point 3:

A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface.The total mechanical energy is 0.12 J.The greatest speed of the block is:

The potential energy of a body of mass m is given by U = -mgx + 1/2kx².The corresponding force is:

A particle moves along the x axis under the influence of a stationary object.The net force on the particle, which is conservative, is given by F = (8N/m³) x³.If the potential energy is taken to be zero for x = 0 then the potential energy is given by:

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) = (8.0 J/m²) x²− (2.0 J/m⁴) x⁴.When the particle is at x = 1.0 m the magnitude of its acceleration is:

A projectile of mass 0.50 kg is fired with an initial speed of 10 m/s at an angle of 60 $\degree$ above the horizontal.The potential energy of the projectile-Earth system when the projectile is at its highest point (relative to the potential energy when the projectile is at ground level) is: