Question 1

The total mechanical energy of a system
A) is either positive or zero.
B) is mainly due to kinetic energy.
C) is mainly due to potential energy.
D) is equally divided between kinetic energy and potential energy.
E) is divided between kinetic energy and potential energy.

Accepted Answer

The total mechanical energy of a system is the sum of its kinetic energy (energy due to motion) and potential energy (energy stored due to an object's position or arrangement). The distribution between kinetic and potential energy varies depending on the system's state and is not necessarily equal, making option E correct.

Question 2

A girl runs up a flight of stairs at a constant speed v, and the gain in her potential gravitational energy is U. When she runs up the same stairs at half that speed, her mechanical energy is
A) zero.
B) smaller.
C) the same.
D) larger.

Accepted Answer

The answer of A girl runs up a flight of...

Question 3

A box of mass m and a box of mass 4m are sliding with equal speeds along a level frictionless surface. Then they both slide up the same frictionless hill. Which rises to a greater height?
A) The box of mass m because it is lighter and its inertia is smaller.
B) The box of mass m because it has less kinetic energy and therefore more potential energy.
C) Both boxes slide to the same height.
D) The box of mass 4m because it is heavier.
E) The box of mass 4m because it has a larger kinetic energy and therefore more potential energy.

Accepted Answer

Since both boxes have the same speed and are moving on a frictionless surface, they will convert their kinetic energy to potential energy equally, regardless of their mass. This means both will reach the same height.

Question 4

A ball of mass 1.0 kg is tied to a string and allowed to revolve in a vertical circle of radius 1.5 m. If the ball's speed at the top of the trajectory is 2.3 m/s, its speed at the bottom of the trajectory is
A) 0 m/s.
B) 2.3 m/s.
C) 5.9 m/s.
D) 7.7 m/s.
E) 8.0 m/s.

Accepted Answer

The answer of A ball of mass 1.0 kg is...

Question 5

A 10-kg toy car moving at 5.0 m/s hits an initially uncompressed horizontal spring with a spring constant of 2.5*10² N/m. Neglecting the mass of the spring, the maximum compression of the spring is A) 0 m. B) 0.20 m. C) 1.0 m. D) 2.0 m. E) 50 m.

Accepted Answer

The maximum compression of the spring can be found using energy conservation. The initial kinetic energy of the car is converted into the potential energy of the spring. Using the formula: (1/2)mv^2 = (1/2)kx^2, where m = 10 kg, v = 5.0 m/s, and k = 250 N/m, solving for x gives x = 1.0 m.

Question 6

What speed should a roller coaster have at a point 30 m above the bottom of a dip if it is to barely reach the top of the next slope, which is 40 m above the bottom of the dip? Neglect friction. A) 0 m/s B) 14 m/s C) 28 m/s D) 98 m/s E) 2.0* 10² m/s

Accepted Answer

To solve this, we use the principle of conservation of mechanical energy, which states that the total mechanical energy (potential energy + kinetic energy) in a system remains constant if only conservative forces are acting. At the top of the next slope, the roller coaster needs just enough kinetic energy to reach but not exceed the height of the slope, implying it would have a speed of 0 m/s at the top. Thus, all its energy at the point 30 m above the bottom would be converted into potential energy at the 40 m height.The potential energy (PE) at a height $h$ is given by $PE = mgh$, where $m$ is the mass, $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$), and $h$ is the height above the reference point. The kinetic energy (KE) is given by $KE = \frac{1}{2}mv^2$, where $v$ is the velocity.At the 30 m point, the roller coaster has potential energy due to its height and needs kinetic energy to reach the 40 m height. The energy conservation between the two points (30 m and 40 m) can be expressed as:$$mgh_1 + \frac{1}{2}mv^2 = mgh_2$$Given $h_1 = 30 \, \text{m}$, $h_2 = 40 \, \text{m}$, and $g = 9.8 \, \text{m/s}^2$, we find $v$. The mass $m$ cancels out from both sides, simplifying to:$$9.8 \times 30 + \frac{1}{2}v^2 = 9.8 \times 40$$Solving for $v$, we find $v = 14 \, \text{m/s}$. Therefore, the roller coaster must have a speed of 14 m/s at the 30 m point to just reach the top of the next slope at 40 m.

Question 7

As a 1.0-kg ball falls to the ground, its potential and kinetic energies are the same when the ball is 3.0 m above the ground. How fast is the ball moving just before the impact with the ground? A) 0 m/s B) 7.7 m/s C) 11 m/s D) 59 m/s E) 1.2 * 10² m/s

Accepted Answer

The potential energy at 3.0 m is equal to the kinetic energy at that point. Using energy conservation, the total energy at 3.0 m is mgh = 1.0 kg * 9.8 m/s² * 3.0 m = 29.4 J. Just before impact, all this energy is kinetic: 0.5 * 1.0 kg * v² = 29.4 J. Solving for v gives v = √(2 * 29.4) = 11 m/s.

Question 8

A flowerpot of mass m, initially at rest, falls a distance h to the ground below. In the absence of air resistance, the graph that best represents the flowerpot's potential gravitational energy as a function of the distance fallen is
A) a straight line with a negative slope.
B) a straight line with a positive slope.
C) a vertical line.
D) a horizontal line.
E) a parabola.

Accepted Answer

The potential gravitational energy decreases linearly as the flowerpot falls, because potential energy is given by $U = mgh$, where $h$ is the height above the ground. As the flowerpot falls (distance fallen increases), $h$ decreases, leading to a linear decrease in potential energy, represented by a straight line with a negative slope.

Question 9

A flowerpot of mass m, initially at rest, falls a distance h to the ground below. In the absence of air resistance, the graph that best represents the flowerpot's mechanical energy as a function of the distance fallen is
A) a straight line with a negative slope.
B) a straight line with a positive slope.
C) a vertical line.
D) a horizontal line.
E) a parabola.

Accepted Answer

The mechanical energy (sum of potential and kinetic energy) of the flowerpot remains constant as it falls, assuming no air resistance. This is because the loss in potential energy is exactly equal to the gain in kinetic energy.

Question 10

A ball of mass 0.50 kg is pushed against a horizontal spring of negligible mass and force constant of 450 N/m until the spring is compressed a distance of 0.40 m. When the spring is released, the ball travels along a frictionless, horizontal surface to point B, at the bottom of a vertical circular track of radius R = 1.00 m, and continues to move up the track, where the ball experiences an average friction force of 7.00 N. The speed of the ball at the top of the track 
A) is 0 m/s.
B) is 4.1 m/s.
C) is 7.0 m/s.
D) is 12 m/s.
E) cannot be determined because the ball does not reach the top of the track.

Accepted Answer

The answer of A ball of mass 0.50 kg is...

Question 11

You need to move a heavy crate by sliding it across a smooth floor-either by pushing it horizontally or by pulling it with a rope that makes a 30^oangle with the floor. If the coefficient of kinetic friction is 0.25, which way should you move the crate so that you do the least amount of work? A) Pushing it horizontally. B) Pulling it with a rope that makes a 30^oangle with the floor. C) Either way the work done will be the same. D) More information is needed to work out the answer.

Accepted Answer

The work done is independent of the angle of the force.

Quiz 7: Work and Energy

The total mechanical energy of a system

A girl runs up a flight of stairs at a constant speed v, and the gain in her potential gravitational energy is U. When she runs up the same stairs at half that speed, her mechanical energy is

A box of mass m and a box of mass 4m are sliding with equal speeds along a level frictionless surface. Then they both slide up the same frictionless hill. Which rises to a greater height?

A ball of mass 1.0 kg is tied to a string and allowed to revolve in a vertical circle of radius 1.5 m. If the ball's speed at the top of the trajectory is 2.3 m/s, its speed at the bottom of the trajectory is

A 10-kg toy car moving at 5.0 m/s hits an initially uncompressed horizontal spring with a spring constant of 2.5*102 N/m. Neglecting the mass of the spring, the maximum compression of the spring is

What speed should a roller coaster have at a point 30 m above the bottom of a dip if it is to barely reach the top of the next slope, which is 40 m above the bottom of the dip? Neglect friction.

As a 1.0-kg ball falls to the ground, its potential and kinetic energies are the same when the ball is 3.0 m above the ground. How fast is the ball moving just before the impact with the ground?

A flowerpot of mass m, initially at rest, falls a distance h to the ground below. In the absence of air resistance, the graph that best represents the flowerpot's potential gravitational energy as a function of the distance fallen is

A flowerpot of mass m, initially at rest, falls a distance h to the ground below. In the absence of air resistance, the graph that best represents the flowerpot's mechanical energy as a function of the distance fallen is

You need to move a heavy crate by sliding it across a smooth floor-either by pushing it horizontally or by pulling it with a rope that makes a 30o angle with the floor. If the coefficient of kinetic friction is 0.25, which way should you move the crate so that you do the least amount of work?

A 10-kg toy car moving at 5.0 m/s hits an initially uncompressed horizontal spring with a spring constant of 2.5*10² N/m. Neglecting the mass of the spring, the maximum compression of the spring is

You need to move a heavy crate by sliding it across a smooth floor-either by pushing it horizontally or by pulling it with a rope that makes a 30^oangle with the floor. If the coefficient of kinetic friction is 0.25, which way should you move the crate so that you do the least amount of work?