Question 1

A heavy sled and a light sled, both moving horizontally with the same kinetic energy, suddenly slide onto a rough patch of snow and eventually come to a stop. The coefficient of kinetic friction
Between the sleds and the rough snow is the same for both of them. Which of the following
Statements about these sleds are correct? (There could be more than one correct choice.)

Accepted Answer

The answer of A heavy sled and a light sled,...

Question 2

A 1-kg ball is released from a height of 6 m, and a 2-kg ball is released from a height of 3 m. Air resistance is negligible as they fall. Which of the following statements about these balls are correct?
(There could be more than one correct choice.)

Accepted Answer

The answer of A 1-kg ball is released from a...

Question 3

A force produces power  P  by doing work  W  in a time  T . What power will be produced by a force that does six times as much work in half as much time?

Accepted Answer

Power is defined as work done per unit time. If the work done is increased by a factor of 6 and the time is reduced by half, the power is increased by a factor of 6 (due to the increase in work) and further doubled (due to the halving of time), resulting in a total increase by a factor of 12.

Question 4

A heavy rock and a light rock are dropped from the same height and experience no significant air resistance as they fall. Which of the following statements about these rocks are correct? (There
Could be more than one correct choice.)

Accepted Answer

When dropped from the same height, both rocks convert their gravitational potential energy to kinetic energy as they fall. The heavier rock has more gravitational potential energy initially due to its greater mass, resulting in more kinetic energy when it reaches the ground. However, both rocks fall at the same rate and have the same speed upon reaching the ground due to the acceleration due to gravity being constant for all objects.

Question 5

Two identical grasshoppers jump into the air with the same initial speed and experience no air resistance. Grasshopper A goes straight up, but grasshopper B goes up at a 66° angle above the
Horizontal. Which of the following statements about these grasshoppers are correct? (There could
Be more than one correct choice.)

Accepted Answer

Grasshopper A reaches a higher vertical height than grasshopper B, so it has more gravitational potential energy at the highest point. Both grasshoppers have the same mechanical energy since they started with the same initial speed and there is no air resistance. Grasshopper B has horizontal velocity at the highest point, so it is moving faster than grasshopper A, which has zero velocity at its highest point.

Question 6

Swimmers at a water park have a choice of two frictionless water slides, as shown in the figure. Although both slides drop over the same height  h , slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed  of a swimmer reaching the bottom of slide 1 compare with $\text { v2, }$ the speed of a swimmer reaching the end of slide 2 ?

Accepted Answer

The answer of Swimmers at a water park have a...

Question 7

A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. They both slide up the same frictionless hill with no air resistance. Which object rises to a
Greater height?

Accepted Answer

Since there is no friction or air resistance, both objects will convert their kinetic energy into potential energy at the same rate, regardless of their mass. Therefore, they will reach the same height.

Question 8

Two cyclists who weigh the same and have identical bicycles ride up the same mountain, both starting at the same time. Joe rides straight up the mountain, and Bob rides up the longer road that
Has a lower grade. Joe gets to the top before Bob. Ignoring friction and wind resistance, which one
Of the following statements is true?

Accepted Answer

The work done is defined as the force times the distance moved in the direction of the force. Since both cyclists are moving to the same height against gravity, and they weigh the same, the work done against gravity is the same for both. However, Joe, who arrives first, does this work in a shorter time, meaning his average power (work done per unit time) is higher than Bob's.

Question 9

If the units of your answer are kg · $\mathrm { m } ^ { 2 } / \mathrm { s } ^ { 3 }$ which of the following types of quantities could your answer be? (There could be more than one correct choice.)

Accepted Answer

The unit kg · m²/s³ is equivalent to watts, which is the unit of power.

Question 10

A heavy frog and a light frog jump straight up into the air. They push off in such away that they both have the same kinetic energy just as they leave the ground. Air resistance is negligible. Which
Of the following statements about these frogs are correct? (There could be more than one correct
Choice.)

Accepted Answer

The answer of A heavy frog and a light frog...

Question 11

Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed twice as high as Bill. If there is no air resistance, the maximum height of Joe's ball will be

Accepted Answer

The maximum height $h$ reached by an object thrown vertically is given by the formula $h = \frac{v^2}{2g}$, where $v$ is the initial speed and $g$ is the acceleration due to gravity. If Joe's initial speed is twice that of Bill's, substituting $2v$ for $v$ in the formula gives $h = \frac{(2v)^2}{2g} = \frac{4v^2}{2g} = 4 \times \frac{v^2}{2g}$, which is four times the height reached by Bill's ball.

Question 12

Two frisky otters slide down frictionless hillsides of the same height but different slopes. The slope of the hill of otter 1 is $30 ^ { \circ }$ while the slope of the hill of otter 2 is $60 ^ { \circ }$ If both start from rest, which otter is moving faster when she reaches the bottom of her hill?

Accepted Answer

Both otters will have the same speed at the bottom because their speeds depend only on the height from which they slide, not on the slope of the hill, according to the conservation of energy principle.

Question 13

A heavy stone and a light stone are released from rest in such away that they both have the same amount of gravitational potential energy just as they are released. Air resistance is negligibly small.
Which of the following statements about these stones are correct? (There could be more than one
Correct choice.)

Accepted Answer

The answer of A heavy stone and a light stone...

Question 14

If a stone is dropped with an initial gravitational potential energy of 100 J but reaches the ground
with a kinetic energy of only 75 J, this is a violation of the principle of conservation of energy.

Accepted Answer

The difference in energy (25 J) could be accounted for by other forms of energy such as heat due to air resistance, indicating no violation of the conservation of energy principle.

Question 15

Jill does twice as much work as Jack does and in half the time. Jill's power output is

Accepted Answer

Power is defined as the work done per unit time. Since Jill does twice as much work in half the time, her power output is $2 \times 2 = 4$ times that of Jack's.

Question 16

A stone can slide down one of four different frictionless ramps, as shown in the figure. For which ramp will the speed of the ball be the greatest at the bottom?

Accepted Answer

The answer of A stone can slide down one of...

Question 17

A heavy dart and a light dart are launched vertically by identical ideal springs. Both springs were initially compressed by the same amount. There is no significant air resistance. Which of the
Following statements about these darts are correct? (There could be more than one correct choice.)

Accepted Answer

A) The light dart goes higher because, for a given amount of energy provided by the spring, a lighter object will achieve a higher velocity and thus a higher maximum height due to the conservation of energy principle. B) At the maximum height, both darts have the same gravitational potential energy because the energy transferred from the spring to each dart is the same initially, and without air resistance, energy conservation ensures that all this energy is converted into gravitational potential energy at the maximum height.

Question 18

A girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case.
Case A: Thrown straight up.
Case B: Thrown straight down.
Case C: Thrown out at an angle of 45° above horizontal.
Case D: Thrown straight out horizontally.
In which case will the speed of the stone be greatest when it hits the water below if there is no
Significant air resistance?

Accepted Answer

In the absence of significant air resistance, all objects near the Earth's surface accelerate downward at the same rate regardless of their initial motion. Thus, the speed of the stone when it hits the water will be the same in all cases, as the vertical component of its velocity will increase at the same rate due to gravity.

Question 19

A heavy sled and a light sled, both moving horizontally with the same speed, suddenly slide onto a rough patch of snow and eventually come to a stop. The coefficient of kinetic friction between the
Sleds and the rough snow is the same for both of them. Which of the following statements about
These sleds are correct? (There could be more than one correct choice.)

Accepted Answer

The frictional force depends on the normal force, which is greater for the heavy sled, causing it to stop sooner. Thus, both sleds will slide the same distance (B) because they have the same initial kinetic energy and frictional force per unit mass. The heavy sled experiences more negative work (E) due to its greater mass and frictional force.

Question 20

A person stands on the edge of a cliff. She throws three identical rocks with the same speed. Rock X is thrown vertically upward, rock Y is thrown horizontally, and rock Z is thrown vertically
Downward. If the ground at the base of the cliff is level, which rock hits the ground with the
Greatest speed if there is no air resistance?

Accepted Answer

In the absence of air resistance, all rocks will hit the ground with the same speed due to the conservation of energy. The initial kinetic energy is converted into potential energy (for the rock thrown upwards) and back into kinetic energy, while the rocks thrown horizontally and downwards are affected by gravity in such a way that they all reach the same final speed upon impact.

Quiz 6: Work and Energy

A 1-kg ball is released from a height of 6 m, and a 2-kg ball is released from a height of 3 m. Air resistance is negligible as they fall. Which of the following statements about these balls are correct? (There could be more than one correct choice.)

A force produces power P by doing work W in a time T . What power will be produced by a force that does six times as much work in half as much time?

A heavy rock and a light rock are dropped from the same height and experience no significant air resistance as they fall. Which of the following statements about these rocks are correct? (There Could be more than one correct choice.)

A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. They both slide up the same frictionless hill with no air resistance. Which object rises to a Greater height?

If the units of your answer are kg · m2/s3\mathrm { m } ^ { 2 } / \mathrm { s } ^ { 3 }m2/s3 which of the following types of quantities could your answer be? (There could be more than one correct choice.)

Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed twice as high as Bill. If there is no air resistance, the maximum height of Joe's ball will be

If a stone is dropped with an initial gravitational potential energy of 100 J but reaches the ground with a kinetic energy of only 75 J, this is a violation of the principle of conservation of energy.

Jill does twice as much work as Jack does and in half the time. Jill's power output is

A stone can slide down one of four different frictionless ramps, as shown in the figure. For which ramp will the speed of the ball be the greatest at the bottom?

A heavy dart and a light dart are launched vertically by identical ideal springs. Both springs were initially compressed by the same amount. There is no significant air resistance. Which of the Following statements about these darts are correct? (There could be more than one correct choice.)

If the units of your answer are kg · $\mathrm { m } ^ { 2 } / \mathrm { s } ^ { 3 }$ which of the following types of quantities could your answer be? (There could be more than one correct choice.)