QuestionQuestions 12-14: In a physics lab, a student uses three light, frictionless wheeled carts as shown to the right. Each cart is loaded with blocks of equal mass.
12. The same force $F$ is applied to each cart and they move equal distances $d$ . In which one of these three cases is more work done by force F? a) cart 1 b) cart II c) cart III d) the same work is done on each cart
13. The same force $F$ is applied, to each cart and they move equal distances $d$ . Which cart will be moving the fastest at the end of distance $d$ ? a) cart 1 b) cart II c) cart Ill d) all three will have the same kinetic energy
14. The same force $F$ is applied to each cart and they move equal distances $d$ . Which cart will move faster at the end of distance d? a) cart 1 b) cart II c) cart III

Studdy Solution

STEP 1

1. The force $F$ is constant and applied to each cart over the same distance $d$ .
2. The blocks on each cart have equal mass.
3. The work done by a force is calculated as $W = F \times d \times \cos(\theta)$ , where $\theta$ is the angle between the force and the direction of motion.
4. The kinetic energy of an object is given by $KE = \frac{1}{2}mv^2$ .
5. The carts are frictionless, so no energy is lost to friction.

STEP 2

1. Determine the work done by force $F$ on each cart.
2. Determine the final speed of each cart after moving distance $d$ .
3. Compare the speeds of the carts to determine which moves faster.

STEP 3

The work done by force $F$ on each cart is calculated using the formula $W = F \times d \times \cos(\theta)$ .
Since the force is applied horizontally and the carts move horizontally, $\theta = 0^\circ$ , so $\cos(\theta) = 1$ .
Thus, the work done on each cart is $W = F \times d$ .

STEP 4

Since the same force $F$ is applied over the same distance $d$ for each cart, the work done is the same for each cart.
Therefore, the answer to question 12 is: d) the same work is done on each cart

STEP 5

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
Since the work done is the same for each cart, the change in kinetic energy is also the same.

STEP 6

The kinetic energy $KE = \frac{1}{2}mv^2$ depends on both mass $m$ and velocity $v$ .
Since the carts have different masses, the cart with the least mass will have the greatest velocity for the same kinetic energy.

STEP 7

Cart I has the least mass (one block), so it will have the highest velocity at the end of distance $d$ .
Therefore, the answer to question 13 is: a) cart 1

STEP 8

Since cart I has the least mass and the same work is done on each cart, cart I will move faster at the end of distance $d$ .
Therefore, the answer to question 14 is: a) cart 1

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Studdy Solution

STEP 1

STEP 2

1. Determine the work done by force $F$ on each cart.
2. Determine the final speed of each cart after moving distance $d$ .
3. Compare the speeds of the carts to determine which moves faster.

STEP 3

The work done by force $F$ on each cart is calculated using the formula $W = F \times d \times \cos(\theta)$ .
Since the force is applied horizontally and the carts move horizontally, $\theta = 0^\circ$ , so $\cos(\theta) = 1$ .
Thus, the work done on each cart is $W = F \times d$ .

STEP 4

Since the same force $F$ is applied over the same distance $d$ for each cart, the work done is the same for each cart.
Therefore, the answer to question 12 is: d) the same work is done on each cart

STEP 5

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
Since the work done is the same for each cart, the change in kinetic energy is also the same.

STEP 6

The kinetic energy $KE = \frac{1}{2}mv^2$ depends on both mass $m$ and velocity $v$ .
Since the carts have different masses, the cart with the least mass will have the greatest velocity for the same kinetic energy.

STEP 7

Cart I has the least mass (one block), so it will have the highest velocity at the end of distance $d$ .
Therefore, the answer to question 13 is: a) cart 1

STEP 8

Since cart I has the least mass and the same work is done on each cart, cart I will move faster at the end of distance $d$ .
Therefore, the answer to question 14 is: a) cart 1

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Studdy Solution

STEP 1

STEP 2

1. Determine the work done by force F F F on each cart.2. Determine the final speed of each cart after moving distance d d d.3. Compare the speeds of the carts to determine which moves faster.

STEP 3

STEP 4

Since the same force F F F is applied over the same distance d d d for each cart, the work done is the same for each cart.Therefore, the answer to question 12 is: d) the same work is done on each cart

STEP 5

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.Since the work done is the same for each cart, the change in kinetic energy is also the same.

STEP 6

The kinetic energy KE=12mv2 KE = \frac{1}{2}mv^2 KE=21​mv2 depends on both mass m m m and velocity v v v.Since the carts have different masses, the cart with the least mass will have the greatest velocity for the same kinetic energy.

STEP 7

Cart I has the least mass (one block), so it will have the highest velocity at the end of distance d d d.Therefore, the answer to question 13 is: a) cart 1

STEP 8

Since cart I has the least mass and the same work is done on each cart, cart I will move faster at the end of distance d d d.Therefore, the answer to question 14 is: a) cart 1

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1. Determine the work done by force $F$ on each cart.
2. Determine the final speed of each cart after moving distance $d$ .
3. Compare the speeds of the carts to determine which moves faster.

Since the same force $F$ is applied over the same distance $d$ for each cart, the work done is the same for each cart.
Therefore, the answer to question 12 is: d) the same work is done on each cart

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
Since the work done is the same for each cart, the change in kinetic energy is also the same.

The kinetic energy $KE = \frac{1}{2}mv^2$ depends on both mass $m$ and velocity $v$ .
Since the carts have different masses, the cart with the least mass will have the greatest velocity for the same kinetic energy.

Cart I has the least mass (one block), so it will have the highest velocity at the end of distance $d$ .
Therefore, the answer to question 13 is: a) cart 1

Since cart I has the least mass and the same work is done on each cart, cart I will move faster at the end of distance $d$ .
Therefore, the answer to question 14 is: a) cart 1