Questions: A 12-kg crate is pushed up an incline from point A to point B as shown in the figure. What is the change in the gravitational potential energy of the crate? +590 J -590 J +1200 J -1200 J This cannot be determined without knowing the angle of the incline.

A 12-kg crate is pushed up an incline from point A to point B as shown in the figure. What is the change in the gravitational potential energy of the crate? +590 J -590 J +1200 J -1200 J This cannot be determined without knowing the angle of the incline.
Transcript text: A 12-kg crate is pushed up an incline from point $A$ to point $B$ as shown in the figure. What is the change in the gravitational potential energy of the crate? +590 J -590 J +1200 J $-1200 \mathrm{~J}$ This cannot be determined without knowing the angle of the incline.
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Solution

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Solution Steps

Step 1: Determine the change in height

The crate is pushed from point A to point B. Point B is 5.0 m (7.0 m - 2.0 m) higher than point A. This is the change in height.

Step 2: Calculate the change in gravitational potential energy

The formula for gravitational potential energy is _mgh_, where _m_ is the mass (12 kg), _g_ is the acceleration due to gravity (9.8 m/s²), and _h_ is the change in height (5.0 m).

Change in GPE = (12 kg) * (9.8 m/s²) * (5.0 m)

Step 3: Calculate the value

Change in GPE = 588 J, which rounds to 590 J. Since the crate is moved upwards, the change is positive.

Final Answer: The final answer is $\boxed{+590 J}$

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