# Help with a Potential Energy Problem

• champ0342
In summary, the conversation discusses a small block of mass 1.0 kg sliding along a frictionless loop-the-loop. The block is released from rest at point P, at a height of 8R above the bottom of the loop. The conversation then asks several questions about the work done by the weight of the block, as well as the potential energy at different points along the loop.
champ0342
In the figure below, a small block of mass m = 1.0 kg can slide along the frictionless loop-the-loop. The block is released from rest at point P, at height h = 8R above the bottom of the loop. (For all parts, answer using g for the acceleration due to gravity, and R and m as appropriate.)
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http://www.webassign.net/hrw/08_33.gif

(a) How much work does the weight of the block do on the block as the block travels from point P to point Q?

(b) How much work does the weight of the block do on the block as the block travels from point P to the top of the loop?

(c) What is the potential energy when the block is at point P? (Assume that the gravitational potential energy of the block Earth system is taken to be zero at the bottom of the loop.)

(d) What is the potential energy when the block is at point Q?

(e) What is the potential energy when the block is at the top of the loop?

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(a) The work done by the weight of the block on the block as it travels from point P to point Q can be calculated using the equation W = mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the change in height. In this case, the change in height is R, since the block is traveling from a height of 8R to a height of 9R. Therefore, the work done by the weight of the block is W = (1.0 kg)(9.8 m/s^2)(R) = 9.8R Joules.

(b) As the block travels from point P to the top of the loop, the work done by the weight of the block is the same as in part (a), since the height change is still R. Therefore, the work done by the weight of the block is again 9.8R Joules.

(c) The potential energy of the block at point P can be calculated using the equation PE = mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height of the block. In this case, the height of the block is 8R, so the potential energy at point P is PE = (1.0 kg)(9.8 m/s^2)(8R) = 78.4R Joules.

(d) At point Q, the height of the block is 9R, so the potential energy can be calculated using the same equation as in part (c). Therefore, the potential energy at point Q is PE = (1.0 kg)(9.8 m/s^2)(9R) = 88.2R Joules.

(e) At the top of the loop, the height of the block is 10R. Therefore, the potential energy can be calculated using the same equation as in parts (c) and (d). The potential energy at the top of the loop is PE = (1.0 kg)(9.8 m/s^2)(10R) = 98R Joules.

## What is potential energy?

Potential energy is the energy possessed by an object due to its position or configuration in a force field. It is stored energy that has the potential to do work.

## How is potential energy calculated?

The formula for calculating potential energy is PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.

## What is the difference between potential energy and kinetic energy?

Potential energy is the energy an object has due to its position, while kinetic energy is the energy an object has due to its motion. Potential energy can be converted into kinetic energy and vice versa.

## How can potential energy be changed?

Potential energy can be changed by altering the height or position of an object, or by changing the force field acting on the object.

## What are some real-life examples of potential energy?

Some real-life examples of potential energy include a roller coaster at the top of a hill, a stretched rubber band, a compressed spring, and a book on a shelf.

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