How Do You Calculate Potential Energy for Different Orientations of a Brick?

[SammyLP250]

Homework Statement

A 1.57 kg brick measures 20.0 cm x 8.00 cm x 5.50 cm. Taking the zero of potential energy when the brick lies on its broadest face. (a) What is the potential energy when the brick is standing on end? Note: You can treat the brick as though all its mass is concentrated at its center. (b) What is the potential energy when it's balanced on its 8 cm edge?

Homework Equations

U_g=mgh

The Attempt at a Solution

I could not figure out the first part of the question because I don't know what "standing on end" means.

As for B:

m = 1.57 kg
g = 9.81
h = 0.08 m

U_g = (1.57)(9.81)(0.08) = 1.23 J

That is the answer I get, but Mastering Physics tells me that there was a rounding error and the answer is 1.17 J and I cannot figure out where I was wrong. This is not supposed to be a hard problem. Maybe I'm thinking too hard about it??

 

[azizlwl]

Check the difference of CM between 20.0 cm x 8.00 cm surface facing the floor and that of
8.00 cm x 5.50 cm.

I guess it is between the broadest and the least broad. There are 3 dimensions of faces.

 

[SammyLP250]

Thanks for replying! Could you explain to me what you mean by check the difference? I'm a little slow...

 

[azizlwl]

If it is standing with height of 20cm, then the height of CM is 10cm.
Likewise if it is standing with height of 5.5cm, then the CM must be (5.5/2)cm

 

[Nickie]

As a scientist, it is important to carefully read and understand the problem before attempting to solve it. In this case, "standing on end" means that the brick is placed vertically on its narrowest edge. This is different from "balanced on its 8 cm edge", which means that the brick is placed horizontally on its 8 cm edge.

For part (a), you can calculate the potential energy by using the formula Ug=mgh, where h is the height of the brick when it is standing on end. Since the brick is treated as a point mass at its center, h would be equal to half of the brick's height, which is 2.75 cm. Therefore, the potential energy would be:

Ug = (1.57 kg)(9.81 m/s^2)(0.0275 m) = 0.43 J

For part (b), you have correctly calculated the potential energy when the brick is balanced on its 8 cm edge. However, the answer given by Mastering Physics is likely due to rounding errors in the values used for g and h. The more accurate answer would be 1.23 J, as you have calculated.

In general, when solving problems in physics, it is important to pay attention to the units and significant figures in order to avoid rounding errors. It is also helpful to double-check your calculations to make sure you have used the correct values and formulas.