Jake T. answered • 04/03/20

Mechanical Engineering PhD Student

First, we will solve for the force of friction by using the numbers given to us from the first push. Then we will us E = Fd to solve for the energy used when given the second push.

First, we know that E = 3.2 J. We also know that d will be equal to the hypotenuse of the triangle made by the 0.4 m north and 0.3 m east triangle. Lastly, we can solve for the force of friction, F_{f}

- E = 3.2 J
- d = √(0.3
^{2}+ 0.4^{2}) = 0.5 m - F
_{f}= E/d = 3.2/ 0.5 = 6.4 N

Now, we will solve for the new distance pushed, and use the E = Fd equation to solve for the lost energy due to frinction:

- d = 0.3 + 0.4 = 0.7 m
- E = F
_{f}*d = 6.4*0.7 = 4.48 J

Answer:

- 4.48 J of energy lost from friction when pushing the book directly north 0.4 m, then 0.3 m east