Answer to Question #253941 in Mechanics | Relativity for Kristine

Question

A body a mass 𝑡𝑒𝑛 𝑠𝑙𝑢𝑔𝑠 is thrown with a velocity of 6𝑓𝑡/𝑠. along a horizontal floor. The coefficient of friction between the body and the floor 𝑖𝑠 0.20. Find a) Kinetics Energy and velocity of the body after traveling a distance of 2𝑓𝑡. b) How far will the body travel before it comes to rest?

Answer 1

a) Apply energy conservation:

$$KE_1=KE_2+W_f,\\\space\\ \frac12mv^2=KE_2+\mu mgx,\\\space\\ KE_2=\frac12mv^2-\mu mgx=1673\text{ ft⋅lb}.$$

b) The distacne:

$$\frac12mv^2=\mu mgd,\\\space\\ d=\frac{v^2}{2\mu g}=2.81\text{ ft}.$$