Answer to Question #185543 in Physics for Amira

Question

We want to slide a 12-kg crate up a 2.5-m-long

ramp inclined at 300. A worker, ignoring friction,

calculate s that he can do this by giving it an initial speed of 5.0m/s at the bottom and letting it go. But friction is not negligible; the crate slides only 1.6 m up the ramp, stops, and slides back down

a. Find the magnitude of the friction force

acting on the crate, assuming that it is

constant.

b. How fast is the crate moving when it reaches the bottom of the ramp.

Answer 1

Find the height that corresponds to the point 1.6 m along the incline:

$$h=1.6\sin30°=0.8\text{ m}.$$

Find the height off the ramp:

$$H=2.5\sin30°=1.25\text{ m}.$$

(a) According to energy conservation, the kinetic energy was spent to overcome friction and to go up the slope:

$$KE=W_f+PE,\\\space\\ \frac 12 mv^2=fx+mhg,\\\space\\ f=\frac{m(v^2-gh)}{2x}=\frac{12(5^2-9.8·0.8)}{2·1.6}=64.35\text{ N}.$$

(b) From energy conservation, find the speed at the bottom required to reach the top of the ramp:

$$KE=W_f+PE,\\\space\\ \frac 12 mv^2=fL+mgH,\\\space\\ v=\sqrt{\frac{2fL}{m}+2gH}=7.16\text{ m/s}.$$