Question

  a. Will a body moving in a circular track has zero acceleration?  Explain your answer.                                       

 

 

b. In a local bar, a customer slides an empty beer mug on the counter for a refill. The bartender does not see the mug, which 

slides off the counter and strikes the floor 1.40m from the base 

of the counter. If the height of the counter is 0.860m, (a) with 

what speed did the mug leave the counter and (b) what was the 

the direction of the mug’s velocity just before it hit the floor?

Answer 1

a. On the whole, the body has centripetal acceleration that makes the velocity vector rotate. But the speed itself will not necessarily change, which means that the tangential acceleration can be zero.

b. Find the horizontal initial speed assuming zero air resistance. The time it took to reach the floor depends on the height only:

$$t=\sqrt{\frac{2h}{g}}.$$

a. The speed the mug leave the counter was:

$$v_x=\frac Rt=\frac{R}{\sqrt{2h/g}}=\frac{1.4}{\sqrt{2·0.86/9.8}}=3.34\text{ m/s}.$$

b. The vertical component of velocity:

$$v_y=\sqrt{2hg}.$$

The angle (below horizontal) of the velocity vector:

$$\theta=\text{atan}\frac{v_y}{v_x}=50.9º.$$