Question

Ball bearings are made by letting spherical drops of molten metal fall inside a tall tower—called a shot tower—and solidify as they fall.

a. If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be? b. What is the bearing’s impact velocity?

Short answer

The height of the tower is 80 m and the impact velocity is 40 m/s

Step-by-step solution

Step 1. Write the given information.

The ball bearing is dropped in the tower to solidify

Let the initial velocity of the ball bearing is $v_i$
The final velocity is given by $v_f$
The acceleration due to gravity is $g=10m/s^2$

Step 2. (a)To determine the height of the tower.

Since, the bearing is dropped from the height, therefore, $v_i=0$

The time taken to touch the ground is$t=4sec$

Let the distance travelled by bearing is$s$

Write the equation of motion to determine the distance travelled by bearing
role="math" localid="1648122931943" $$\begin{gathered} s=v_{i}t+\frac{1}{2}g{t}^2 \\ s=\left(0\right)\left(4\right)+\frac{1}{2}\left(10\right){\left(4\right)}^2 \\ s=80m \end{gathered}$$

The distance travelled by the ball is 80m. Therefore, the height of the tower is 80m

Step 2. (b)To determine the impact velocity of bearing

Let the final velocity of the bearing is $v_f$

Using the equation of motion

$$\begin{gathered} v_f=v_i+gt \\ {v}_f=0+10\left(4\right) \\ {v}_f=40m/s \end{gathered}$$

Thus, the impact velocity of the bearing is 40 m/s