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Chapter 2: Q 20. (page 60)

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

Expert verified

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

Step by step solution

01

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 vi
The final velocity is given by vf
The acceleration due to gravity is g=10m/s2

02

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

Since, the bearing is dropped from the height, therefore, vi=0

The time taken to touch the ground ist=4sec

Let the distance travelled by bearing iss


Write the equation of motion to determine the distance travelled by bearing
role="math" localid="1648122931943" s=vit+12gt2s=(0)(4)+12(10)(4)2s=80m

The distance travelled by the ball is 80m. Therefore, the height of the tower is 80m
03

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

Let the final velocity of the bearing is vf

Using the equation of motion

vf=vi+gtvf=0+10(4)vf=40m/s

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

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