To test the impact performance of a 10 cm thick gymnastics mat, a 20 kg cylindrical
mass is dropped onto the mat from a height of 1 m above the mat. During the impact,
the cylinder’s vertical velocity reaches zero at the instant the mat has compressed to
only 4 cm thick.

a. How much kinetic energy does the cylinder have at the instant just before it
contacts the mat?

b. How much work does the mat do to stop the fall of the cylinder?

c. What average vertical force does the mat exert on the cylinder during the impact,
from contact until the cylinder’s vertical velocity is zero?

We are given that a 20 kg cylindrical mass is dropped onto the mat from a height of 1 m above the mat. During the impact, the cylinder’s vertical velocity reaches zero at the instant the mat has compressed to only 4 cm thick.

So, The Mat gets compressed by : 10cm - 4 cm = 6 cm=0.06 m

a)

Using Conservations of energy

Potential energy at the top = Kinetic energy at the point before touching the surface

Kinetic energy = mgh= [tex]20 \times 9.8 \times 1 = 196 J[/tex]

b)

Work done by the mat do to stop the fall of the cylinder =[tex]-mg(h+0.06)=-20 \times 9.8(1+0.06)=-208 J[/tex]

C)

Work done=[tex]\text{Average force} \times \text{ Compression of mat}[/tex]

[tex]208=F \times 0.06[/tex]

F=3467J