Question

To test the impact performance of a 10 cm thick gymnastics mat, a 20 kg cylindrical

Answer 1

Answer:

A)196J

B)-208J

C)3467J

Step-by-step explanation:

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= $20 \times 9.8 \times 1 = 196 J$

b)

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

C)

Work done=$\text{Average force} \times \text{ Compression of mat}$

$208=F \times 0.06$

F=3467J