Question

The mass of an iron sphere is 90 kg . The sphere is dropped from a height of 9.8 m on sand so that it penetrates the sand upto 2 cm. Calculate the resistive force applied by sand on the sphere.​

Answer 1

Explanation:

Consider the motion of ball from A to B.

B→ just above the sand ( just to penetrate)

u=0,a=9.8 m/s

2

,s=5 m

The distance covered by the ball is:

S=ut+

2

1

at

2

⇒5=0+

2

1

(9.8)t

2

⇒t

2

=

4.9

5

=1.02

⇒t=1.01.

∴ velocity at B,v=u+at=9.8×1.01(u=0)=9.89 m/s.

From motion of ball in sand

u

1

=9.89 m/s,v

1

=0,a=?,s=10 cm=0.1 m

a=

2s

v

1

2

−u

1

2

=

2×0.1

0−(9.89)

2

=−490 m/s

2

The retardation in sand is 490 m/s

2