Question 296: Work, Energy and Power & Circular Motion

Question

A ball of mass 4 kg, moving with a velocity of 10 ms
$-$1
, collides with a spring of length 8 m and force constant 100 Nm
$-$1
. The length of the compressed spring is x m. The value of x, to the nearest integer, is ____________.

Accepted Answer

If spring compressed by x,
then work done by spring = 0 $-$ ${1 \over 2}$ $	imes$ 4 $	imes$ 10
2
Applying work energy theorem,
$-$${1 \over 2}$ kx
2
= $-$${1 \over 2}$ $	imes$ 4 $	imes$ 10
2
$ \Rightarrow $ 100x
2
= 4 $	imes$ 10
2
$ \Rightarrow $ x = 2
$ 	herefore $ Final length of the spring = 8 $-$ 2 = 6 m

Work, Energy and Power & Circular Motion

A ball of mass 4 kg, moving with a velocity of 10 ms -1 , collides with a spring of length 8 m and force constant 100 Nm -1 . The length of the compressed spring is x m. The value of x, to the nearest integer, is ____________.

Integer / Numeric Answer Type