Question 295: 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