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Work

Question

A 2kg Block slides on a horizontal floor with speed of 4 m/s. It strikes a uncompressed spring and compresses it till the block is motionless. The kinetic friction force is 15N and spring constant is 10,000 N/m. The spring compressed by

Moderate

A

8.5 cm
B

5.5 cm
C

2.5 cm
D

11 cm

Solution

Let the spring compresses by x
Initial K.E. of the mass = P.E. of the spring + work done
due to friction
$K E o f t h e m a s s = \frac{1}{2} m v^{2}; P E o f s p r i n g = \frac{1}{2} k x^{2}; w o r k d o n e b y f r i c t i o n = f r i c t i o n f o r c e . d i s p l a c e m e n t s u b s t i t u t e \frac{1}{2} m v^{2} = \frac{1}{2} k x^{2} + f . x s u b s t i t u t e t h e g i v e n v a l u e s ∴ \frac{1}{2} \times 2 \times 4^{2} = \frac{1}{2} \times 10000 \times x^{2} + 15 x s o l v e t h e q u a d r a t i c e q u a t i o n x = 0.055 m s p r i n g i s c o m p r e s s e d b y 5.5 c m$

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