First slide

Simple hormonic motion

Question

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

Moderate

A

11.0 cm
B

8.5 cm
C

5.5 cm
D

2.5 cm

Solution

Here, we have
$\frac{1}{2} {mv}^{2} = Fx + \frac{1}{2} {kx}^{2} or \frac{1}{2} (2) (4)^{2} = 15 x + \frac{1}{2} (10000) (x^{2}) or 5000 x^{2} + 15 x - 16 = 0 ohring it, we get X = 5 \cdot 5 cm$

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