Question

A body of mass 0.1 kg moving with a velocity of 10 m/s hits a spring (fixed at the other end) of force constant 1000 n/m and comes to rest after compressing the spring. The compression of the spring is

Answer 1

by using this formula:
$\frac{1}{2} \times 10 \times 10 = \frac{1}{2} \times 1000 \times x {}^{2} \\ \frac{1}{2} \times 100 = 500 \times x { }^{2} \\ 50 = 500 \times x { }^{2}{ } \\ \frac{50}{500} = x { }^{2} \\ \frac{1}{10} = x { }^{2} \\ x {}^{2} = 0.1 \\ x = \sqrt{0.1}$

Answer 2

Hey dear,

◆ Answer-
x = 0.1 m

◆ Explaination-
# Given-
m = 0.1 kg
v = 10 m/s
k = 1000 N/m

# Solution-
As moving object strikes on the spring, the kinetic energy of object is used in compressing the spring.

Kinetic energy of object = Work done in compression
1/2 mv^2 = 1/2 kx^2
x^2 = mv^2 / k
x^2 = 0.1 × 10^2 / 1000
x^2 = 10^-2
x = 0.1 m

Compression produced in the spring is 0.1 m.

Hope this helps you...