Question

A 2 kg object is attached to a spring and is oscillating on a horizontal surface. When the object has a speed of 10 m/s, the spring is stretched 2 m. The spring constant is 10 N/m. Neglect friction.

Find the maximum speed of the object.

What is the maximum stretch in the spring?

What is the object's speed when the spring is stretched 1 m?

What is the stretch in the spring when the object's speed is 5 m/s?

Answer 1

m = 2kg, u= 10m/s, x = 2m , k =10 N/m
(A) from conservation of energy
KE max = KE+PE
0.5mvmax^2 = 0.5mu^2 +0.5kx^2
0.5*2*v^2 = 0.5*2*10^2+0.5*10*2^2
vmax = 10.95 m/s
(b) from conservation of energy
PE max = KE+PE
0.5kA^2 = 0.5mu^2 +0.5kx^2
0.5*10*A^2 = 0.5*2*10^2+0.5*10*2^2
A = 4.9 m
(c) x= 1 m
from conservation of energy
KE2+PE2 = KE1+PE1
0.5*2*v^2 +0.5*10*1^2 = 0.5*2*10^2+0.5*10*2^2
v = 10.72 m/s
(d) v = 5m/s
from conservation of energy
KE2+PE2 = KE1+PE1
0.5*2*5^2 +0.5*10*x^2 = 0.5*2*10^2+0.5*10*2^2
x =4.36 m