a 15kg mass is attached to and held against a compressed ide

a 1.5kg mass is attached to and held against a compressed ideal spring and then released on a horizontal rough surface. The spring constant is 300N/m and the compression distance is d=15cm. The mass moves from position 1 past the spring to equilibrium position 3, and momentarily comes to rest in position 4.

a) find the frictional force if the total distance the mass travels before coming to rest again is d+d\'=20cm. Must show work energy equation from positions 1 to 4

b)find d\' if no friction were present.

c)at some position 2, the block\'s acceleration is zero and hence its speed is maximum. using your answer in part a, find the equation for the distance x(from position 2 to the equilibrium position) Where the speed is a maximum.

Solution

a)
initial spring potential energy = 0.5*K*x^2
= 0.5*(300)*(0.15)^2
= 3.375 J

This energy is lost as work done against friction
So,
work done against friction = 3.375
f* distance = 3.375
f*(0.2 m)= 3.375
f= 16.875 N
Answer: 16.875 N

b)
If there is no friction, object will keep moving for ever since there is no force to stop it
So, d\' = infinity

c)
V will be maximum when acceleration will be 0
Acceleration will be 0 when net force on it will be 0
so,
spring force must balance frictional force
K*x = f
300*x = 16.875
x= 0.056 m
= 5.6 cm