A spring with a constant of #2 (kg)/(s^2)# is lying on the ground with one end attached to a wall. An object with a mass of #4 kg # and speed of # 3 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

Question

A spring with a constant of #2  (kg)/(s^2)# is lying on the ground with one end attached to a wall. An object with a mass of #4   kg # and speed of # 3  m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

William Audy · Accepted Answer

#Delta x=sqrt 18 m# #"The kinetic energy of an object with ,mass of m and velocity of v is given as:"# #E_k=1/2*m*v^2# #E_k=1/2*4*3^2# #E_k=18 J" Object has a kinetic energy of 18 J"# #"The kinetic energy of object changes to potential energy on spring, if object stops:"# #"The potential energy of compressed spring is given by:"# #E_p=1/2*k*Delta x^2# #E_p=1/2*2*Delta x^2# #E_p=Delta x^2# #E_p=E_k " Energy not lost"# #18=Delta x^2# #Delta x=sqrt 18 m#

Nathan Ashcroft · Answer

undefined To calculate the compression of the spring, you can use the principle of conservation of mechanical energy. The initial kinetic energy of the object is equal to the potential energy stored in the compressed spring.

Initial kinetic energy = 1/2 * mass * velocity^2
Potential energy stored in the spring = 1/2 * spring constant * compression^2

Set the initial kinetic energy equal to the potential energy stored in the spring and solve for compression.

(1/2) * mass * velocity^2 = (1/2) * spring constant * compression^2

(1/2) * 4 kg * (3 m/s)^2 = (1/2) * 2 (kg/s^2) * compression^2

Compression^2 = (4 kg * (3 m/s)^2) / (2 kg/s^2)

Compression^2 = 18 m^2 / 2

Compression^2 = 9 m^2

Compression = sqrt(9 m^2)

Compression = 3 m