Question

Five different experiments are carried out. In each experiment, a block is attached to a horizontal spring. The block is pulled back a certain distance and released. The block oscillates back and forth on a frictionless surface. Rank the maximum force on the block for each of the following situations. (Rank the smallest force as 1).

A block of mass M is attached to a spring with a spring constant k, pulled back a distance d, and released.

A block of mass M is attached to a spring with a spring constant k, pulled back a distance (1/2)d, and released.

A block of mass 2M is attached to a spring with a spring constant k, pulled back a distance d, and released.

A block of mass M is attached to a spring with a spring constant 2k, pulled back a distance d, and released.

A block of mass M is attached to a spring with a spring constant (1/2)k, pulled back a distance (1/2)d, and released.

Answer 1

using F = kx

1 )

A block of mass M is attached to a spring with a spring constant k, pulled back a distance d, and released

F = k d

2 )

A block of mass M is attached to a spring with a spring constant k, pulled back a distance (1/2)d, and released.

F = k (d/2)

F = kd/2

3 )

A block of mass 2M is attached to a spring with a spring constant k, pulled back a distance d, and released.

F = kd

4 )

A block of mass M is attached to a spring with a spring constant 2k, pulled back a distance d, and released.

F = 2k d

F = 2 kd

5 )

A block of mass M is attached to a spring with a spring constant (1/2)k, pulled back a distance (1/2)d, and released.

F = k/2 X d/2

F kd / 4

so 5 is small

and

2 is next small

and

3 and 1 is same

next is 4 is bigger than all

so the smaller order is 5 < 2 < 3 = 1 < 4