Question

An ideal spring is hung vertically from the ceiling. when a 2.0-kg mass hangs at rest from it the spring is extended 6.0 cm from its relaxed length. an upward external force is then applied to the block to move it upward a distance of 16 cm. while the the block is being extended by the force, the work done by the spring is

Answer 1

The work done by a spring can be calculated using the formula: Work = (1/2)kx². To calculate the spring constant, use Hooke's Law. Once you have the spring constant, you can calculate the work done by the spring when the block is being extended by the external force using the formula: Work = (1/2)k(Δx)².

Step-by-step explanation:

The work done by a spring can be calculated using the formula:

Work = (1/2)kx²

where k is the spring constant and x is the displacement of the spring from its relaxed length.

In this case, the spring constant is not given. However, we can calculate it using the information provided. When a 2.0-kg mass hangs at rest from the spring, the spring is extended 6.0 cm from its relaxed length. We can use this information to calculate the spring constant using Hooke's Law:

F = kx

k = F/x

where F is the force and x is the displacement. In this case, the force can be calculated using the formula F = mg, where m is the mass and g is the acceleration due to gravity.

Once we have the spring constant, we can calculate the work done by the spring when the block is being extended by the external force. This can be calculated using the formula:

Work = (1/2)k(Δx)²

where Δx is the change in displacement.

Answer 2

The force for a spring can be determined from Hooke's law: F=-kx, where k is the spring constant and x is the length of the spring. The work done can be determined using the equation: W=Fd. If you want to know the work done by the spring, you can substitute the force for a spring into the work equation, so the equation becomes W=-Fxd. If we solve the equation, F=mg where g is the acceleration due to gravity, so F=(2.0 kg)(9.8 m/s^2)= 19.6 N. We have the force. The work done is W=(19.6 N)(0.06 m)(0.16 m)=.188 J