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Hello everyone! I’m back. Today we continue to solve the exercise “A 2kg Block On A Horizontal Surface Is Attached To A Horizontal Spring Of Negligible Mass. The Other End Of The Spring Is..” Please follow the tutorial below!

## Question: A 2kg Block On A Horizontal Surface Is Attached To A Horizontal Spring Of Negligible Mass. The Other End Of The Spring Is..

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Here is our question: A 2kg block on a horizontal surface is attached to a horizontal spring of negligible mass. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. The block is released from rest after the spring is stretched such that the block-spring system experiences simple harmonic motion, as shown in the graph that represents the block’s velocity as a function of time.

How could a student use the known information and the graph to determine the magnitude of the change in spring potential energy of the system from the release point of the block to the moment when the system’s spring potential energy is zero?

A By determining the kinetic energy of the block at 8 s by using K = 1/2 mv^{2} ?

B By determining the kinetic energy of the block at 2 s by using K = 1/2 mv^{2} ?

с By determining the kinetic energy of the block at 2 s and 6 s by using K = 1/2 mv^{2} ? and adding the two values of kinetic energy together.

D By determining the kinetic energy of the block at 2 s and 6 s by using K = 1/2 mv^{2} ?, subtracting the two values of kinetic energy, and determining the magnitude of the result.

## Answer

We know that kinetic energy (K)=1/2 mv^{2}

and potential energy of spring (P)=1/2 x KX^{2}

For this problem most of block is given by spring const (K) is not given.

to find the magnitude of change of spring potential energy from X=0 to X=0 (at zero spring potential)

by conservation of energy given in kinetic energy(maximum)= loss in spring potential energy

To find the change we have to find the kinetic energy at maximum velocity points of the graph (at peak) i-e at, t=2 sec, or t = 6 sec or t=10sec

among the given option, t=2s is given in only option B

## Relevant knowledge

The elastic potential energy of the spring is the potential energy of the elastic force generated from the spring, it has the ability to generate or not, the expression for the elastic potential energy of the spring only makes sense when we choose frame of reference to calculate potential energy.

## Conclusion

Above we have given the answer to the question “A 2kg Block On A Horizontal Surface Is Attached To A Horizontal Spring Of Negligible Mass. The Other End Of The Spring Is..”. If you have any questions, please leave us a comment.

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