Question

A block is initially at position x = 0 and in contact with an uncompressed spring of negligible mass. The block is pushed back along a frictionless surface from position x = 0 to x = -D , as shown above, compressing the spring by an amount Δx = D . The block is then released. At x = 0 the block enters a rough part of the track and eventually comes to rest at position x = 3D . The coefficient of kinetic friction between the block and the rough track is µ.
On the axes below, sketch and label graphs of the following two quantities as a function of the position of the block between x = -D and x = 3D . You do not need to calculate values for the vertical axis, but the same vertical scale should be used for both quantities.
i. The kinetic energy K of the block
ii. The potential energy U of the block-spring system

Answer 1

Answer:

(See attachment)

Explanation:

The kinetic energy K and the potential energy U of the block are presented below.

Answer 2

Kinetic energy of spring is the energy associated with motion by the spring. The graph is plotted between displacement and the potential energy/kinetic energy for the given spring.

Given information-

A block is initially at position ($x$ equals to zero) and in contact with an uncompressed spring of negligible mass.

The block is pushed at distance $-D$ by compressing the spring an amount of $D$.

The block enters a rough part of the track and eventually comes to rest at position $x$ equal to $3D$.

The coefficient of kinetic friction between the block and the rough track is µ.

What is potential energy of spring?

Potential energy of spring is the energy required to change the length of spring which is equal to the half of the product of square of displacement and spring constant.

What is kinetic energy of spring?

Kinetic energy of spring is the energy associated with motion by the spring.

Graph

Below is the graph attached for the given problem. In the graph on the x axis, the displacement of spring is represented. The energy is shown on the y axis.

The kinetic energy is represented with symbol K and potential energy is represented with symbol U.

The compression of spring will result in more kinetic energy for the block given, when the spring is released.

With more displacement, the potential energy will be more.

Hence the graph is plotted between displacement and the potential energy/kinetic energy for the given spring.

Learn more about the spring energy here;

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