Question

A 2kg block slides on a horizontal floor with a speed of 4m/s. It strikes an uncompressed spring and compresses it till the block is motionless. The kinetic friction force is 15N and spring constant is 10,000N/m. The spring compresses by
A) 8.5
B) 5.5
C) 2.5
D) 11.5

Answer 1

The potential energy stored in the spring is nothing but the elastic potential given by
${\text{U = }}\dfrac{1}{2}{\text{k}}{{\text{x}}^2}$

Complete Step by step solution: The total kinetic energy held by the block goes to the potential energy of the spring and the work done against friction.
Let x be the compression of the spring.
\eqalign{ & {\text{Thus }}\dfrac{1}{2}{\text{ m}}{{\text{v}}^2}{\text{ = }}{{\text{f}}_r}{\text{X + }}\dfrac{1}{2}{\text{k}}{{\text{x}}^2} \cr & \Rightarrow {\text{ 5000 }}{{\text{x}}^2}{\text{ + 15x - 16 = 0}} \cr & \Rightarrow {\text{ x = 0}}{\text{.055 m}} \cr & \therefore {\text{ x = 5}}{\text{.5 cm}} \cr}

Hence option B is correct

Additional Information: Friction is the force that resists motion when the surface of one object comes in contact with the surface of another. The mechanical advantage of a machine is reduced by friction, or in other words, the ratio of input to output decreases due to friction. An automobile uses one-quarter of its energy at limiting friction. Nevertheless, it is also the friction in the tire that allows the car to stay on the road and the friction in the clutch that makes it possible to drive.

Frictional force refers to the force generated by two surfaces that contact and slide against each other.

Notes: Frictional forces are mainly influenced by the surface texture and the amount of force that holds them together. The angle and position of the object affect the amount of friction force.
If an object is placed flat against an object, the force of friction will be equal to the weight of the object.
If an object is pushed against the surface, the force of friction will be increased and will exceed the weight of the object.