Question

1. If you compress a spring of spring constant 223 N/m by 1.29 cm, what is the elastic potential energy of the spring?

2. You have a piano of mass 1,946 kg, which is suspended 14 m above the ground. If we decide that the zero of our height coordinates is at the ground, what is the gravitational potential energy of the piano?

3. You have a kinetic friction force of 42.5 acting on a box that is moving across a rough table. If the box slows to a stop in 19.6 cm, how much work is done by friction?

4. Find the scalar product of A⇀⋅B⇀

where A⇀=10.2iˆ+ 9.8jˆ and B⇀= 4.7iˆ+9.3jˆ

Answer 1

1)

We have the spring is compressed by a distance of,

Also the spring constant of the spring,

So,we have the potential energy stored in the spring,

the potential energy stored in the spring,

2)

We have the mass of piano,

Also taken that the zero of the hieght coordinates for the ground level.

Also,the hieght of the piano from the ground,

So,The potential energy of the piano,

3)

Here the box is moving upon the surface the rough table.and due to the kinetic frictional force of 42.5N which opposes the motion of the box and directing opposite to the displacement or motion of the box,doing a negetive work on the box reduces its kinetic energy,and stops or comes to rest after travelling a distance of 1.29cm.

So,Work done by the frictional force,(-ve sign indicates the negetive work)

So,The work done by the frictional force,.

d)

Given the vector,

And vector,

So,to find the scalar or dot product of the vectors,

So,The scalar product of the vectors,