Work, Energy, and Power

Work,energy and power-Test 1
MATHMANIA
September 24, 2013
Instructions - All questions carry 1 mark each TOTAL - 20 marks
1. A rod of mass m and length l is lying on a horizontal table. Find the work required to make it stand on one end.
2. A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to what power of time?
3. When kinetic energy of a body is increased by 300%, its momentum increases by what %?
4. If the linear momentum of a body is increased by 50%,its kinetic energy is increased by what %?
5. A mass m covers a certain distance s under the action of a constant force,starting from rest. The kinetic energy acquired by it depends on what power of its mass?
6. At time t=0,a particle starts moving along the x-axis. If its kinetic energy increases uniformly with time t,the net force acting on it is proportional to what power of time?
7. A ball of mass 50g is thrown upwards. It rises to a maximum height of
100m. At what height its kinetic energy will be reduced to 70%?
8. An automobile moves along a straight horizontal road with a speed (i)v and (ii)3v. Assuming identical conditions,find the ratio of the shortest distances in which the automobile can be stopped.
9. A body of mass m accelerates uniformly from rest to a speed v in time t.
Find the instantaneous power delivered to the body as a function of time.
10. Two trucks,one loaded (A) and the other unloaded (B) are moving and have same kinetic energy. The mass of A is double that of B. Brakes are applied and both are brought to rest. Find the ratio of the distance covered by A before coming to rest,to that of B.

1

11. A uniform chain of mass m and length L is lying on a table with (1/4)th of its length hanging freely from the edge of the table. Find the amount of work done in dragging the chain on the table completely.
12. A simple pendulum of length L has maximum angular displacement α.
Find the maximum kinetic energy of the bob of mass M.
13. A certain mass is under free fall. When it loses potential energy equal to
U,its speed is found to be v. Find the expression for its mass.
14. A particle moves along x-axis from x = x1 to x = x2 under a force F=2x.
Find the work done in this process.
15. A block of mass 10kg is moving in x-direction at 10m/s. It is subjected to a constant retarding force F=0.1x J/m during its travel from x=20m to x=30m. Find its final kinetic energy.
16. The power of a water pump is 2kW. Taking g=10ms−2 ,find the amount of water it can raise in 1 min, to a height of 10m.
17. A bullet fired into a fixed target loses half of its velocity after penetrating
3cm. How much further will it penetrate before coming to rest,assuming that it faces constant resistance to motion?
18. The potential energy of 1kg particle free to move along x-axis is given by
2
2
V(x)=( x − x )J. The total mechanical energy of the particle is 2J. Find
4
2 its maximum speed in m/s.
19. A body of mass 3kg is under a constant force which causes a displacement s metre in it,given by the relation s = (1/3)t2 , where t is in seconds. Find the work by the force in 2 seconds.
20. 300J of work is done in sliding a 2kg block up an inclined plane of height
10m. Taking g=10ms−2 ,find the work done against friction.
END

2