Work and Energy Worksheet-2

Work and Energy Worksheet-2

How much work is done by a force of 10 N in moving an object through a distance of 1 m in the direction of the force?

A. 10 joules B. 1 joule C. 0 joule D. None of these

Calculate the work done in lifting 200 kg of water through a vertical height of 6 meters (Assume g = 10 m/s²).

A. 1200 J B. 12000 J C. 120 J D. 0 J

A child pulls a toy car through a distance of 10 meters on a smooth, horizontal floor. The string held in child's hand makes an angle of 60° with the horizontal surface. If the force applied by the child be 5 N, calculate the work done by the child in pulling the toy car.

A. 12.5 J B. 0 J C. 50 J D. 25 J

Calculate the kinetic energy of a body of mass 2 kg moving with a velocity of 0.1 metre per second.

A. 0.01 J B. 0.02 J C. 0.04 J D. None of these

Two bodies of equal masses move with uniform velocities v and 3v respectively. Find the ratio of their kinetic energies.

A. 3 : 1 B. 9 : 1 C. 1 : 3 D. 1: 9.

How much work should be done on a bicycle of mass 20 kg to increase its speed from 2 ms^–1 to 5 ms^–1 ? (Ignore air resistance and friction).

A. 210 J B. 40 J C. 250 J D. 290 J

If acceleration due to gravity is 10 m/s²what will be the potential energy of a body of mass 1 kg kept at a height of 5 m?

A. 250 J B. 50 J C. 100 J D. None of these

A bag of wheat weighs 200 kg. To what height should it be raised so that its potential energy may be 9800 joules? (g = 9.8 ms^–2)

A. 5 m B. 10 m C. 2.5 m D. 20 m

A body does 20 joules of work in 5 seconds. What is its power ?

A. 4 W B. 80 W C. 0.2 W D. None of these

What is the power of a pump which takes 10 seconds to lift 100 kg of water to a water tank situated at a height of 20 m ? (g = 10 m s-²)

A. 20 KW B. 200 KW C. 2000 KW D. 2 kW

Answer:

Explanation: The work done is calculated by using the formula :

W = F × S

Force, F = 10 N

Distance, S = 1 m

Work done W = 10 × 1 J = 10 J

Thus, the work done is 10 joules.

Explanation: In this case work is being done against gravity in lifting water. Now the formula the work done against gravity is :

W = m × g × h

Mass of water, m = 200 kg

Acceleration due to gravity g = 10 m/s²

Height h = 6 m

By putting the values in the we get :

W = 200 × 10 × 6

W= 12000 J

Thus, the work done is 12000 joules.

Explanation:

The toy car is moving along horizontal floor, so we can draw a horizontal line OX to show the direction of motion the car. Now the force of 5 N is applied along the string tied to the toy car making an angle of 60° with the floor. Now we draw another line OA making an angle of 60° with horizontal floor OX. In the diagram, OX represents the direction of motion and OA represents the direction of force, the angle between them being 60°.

Now the formula for work done when a body moves at an angle to the direction of force is :

W = F cos θ × S

Here, Force, F = 5 N

Angle θ = 60°

Distance, s = 10 m

So, Work done, W = 5 × cos 60° × 10

cos 60° = 0.5.

W = 5 × 0.5 × 10 = 25 J

Thus, the work done is 25 joules.

Explanation: Kinetic energy = (1/2) mv²

Mass, m = 2 kg

Velocity, v = 0.1 m/s

Kinetic energy = (1/2) × 2 × (0.1)²

= (1/2) × 2 × 0.1 × 0.1

= 0.01 J

Thus, the kinetic energy of the body is 0.01 joule.

Explanation:

(i) Mass of first body = m

Velocity of first body = v

So, K.E. of first body = (1/2) mv² ... (1)

(ii) Mass of second body = m

Velocity of second body = 3v

So, K.E. of second body = (1/2) m (3v)²

= 9/2 mv² ...(2)

Now, to find out the ratio of kinetic energies of the two bodies, we should divide equation (1) by equation (2), so that:

Thus, the ratio of the kinetic energies is 1: 9.

K.E. of second body = 9 × K.E. of first body

That is, the kinetic energy of second body is 9 times the kinetic energy of the first body.

Explanation: We know that whenever work is done, an equal amount of energy is used up.

Hence the work done in this case will be equal to the change in kinetic energy of bicycle when its speed changes from 2 ms^–1to 5 ms^–1.

Initially

Mass of bicycle m = 20 kg

Speed of bicycle v = 2 ms^–1

Kinetic energy, E^K = (1/2) mV²

= 10 × 4

= 40 J

(b) In the second case :

Mass of bicycle, m = 20 kg

Speed of bicycle, v = 5 ms^–1

So, Kinetic energy, E^K = (1/2) mV²

= (1/2) × 20 × (5)²

= 10 × 25

= 250 J

Now, Work done = Change in kinetic energy

= 250 – 40

= 210 J

Thus, the work done is 210 joules.

Explanation:

The potential energy of a body is calculated by using the formula :

Potential energy = m × g × h

Mass, m = 1 kg

Acceleration due to gravity, g = 10 m/s²

Height, h = 5m

Potential energy = 1 × 10 × 5 = 50 J

Thus, the potential energy of the body is 50 joules.

Explanation:

Here, Potential energy, P.E. = 9800 J

Mass m = 200 kg

Acceleration due to gravity, g= 9.8 ms^–2

Height, h= ?

P.E. = m × g × h

9800 = 200 × 9.8 × h

So,

h = 5 m

Thus, the bag of wheat should be raised to a height of 5 meters.

Explanation:

Powers

Work done = 20 J

Time taken = 5 s

Power = (20 J/ 5S) = 4 J/s

Thus, Power = 4 W (because 1 J/s = 1 W)

Thus, the power of this body is 4 watts.

Explanation: Let’s calculate the work done by the pump in lifting the water against the force of gravity.

W = m × g × h

Mass of water, m = 100 kg

Acceleration due to gravity, g = 10 ms^–2

Height, h = 20 m

Work done, W = 100 × 10 × 20 = 20000 J

Time taken, t = 10 s

Now, we know that:

Power, P = (W/t)

= (20000/10) = 2000 watts (or 2000 W)

Thus, the power of this pump is 2000 watts. This power can be converted from watts into kilowatts by dividing it by 1000.

So, Power = (2000/1000) kilowatts

= 2 kilowatts (or 2 kW)