Energy Sources and Transfer of Energy - Physics For Class IX (Science Group) - Numericals

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Physics For Class IX (Science Group)
UNIT 8 ENERGY SOURCES AND TRANSFER OF ENERGY
Numericals

Worked Example

Worked Example 1

1. Find the work done when a force of 50 N is applied to move a trolley at a shopping mall through a distance of 200 m? Assume the angle to be of 0° between the force and the distance the trolley moved.

Solution:
Step 1: Write down known quantities and quantities to be found.

• F = 50 N
• d = 200 m
• θ = 0°
• W = ?

Step 2: Write down formula and rearrange if necessary.

W = F x d
W = Fd cosθ

Step 3: Put the values in formula and calculate:

W = 50 N x 200 m x cos 0°
W = 10000 x 1 = 10000
W = 10⁴ J

Ans: Hence, the work done is 10000 Joules.

Worked Example 2

2. A ball of mass 400 gram, strikes the wall of velocity 4m/sec. How much is the kinetic energy of the ball at the time it strikes the wall?

Worked Example 3

3. A ball of mass 50 gram is raised to a height of 7m from the ground. Calculate its gravitational potential energy?

Worked Example 4

4. Calculate the power of a machine. If the machine performs 900 joules of work in 30 minutes.

Numerical From Self Assessment Questions

Q.4: A car of mass 50 kg moving with velocity 10 ms^-1 in the direction of force. Calculate its Kinetic energy.
Solution:
Data:

• mass = m = 50 kg
• velocity = v = 10 ms^-1
• K.E = ?

Working Formula:

K.E = ¹/₂ mv²

Calculation:

K.E = ¹/₂ (50)(10)²

= ¹/₂ (50)(100)

= ¹/₂ (5000) = 2500 Joules

Ans: Hence its kinetic energy is 2500 Joules.

Q.5: A body of mass 10 kg is dropped from a height of 20 m on the ground. What will be its potential energy, if g = 9.8 m/sec²?
Solution:
Data:

• mass = m = 10 kg
• height = h = 20 m
• gravitational force = g = 9.8 m/sec²
• P.E = ?

Working Formula:

P.E = mgh

Calculation:

P.E = (10)(9.8)(20)

= (98)(20) = 1960 Joules

Ans: Hence, Its potential energy is 1960 Joules.

Q.13: A man pushes a car 18 m with a force of 2 N in 4 second. Calculate the power of the man.
Solution:
Data:

• Distance = d = 18 m
• Force = F = 2N
• Time = t = 4 sec
• Power = P = ?

Working Formula:

Calculation:
To calculate power, we need to know the work done and the time.
We know that

Work done = W = F.d

W = (2).(18) = 36 J

Now, putting this value in the working formula, we get:

P = ³⁶ / ₄ = 9 W

Ans: Hence The power of the man is 9 W.

Numerical From Text Book Exercise

Section (B) Structured Questions

Work

2. How much work is needed to move horizontally a body 20 m by a force of 30 N, the angle between the body and the horizontal surface is 60°?
Solution:
Data:

• Distance = d = 20 m
• Force = F = 30 N
• Angle = θ = 60°
• Work = W = ?

Working Formula:

W = Fdcosθ

Calculation:
W = (30)(20) cos60°
W = 600 x 0.5 = 300 N
Ans: Hence the work done is 300 N.

3. How much work is done, if a crate is moved at a distance of 50 m, when a force of 30 N is applied along the surface.
Solution:
Data:

• Distance = d = 50 m
• Force = F = 30 N
• Angle = θ = 0°
• Work = W = ?

Working Formula:

W = Fdcosθ

Calculation:
W = (30)(50) cos0°
W = 1500 x 1 = 1500 N
Ans: Hence the work done is 1500 N.

4. What is the work done by Usman? If a bar of weight 100 N is brought by him from A to B, then brought back to A.
Solution:
Data:

• Force = Weight = W = 100 N
• Distance = d = 0 (As the bar is brought from A to B, then brought back to A)
• Work = ?

Working Formula:

W = Fd

Calculation:
W = (100)(0)
W = 0
Ans: Hence the work done is 0.

Energy Forms

6. What will be the Kinetic energy of a boy of mass 50 kg driving a bike with velocity of 2 ms^-1.
Solution:
Data:

• Mass = m = 50 kg
• Velocity = v = 2 ms^-1
• Kinetic Energy = K.E = ?

Ans: Hence, the Kinetic energy will be 100 J.

8. a) If LED screen of mass 10 kg is lifted up and kept it on a cupboard of height 2 m. Calculate the potential energy stored in the LED screen.
Solution:
Data:

• Mass = m = 10 kg
• Height = h = 2 m
• Acceleration due to gravity = g =10 ms^-2
• Potential Energy = P.E = ?

Working Formula:

P.E = mgh

Calculation:
P.E = (10)(10)(2) = (100)(2)
P.E = 200 J
Ans: Hence The potential energy stored is 200 J.

b) Calculate the potential energy of 3 kg water raised to the tank at the roof of a home 4 m high. (assume g = 10 ms^-2)
Solution:
Data:

• Mass = m = 3 kg
• Height = h = 4 m
• Acceleration due to gravity = g =10 ms^-2
• Potential Energy = P.E = ?

Working Formula:

P.E = mgh

Calculation:
P.E = (3)(10)(4) = (30)(4)
P.E = 120 J
Ans: Hence The potential energy stored is 120 J.