Energy Source and Transfer of Energy || Solved Numericals

Q1: How much work is needed to move horizontally a body 20m by a force of 30N, the angle between the body and the horizontal surface is 60 degree?

Given:
Force, F = 30 N
Distance, d = 20 m
Angle, θ = 60°

Formula: Work = F × d × cosθ

Calculation:
Work = 30 × 20 × cos60°
cos60° = 0.5
Work = 30 × 20 × 0.5
Work = 300 J

Answer: 300 Joules

Q2: How much work is done, if a crate is moved at a distance of 50m, when a force of 30N is applied along the surface.

Given:
Force, F = 30 N
Distance, d = 50 m
Angle, θ = 0° (force applied along the surface)

Formula: Work = F × d × cosθ

Calculation:
Work = 30 × 50 × cos0°
cos0° = 1
Work = 30 × 50 × 1
Work = 1500 J

Answer: 1500 Joules

Q3: 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.

Given:
Weight = Force = 100 N
Displacement = 0 m (returns to starting point)

Formula: Work = Force × Displacement

Calculation:
Work = 100 × 0
Work = 0 J

Answer: 0 Joules (Zero work done as displacement is zero)

Q4: What will be the Kinetic energy of a boy of mass 50kg driving a bike with velocity of 2ms⁻¹?

Given:
Mass, m = 50 kg
Velocity, v = 2 m/s

Formula: K.E = ½ mv²

Calculation:
K.E = ½ × 50 × (2)²
K.E = ½ × 50 × 4
K.E = 25 × 4
K.E = 100 J

Answer: 100 Joules

Q5: Calculate the efficiency of a machine which consumes 200 J of energy and performs 50J of work.

Given:
Input Energy = 200 J
Output Energy = 50 J

Formula: Efficiency = (Output / Input) × 100%

Calculation:
Efficiency = (50 / 200) × 100
Efficiency = 0.25 × 100
Efficiency = 25%

Answer: 25%

Q6: If the efficiency of a machine is 70% and its output is 100 J then calculate its input.

Given:
Efficiency = 70% = 0.7
Output Energy = 100 J

Formula: Efficiency = Output / Input
Input = Output / Efficiency

Calculation:
Input = 100 / 0.7
Input = 142.86 J

Answer: 142.86 Joules

Q7: Which machine is more efficient, machine "A" which has an output of 200J after consuming 400J of energy or machine "B" which has an output of 300J after consuming 450J of energy?

Given:
Machine A: Input = 400 J, Output = 200 J
Machine B: Input = 450 J, Output = 300 J

Formula: Efficiency = (Output / Input) × 100%

Calculation for Machine A:
Efficiencyₐ = (200 / 400) × 100
Efficiencyₐ = 0.5 × 100 = 50%

Calculation for Machine B:
Efficiencyᵦ = (300 / 450) × 100
Efficiencyᵦ = 0.667 × 100 = 66.7%

Answer: Machine B (66.7%) is more efficient than Machine A (50%)

Q8: The energy of 600J dissipated by a bulb in 50 minutes. Find the power of the bulb.

Given:
Energy = 600 J
Time = 50 minutes = 50 × 60 = 3000 seconds

Formula: Power = Energy / Time

Calculation:
Power = 600 / 3000
Power = 0.2 W

Answer: 0.2 Watts

Q9: Convert 20watt into horse power.

Given:
Power = 20 Watts
1 Horse Power = 746 Watts

Formula: Horse Power = Watts / 746

Calculation:
Horse Power = 20 / 746
Horse Power = 0.0268 HP

Answer: 0.0268 Horse Power

Q10: Calculate the power of a machine, if it does 40 Joules of work in 10 sec.

Given:
Work = 40 J
Time = 10 s

Formula: Power = Work / Time

Calculation:
Power = 40 / 10
Power = 4 W

Answer: 4 Watts

Q11: A student of weight 400N takes 5 sec to climb up an obstacle of height 2m. Calculate the power consumed?

Given:
Weight = Force = 400 N
Height = Distance = 2 m
Time = 5 s

Formula: Work = Force × Distance
Power = Work / Time

Calculation:
Work = 400 × 2 = 800 J
Power = 800 / 5
Power = 160 W

Answer: 160 Watts

Q12: If a machine consumes 250J of energy per hour then what will be its power?

Given:
Energy = 250 J
Time = 1 hour = 60 × 60 = 3600 seconds

Formula: Power = Energy / Time

Calculation:
Power = 250 / 3600
Power = 0.0694 W

Answer: 0.0694 Watts