Work, Energy and Power
Numerical Problems based on Class 9 Physics NCERT Chapter
Q1(CBSE 2012): State the relation between the commercial unit of energy and joules.
Answer: Kilowatt hour (kWh)
1 kwh - 3.6 x 106 joules
Q2: How much work is done on a body of mass 1kg whirling on a circular path of radius 5m?
Answer: Zero
Q3: A body of mass 15 kg undergoes downward displacement of 40m under the effect of gravitational force. How much work is done? (take g = 10 m/s2)
Answer:
Given
acceleration (a) = g = 10 m/s2
mass (m) = 15 kg
displacement (s) = 40 m
Work W = F × s
= m × a × s = 15 × 10 × 40 = 6000 J
Since gravitational force and displacement are in the same direction, work is said to be positive and done on the body.
Q4: A body of mass 120 g is taken vertically upwards to reach the height of 5m. Calculate work done. (Take g = 10 m/s2)
Answer: Given,
a = g = - 10 m/s2
m = 120g = 0.120 kg
s = 5m
Work W = F × s
= m × g × s = 0.12 × -10 × 5 = -6 J
Q6: A 30g bullet initially travelling at 500 m/s penetrates 12 cm into a wooden block. How much average force does it exerts?
Answer: Given,
displacement (s) = 12 cm = 0.12 m
velocity (u) = 500 m/s
mass (m) = 30g = 0.03 kg
Applying work energy theorem,
KE = Work Done
⇒ ½ mv2 = F × s
⇒ F = ½ mv2 × (1/s) = ½ × 0.03 × (500)2 × (1/0.12) = 31250 N
Q7: Calculate potential energy of a person having 60 kg mass on the summit of Mt. Everest. The height of Mt. Everest is 8848 m from sea level. (g = 9.8 m/s2)
a = g = - 10 m/s2
m = 120g = 0.120 kg
s = 5m
Work W = F × s
= m × g × s = 0.12 × -10 × 5 = -6 J
Since Force and displacement act in opposite directions, work is negative. Here work is considered to be done by the body against the applied force.
Q5: A momentum of the body is increased by 20%. What is the percentage increase in its kinetic energy?
Answer: Let m be the mass of the body.
initial velocity = u m/s
final velocity = v m/x
Final momentum = 1.2 times of initial momentum
⇒ mv = 1.2 × mu
⇒ v = 1.2 u
⇒ KE (final) = ½ mv2 = ½ m(1.2u)2 = ½ m × 1.44u2
⇒ KE (final) = 1.44 KE (initial)Q6: A 30g bullet initially travelling at 500 m/s penetrates 12 cm into a wooden block. How much average force does it exerts?
Answer: Given,
displacement (s) = 12 cm = 0.12 m
velocity (u) = 500 m/s
mass (m) = 30g = 0.03 kg
Applying work energy theorem,
KE = Work Done
⇒ ½ mv2 = F × s
⇒ F = ½ mv2 × (1/s) = ½ × 0.03 × (500)2 × (1/0.12) = 31250 N
Q7: Calculate potential energy of a person having 60 kg mass on the summit of Mt. Everest. The height of Mt. Everest is 8848 m from sea level. (g = 9.8 m/s2)
Answer: Given,
mass m = 60 kg
height h = 8848 m
g = 9.8 m/s2
Potential energy U = mgh = (60) × (9.8)× (8848) = 52,02,624 J
Q8: A boy of mass 20 kg climbs up a ladder in 20 seconds. If the height of a ladder is 10 metres, calculate the amount of power used.(Take g = 10 m/s2)
Answer: Given mass (m) = 20 kg
displacement (h) = 10m
g = 10 m/s2
time (t) = 20s
PE = mgh = 20 × 10 × 10 = 2000 J
Power (P) = W / t
= 2000 / 20 = 100 J/s = 100 Watt = 0.1 kW
Video below shows lowering a ramp affects on the velocity. Can you state the reason?
