A
In the case of maximum work, the angle between force and displacement is:
Zero
(F.s Cos0 = F.s ∗ 1 = F.s )
The work done on a body of mass 50 kg moving in a circular path is:
0 J
When a body falls freely towards the earth, then its total energy:
Remains constant
When the speed of the body is doubled, its kinetic energy:
Increases 4 times
Define one joule of work
One joule of work is done on an object when a force of 1 N displaces it by 1 m along the line of action of the force.
When do we say that work is done?
Work is done when
(i) A force acts on the body
(ii) There is a displacement of the body
When displacement is in a direction opposite to the direction of force applied, what is the type of work done?
Work done is negative.
Archana tried to push a heavy rock of 200 kg for 80 seconds but could not move it. Find the work done by Archana after 80 seconds.
The work done by Archana is zero because there is no displacement.
A bullet of mass 15g has a speed of 400m/s. What is its kinetic energy?
Mass(m)=15g=0.015kg
Speed (v)=400m/s
K.E. = ½ mv2 = ½ × 0.015 × (400)2 = 1200 J
58800J energy is utilized in lifting a mass of 50 kg. Find out the height to which the mass was lifted. (Given, g = 9.8 m/s2 )
P.E.= m × g × h
58800 = 50 × 9.8 × h
58800 = 490 × h
h = 58800/490
= 120 m
Certain force acting on a 20 kg mass changes its velocity from 5 m/s to 2 m/s. Calculate the work done by the force.
m = 20 kg, u = 5 m/s, v = 2 m/s
Work = Change in kinetic energy = 𝟏/𝟐 m (v2 - u 2 )
= 𝟏/𝟐 ×20 × (4 - 25) = - 210 J
Work is done in opposite direction to displacement of mass
What is the work to be done to increase the velocity of the car from 10 m/s to 20 m/s if the mass of the car is 1000 kg?
u= 10 m/s v= 20 m/s m = 1000 kg
W= change in kinetic energy
W= (K.E) final - (K.E) initial
W= ½ mv2 – ½ mu2
W=½ × 1000 × (20)2 – ½× 1000 × (10)2
W= 2,00,000 – 50,000 W
= 1,50,000 J
Rachna states that the law of conservation of energy does not remain true all the time and has certain exceptions. For example, when an object falls down from a certain height, its potential energy does not remain the same but decreases progressively. Is Rachna correct? Justify your answer.
Rachna is incorrect.
The Law of conservation of energy remains true all the time. When the body falls from a height, then its potential energy gets converted into kinetic energy progressively. A decrease in the potential energy is equal to an increase in the kinetic energy of the body. During the process, the total mechanical energy of the body remains conserved.
What will happen to the kinetic energy of the body if mass remains the same, and
(a) the velocity of the body is doubled
(b) the velocity of the body is halved?
(a) If mass remains the same, and velocity is doubled, the kinetic energy increases by four times.
(b) If mass remains the same, and velocity is halved, the kinetic energy decreases by four times.
An object of mass 2 kg is raised to a height of 1.5 m above the earth by Amit and Rakesh as shown in the diagram. ( given g = 9.8 m/s2 )
(a) Who does more work? Justify your answer.
(b) Calculate the work done in both situations.
Work done by both Amit and Rakesh is the same because work done is independent of the path followed and depends on the initial and final positions which are the same in both cases.
Work done = F × s
= mgh
= 2 × 9.8 × 1.5
= 29.4 J
Two friends, Sam and John, each with having weight of 40 kg, go rock climbing. Sam climbs to a height of 3 m in 10 s and John covers the same height in 12 s. (a) Is the work done by Sam and John equal? Why? Calculate work done by both
Yes, because both have the same weight and both climb equal height.
Work done: 1176J