Work, Energy and Power
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6.22 A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated.
(a) How much work does she do against the gravitational force ?
(b) Fat supplies 3.8 × 107J of energy per kilogram which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?
6.22 A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated.
(a) How much work does she do against the gravitational force ?
(b) Fat supplies 3.8 × 107J of energy per kilogram which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?
6.22 Mass lifted, m = 10 kg
Height to which the mass lifted, h = 0.5 m
No of repetitions, n = 1000
(a) Work done against gravitational force,
W = nmgh = 1000 49050 J
(b) Mechanical energy supplied by 1 kg fat, with 20% efficiency rate = 0.2 3.8 = 0.76 J/kg
F
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6.21 The blades of a windmill sweep out a circle of area A.
(a) If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it in time t ?
(b) What is the kinetic energy of the air ?
(c) Assume that the windmill converts 25% of the wind’s energy into electrical energy, and that A = 30 m2, v = 36 km/h and the density of air is 1.2 kg m–3. What is the electrical power produced ?
6.21 The blades of a windmill sweep out a circle of area A.
(a) If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it in time t ?
(b) What is the kinetic energy of the air ?
(c) Assume that the windmill converts 25% of the wind’s energy into electrical energy, and that A = 30 m2, v = 36 km/h and the density of air is 1.2 kg m–3. What is the electrical power produced ?
6.21 Given, the area of the windmill sweep = A, Wind velocity = v
The volume of air passing through the blade = Av
Let the density of air be , the mass of air passing through the blade =
(a) The mass of air passing through the blade in time t =
(b) The kinetic energy of air = &
Upvote 6.20 A body of mass 0.5 kg travels in a straight line with velocity v =a x 3/2 where a = 5 m–1/2 s–1. What is the work done by the net force during its displacement from x = 0 to x = 2 m?
6.20 A body of mass 0.5 kg travels in a straight line with velocity v =a x 3/2 where a = 5 m–1/2 s–1. What is the work done by the net force during its displacement from x = 0 to x = 2 m?
6.20 Mass of the body = 0.5 kg
Velocity, v = a x 3/2
a = 5 m–1/2 s–1
At x =0, the initial velocity, u = 0
At x = 2, the final velocity, v = 5 = 14.142 m/s
Work done by the system = increase in K.E. of the body = (1/2)m ( - )
= (1/2) 14.142 = 50 J
Upvote 6.19 A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of 0.05 kg s–1. What is the speed of the trolley after the entire sand bag is empty?
6.19 A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of 0.05 kg s–1. What is the speed of the trolley after the entire sand bag is empty?
6.19 Given, the mass of the trolley, = 300 kg, mass of the sand bag, = 25 kg, uniform velocity of the trolley, v = 27 kmph = 0.75 m/s
Since there is no external force acting on the system, the speed of the trolley will remain unchanged even after entire sand is empty. 27 kmph
Upvote 6.18 The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?
6.18 The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?
6.18 The length of the pendulum, l = 1.5 m
The potential energy of the bob at horizontal position = mgl
Since it dissipates 5% of its kinetic energy to come to the horizontal position, from the law of conservation of energy we get,
= (0.95)
= 2
v = 5.287 m/s
Upvote 6.17 The bob A of a pendulum released from 30 to the vertical hits another bob B of the same mass at rest on a table as shown in Fig. 6.15. How high does the bob A rise after the collision ? Neglect the size of the bobs and assume the collision to be elastic.
6.17 The bob A of a pendulum released from 30 to the vertical hits another bob B of the same mass at rest on a table as shown in Fig. 6.15. How high does the bob A rise after the collision ? Neglect the size of the bobs and assume the collision to be elastic.
6.17 In an elastic collision, when the ball A will hit the ball B, A comes to rest immediately and the ball B acquires the velocity of ball A. The momentum thus gets transferred from a moving body to a stationary body.
Upvote 6.16 Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V. If the collision is elastic, which of the following (Fig. 6.14) is a possible result after collision ?
6.16 Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V. If the collision is elastic, which of the following (Fig. 6.14) is a possible result after collision ?
6.16 The mass of the ball bearing = m
Before the collision, the total K.E. of the system = K.E. of the stationary ball bearing + K.E. of the striking ball bearing = 0 +
After the collision, the K.E. of the total system is
(a) Case (i) = 0 + =
(b) Case (ii) = 0 +
(c) Case (iii) = &nb
Upvote 6.15 A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m3 in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump?
6.15 A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m3 in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump?
6.15 Given, the volume of the tank, V = 30
Time required to fill the tank, t = 15 min = 900 s
Height of the tank above the ground, h = 40 m
The efficiency of the pump? = 30%
The density of water, = kg/
Now, the mass of the water pumped, m = = 30 kg
Upvote 6.14 A molecule in a gas container hits a horizontal wall with speed 200 m s–1 and angle 30° with the normal, and rebounds with the same speed. Is momentum conserved in the collision ? Is the collision elastic or inelastic ?
6.14 A molecule in a gas container hits a horizontal wall with speed 200 m s–1 and angle 30° with the normal, and rebounds with the same speed. Is momentum conserved in the collision ? Is the collision elastic or inelastic ?
6.14 Momentum is always conserved for an elastic or inelastic collision.
The molecule's initial velocity, u = final velocity v = 200 m/s
Initial kinetic energy = (1/2)m
Final kinetic energy = (1/2)m = (1/2)m
Therefore, kinetic energy is also conserved
Upvote 6.13 A rain drop of radius 2 mm falls from a height of 500 m above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height, it attains its maximum (terminal) speed, and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey ? What is the work done by the resistive force in the entire journey if its speed on reaching the ground is 10 m s–1 ?
6.13 A rain drop of radius 2 mm falls from a height of 500 m above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height, it attains its maximum (terminal) speed, and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey ? What is the work done by the resistive force in the entire journey if its speed on reaching the ground is 10 m s–1 ?
6.13 The radius of the rain drop = 2 mm = 2 m
The height of drop, s = 500 m
Density of water, = kg/
Mass of the rain drop = volume = (4/3) = 3.35 kg
The gravitational force on the raindrop, F = mg = 3.28 N
Work done
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