Chapter#03: Work, Power and Energy - Quanta: BS/MSc Physics Books

Team Quanta gladly presents all possible short questions of BS Physics book Mechanics – I’s Chapter#03: Work. Power and Energy for the ease of students.

Q.1 Explain why you become physically tired when you push against a wall, fail to move it and therefore do no work the wall?

Answer: Physically work is done by a force if it displaces the object through some distance. In this case displacement is zero.

Q.2 Consider a tug of war in which two teams pulling on a rope are evenly matched so that no motion takes place. Is work done on rope? On the pullers? On the ground?

Answer: Since no motion is taking place, the rope experiences no displacement and there is no work done. For same reason no work is done on pullers or on ground.

Q.3 Suppose that the earth revolves around sun in a perfectly circular orbit. Does sun do any work on the earth?

Answer: The sun does no work on the earth because the force is pointed toward the center of the circle and there is therefore perpendicular to the direction of the displacement.

Q.4 You cut a spring in a half. What is relation of force constant K for original spring to that for either of half spring?

Answer: Spring constant of .either smaller spring will be twice of original spring according to Hook’s Law as explained below:

Spring constant of original spring is given by,

$K = \frac{F}{x}$

Considering original spring as being composed of two half springs, the same force F that stretches the whole spring by stretches each of the half-spring by $x^\prime =\ \frac{x}{2}$ therefore, the spring constant for each of the half-spring is,

$k^\prime = \frac{F}{x} = \frac{F}{\frac{x}{2}} = 2\left(\frac{F}{x}\right) = 2k$

Q.5 Does kinetic energy depend on direction of motion involved? Can it be negative? Does it value depend on reference frame of observer?

Answer: Kinetic energy depends upon mass and square of velocity which are both scalar quantities. Kinetic energy cannot be negative. Kinetic energy depends upon reference of frame of observer, for example as we ride a train, a backpack at our feet has no kinetic energy as measured by us since, according to us, the backpack is not moving. In the frame of reference of someone on the side of the tracks as the train rolls by , the backpack is moving and has mass and thus has kinetic energy.

Q.6 Can a force of static friction do work? If not , prove it. If so, give an example.

Answer: Force of static friction can do work if it is exerted by an object that is moving in our frame of reference. The flat bed of truck exerts a static friction force to start a pumpkin moving forward as it slowly starts up.

Q.7 In picking up a book from the floor and putting it on table, you do work. However the kinetic energy of the book does not change. Is there a violation of work- energy theorem?

Answer: There is no violation of work-energy theorem because in this case work done is equal to change in potential energy instead of kinetic energy.

Q.8 Does the work-energy theorem hold if friction acts on an object? Explain your answer.

Answer: In order to calculate work done by frictional forces, let us start from Newton’s second law of motion,

$\ \sum F_x=ma$

$\left(\ \ \ \sum F_x\right)\Delta x=ma\Delta x$

Using equations of motion,

$\left(\ \ \ \sum F_x\right)\Delta x=m\left(\frac{v-v_0}{t}\right)\frac{1}{2}\left(v-v_0\right)t=\ \frac{1}{2}mv^{2\ \ \ }-\frac{1}{2}mv_0^2$

This looks like the work-energy theorem, but the left hand side has not been called work. The quantity is the displacement of the object- not the displacement of the point of application of the friction force.

Let us now apply this equation to an object that has been projected across a surface. We imagine that the object has an initial speed and slows down due to friction, the only force in the horizontal direction. The net force on the object is the kinetic friction , which is directed opposite to the displacement . Thus,

$-f_k\Delta x= \Delta k$

–

which mathematically describes the decrease in kinetic energy due to the friction force.

Q.9 Does the work done in raising a box onto a plate form depends upon how fast it is raising up? If not, why?

Answer: No, work done depends upon height and weight of box.

Q.10 A student drops a ball from the top of a building while his friend at the bottom observes its motion. These two students will agree on which of the following quantities? (a)- potential energy of the ball-Earth system (b)-change in potential energy (c)-kinetic energy of the ball at some point in its motion.

Answer: (a) Both students will not agree on the energy if they measure it from different reference points.

(b) & (c)- Both students will observe the same change in elevation and the same speed, so they do agree on the change in gravitational energy and on the kinetic energy.

Q.11 Mountain roads rarely go straight up the slope but wind up gradually, Explain why?

Answer: Mountains roads wind up gradually because it require less force of static friction on the rolling drive wheels of a car to propel the car up the gentler slope. Less power is required if the work can be sone over a longer period of time.

Q.12 An automobile is moving along a highway. The drivers jams on brakes and car skids to a halt. In what form does the lost kinetic energy of car appear?

Answer: The kinetic energy of the skidding can be degraded into kinetic energy of random molecular motion of tires across the road: it is internal energy.

Q.13 Object A pushes on object B as the objects move together, like a tractor pushing a stone. Assume object A does 15J of work on object B. Does object B do work on object A?

Answer: By Newton’s third law, object B exerts an equal force in the opposite direction on object A. According to given condition, the energy transfer is 15J from object A to object B , which can be represented as a change in energy of -15J for object A and a change in energy of +15J for object B.

Q.14 A ball of mass m is held at height h₁ above table. The table top is at height h₂ above floor. Atif says that ball has potential energy mgh₁but Imran says that the potential energy is the (mgh₁ + h₂), who is correct?

Answer: Both are correct. Atif is taking table as reference level where as Imran is taking earth as reference level.

Q.15 In class, a student said that the total work done on an object is equal to its final kinetic energy. What you can say about this statement?

Answer: This statement is not valid for all situations. This is true only when the object is a particle initially at rest, the net work done on the object is equal to its final kinetic energy.

Q.16 A man rowing boat upstream is at rest with respect to shore. Is he doing work?

Answer: No work is done because in this case displacement is zero.

Q.17 If potential energy of a system is zero, does it mean that force is zero?

Answer: A conservative force and potential are related by,

$\vec{F} = - \nabla U$

If potential energy is zero , force is zero. But in case of non- conservative force, force is not zero.

Q.18 A bus and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding force. Which of them will come to rest in a shorter distance?

Answer: By work energy-theorem, work done by retarding force is equal to loss in kinetic energy. As kinetic energy and force are same, so distance travelled before coming to rest will be same.

Q.19 A satellite is revolving around earth. With the help of work-energy theorem, explain why no work is done on satellite?

Answer: A satellite is revolving in orbit, force is always perpendicular to displacement, so no work is done on satellite. By work energy theorem, as speed of satellite is uniform, kinetic energy is constant hence work done is zero.

Q.20 In order to clean them you pop all the removable keys off a computer keyboard. Each key has the shape of a tiny box with one side open. By accident, you spill the keys onto the floor. Explain why many more keys land letter-side down than land open side down.

Answer: Force is related to potential energy by relation,

$F=\ -\ \frac{dU}{dx}$

According to this equation, a force pushes the key downhill in potential energy toward the bottom of graph of potential versus orientation angle. Friction removes mechanical energy from the key earth system, tending to leave the key in its minimum-potential energy configuration.

Q.21 When an arrow is shot from bow, it has kinetic energy. From where does it get kinetic energy?

Answer: The work done in pulling the string of bow in backward direction is stored in it as potential energy and it converts into kinetic energy when arrow is fired.

Q.22 Does the kinetic energy of an object depends on the frame of reference in ehich its motion is measured? Give an example in support of your answer.

Answer: Yes kinetic energy of an object depends upon reference of frame in which its motion is measured.

Example: As one rides a train, a backpack at his feet has no kinetic energy as measured by him since, according to him, the backpack is not moving. In the frame of reference of someone on the side of the tracks as the train rolls by, the backpack is moving and has mass and thus has kinetic energy.

Q.23 In case of simple pendulum, three forces; tension in string, air resistance and force of gravity act. Which of these forces do no work?

Answer: The tension in string does no work since it is perpendicular to displacement.

Q.24 A car is moving with constant speed along a level road with no force acting on it. Is any work being done on car? By car against friction?

Answer: When car is moving with constant speed with no net force acting on it, no work is done on car. But car exerts a force and keeps doing work continuously against the friction.

Q.25 Considering object-Earth system, answer the following question in yes or no.

(a )-can the system have kinetic energy and not gravitational potential energy?

(b)- can the system have gravitational potential energy and not kinetic energy?

(c)- can the system have both types of energy at the same moment?

(d)- can the system have neither?

Answer: Answers to the following questions are in yes according to the following situations;

(a)-When block slides on the floor where we choose h=0

(b)-For a picture on the classroom wall high above the floor.

(c)-When a pencil is hurtling across the room.

(d)-When the block is stationary on the floor.

Q.26 Give some examples of conservative and non-conservative forces?

Answer: Examples of conservative forces are electric force , gravitational force, normal force, elastic spring force.

Examples of non- conservative forces are frictional force, air resistance and tension in string etc.

Q.27 A meteor when enters into earth’s atmosphere burn. What happens to its energy?

Answer: Some amount of energy is destroyed by resistive force of atmosphere in bringing the meteor to rest and remaining energy appears in form of heat energy which burns the meteor to ashes.

Q.28 You have read in the text that gravitational force is conservative. How you will prove it?

Answer: Suppose a ball of mass m is projected upward with initial velocity v₀ . A s the ball rises, force of gravity does work on it and brings it to rest at maximum height h. Work done o it by force of gravity is,

$W_1=\ -mgh=\ \left(0-\ \frac{1}{2}mv_0^2\right)=\ -\frac{1}{2}\ mv_0^2$

By work-energy theorem, this work done is equal to change in kinetic energy i.e.

.When balls returns from height h to ground, then work done is,

$W_2=\ -mgh=\ \left(\ \frac{1}{2}mv_0^2-0\right)=\ \frac{1}{2}\ mv_0^2$

Since $W_1+W_2=0$ i.e. work done by force of gravity along a closed path is zero, so gravitational is conservative.

Q.29 If you are on a bed ( at specific height from earth), tell in which state ( standing, sitting, sleeping) your blood pressure will be high and low. Explain it by giving reason.

Answer: Blood pressure will be low in sleeping position on a horizontal surface because all parts of body are at same level and will be high in standing position by same reason.

Q.30 What average power is generated by a 70kg mountain in climber who climbs a summit of height 325m in 95min?

Answer: Average power is given by,

$P=\ \frac{W}{t}=\ \frac{mgh}{t}=\frac{70kg \times 9.8ms-2 \times 325m}{95 \times 60s}=39\ W$

Q.31 Give two examples in which a force is exerted on an object without doing any work on the object.

Answer: (i) Force of tension and a ball moving in a circle on the end of a string does no work.

(ii) Normal force on an object at rest or moving across a level floor does no work.

(iii) Gravitational force on an object at rest or moving across a level floor does no work.

Q.32 For arrangement of books in library, one lifted a book from the floor to the top shelf. The of the book on floor was zero and the kinetic energy of the book on the top shelf is zero, so no change was occurred in the kinetic energy, yet you did some work in lifting the book. Is the work-kinetic energy theorem violated?

Answer: No, there is no violation of work-energy theorem. Choosing the book as system, one did positive work and earth did negative work on the book. The net work on the book is zero, and is equal to its overall change in kinetic energy.

Q.33 Give an example of neutral equilibrium?

Answer: A ball rolling on a horizontal surface is an example of neutral equilibrium.

Q.34 A man is sitting in a car. Which type of energy he has?

Answer: In car a man is at some height from the earth, so it has partially potential energy.

Q.35 A block of wood is taken to bottom of lake. Does the block posses the potential energy?

Answer: W hen block of wood is taken to bottom of lake, work is done on it, which is stored in the form of potential energy in block. Therefore block has potential energy as if block is released; it has ability to rise to water surface.

Q.36 Discuss whether any work is being done by each of the following agents and, if so, whether the work is positive or negative.(a)- a chicken scratching the ground (b)- a person studying (c)- the leg of a person in the act of sitting down.

Answer: (a) -Work is done by the chicken on the dirt and it is positive. (b)- The person studying does no work on anything in the environment. (c)-Work is done on the person’s torso and is negative.

Q.37 The momentum of a body increases by 20%. How much kinetic energy increases?

Answer: Final momentum = p+20%p

Final momentum = $p+\frac{p}{5}=\ \frac{6p}{5}$

% increase in kinetic energy = $\left{\frac{\left(\frac{6p}{5}\right)^2}{2m}-\ \frac{p^2}{2m}\right} \times 100%=44%$

Q.38 What amount of energy we can get from food we eat in a full day?

Answer: This is almost 1/3 liter of petrol.

Q.39 A body falls under the action of gravity. Its velocity is v when it has lost potential energy U, then find a relation for mass of body.

Answer: Using,

Gain in kinetic energy = loss in potential energy

$\frac{1}{2}mv^2=U\ \ \ \ \ \ \ \rightarrow\ \ \ \ \ \ \ m=\ \left(\frac{2U}{v^2}\right)^\frac{1}{2}$

which is required relation for mass ‘m’

Q.40 A block is connected to a spring that is suspended from the ceiling. Assuming air resistance is ignored; described the energy transportation that occur within the system consisting of the block, the earth, and the spring when the block is set into vertical motion.

Answer: Let the gravitational energy of the system be zero then the block is at the lowest point in the motion. When the block moves downward, its kinetic energy converts into elastic potential energy in the spring. After the block starts moving up at its lower turning point, this energy becomes both kinetic energy and gravitational potential energy, and then just gravitational energy when the block is at its highest where its elastic potential energy is the least. The energy then turns back into kinetic and elastic potential energy. As the block descends, and the cycle repeats.

Q.41 If only one external force acts on a particle, does it necessarily change kinetic energy and velocity of the particle?

Answer: When only one external force acts on a particle, its kinetic energy may or may not change depending on speed of particle. However velocity of particle changes according to Newton’s second law.

Q.42 Do the tidal effects hold only to pull the water of sea up and up?

Answer: The pull of moon not only pulls sea water up and down, but tidal effect can distort the continent pulling land up and down almost 25 cm.

Q.43 What happens to kinetic energy of bullet when it penetrates into the target?

Answer: When a bullet hits the target, it penetrates into it and comes to rest after travelling some distance. Most of kinetic energy if used in doing work against resistance of target and remaining energy is converted to heat.

Q.44 A light body and heavy body equal momenta. Which of two has large kinetic energy?

Answer: kinetic energy is,

$K=\ \frac{1}{2}mv^2=\frac{m^2v^2}{2m}=\ \frac{p^2}{2m}$

For same momentum, $K\propto\ \frac{1}{m}$

That is lighter body have more kinetic energy.

Q.45 The force between pair of proton is that of repulsion. What happens to potential energy when protons are brought closer?

Answer: When protons are brought closer, the force of repulsion increases and work done against field also increases, hence potential energy also increases numerically.

Q.46 What shape would the graph U versus x have if a particle were in a region of natural equilibrium?

Answer: For a particle in natural equilibrium, graph of potential energy versus position is a straight horizontal line.

Q.47 What type of energy is stored in spring of watch?

Answer: Elastic potential energy which comes by compressing the spring.

Q.48 What is velocity of a particle if its momentum and kinetic energy are equal?

Answer: As given,

$\frac{1}{2}mv^2=mv\ \ \ \ \ \ \ \ \rightarrow v=2m/s$

Q.49 A man drops a cup from a certain height, which breaks into pieces. What energy changes are involved?

Answer: When cup is dropped from certain height, its potential energy changes into kinetic energy. On collision with ground, some kinetic energy is used to break up into pieces and remaining is converted to sound and heat energy.

Q.50 Can a normal force do work? If not, prove it. If so, give an example.

Answer: Normal forces can do work. For Example, the floor of a rising elevator does work on a passenger. But a normal forces exerted by a stationary solid surface does no work.

Mechanics-I