Work, Energy and Power: Formulas, Units and Conversions

The correct answer is B, joule. Work is the product of force and displacement, so its unit is the newton metre, which is given the name joule; one joule of work is done when a force of one newton moves a body through one metre in its own direction. Energy is measured in the same unit, because work done is energy transferred.

Option A, the newton, is the SI unit of force alone. Option C, the watt, is the unit of power, that is the rate of doing work, and equals one joule per second. Option D, the pascal, is the unit of pressure and equals one newton per square metre. Candidates who confuse the joule with the watt lose marks in the very next question of a paper, so learn the pair as work in joule and power in watt.

The correct answer is C, 90 degrees. Work equals force into displacement into the cosine of the angle between them, and the cosine of ninety degrees is zero, so a force at right angles to the motion does no work at all. This is why the centripetal force in circular motion does no work and why a person carrying a load on the head along a level road does none against gravity.

Option A, zero degrees, gives the maximum positive work, since the cosine of zero is one and force and displacement point the same way. Option B, forty five degrees, gives partial positive work, as the cosine is about 0.707. Option D, 180 degrees, gives the maximum negative work, the case of friction opposing motion. Learning the four cosine values, one, 0.707, zero and minus one, settles this whole family of questions.

The correct answer is B, half of mass into the square of the speed. Kinetic energy is the energy a body has because of its motion, and it grows with the square of the speed, so a body moving twice as fast carries four times the kinetic energy.

Option A is the expression for gravitational potential energy near the surface of the Earth, that is mass into acceleration due to gravity into height, and it depends on position rather than motion. Option C, mass into speed, is the linear momentum of the body, a vector quantity measured in kilogram metre per second, not an energy at all. Option D leaves out the factor of one half and is the standard careless error in this question. Remember also that kinetic energy can be written as the square of momentum divided by twice the mass.

The correct answer is B, watt. Power is the rate of doing work, that is work divided by the time taken, so its unit is the joule per second, which is named the watt after James Watt. A machine of one kilowatt does one thousand joule of work every second.

Option A, the joule, measures work or energy, not the rate at which it is delivered. Option C, the newton second, is the unit of impulse and of momentum. Option D, the kilowatt hour, is a unit of energy in spite of its name, because it is a power multiplied by a time; it is the commercial unit of electricity and equals 3.6 million joule. The confusion between the watt and the kilowatt hour is deliberate in many papers, so keep the distinction of rate against quantity clear.

The correct answer is C, 746 watt. The horsepower is an older unit of power that survives in the rating of motors and vehicles, and one horsepower is taken as about 746 watt, that is roughly three quarters of a kilowatt.

Option A, 100 watt, is close to the rating of an old filament bulb and has no connection with the horsepower. Option B, 500 watt, is simply half a kilowatt and is offered as a plausible round figure. Option D, 1000 watt, is one kilowatt; a common mistake is to treat the horsepower and the kilowatt as equal, when in fact one kilowatt is about 1.34 horsepower. The figure 746 is worth memorising exactly, because the question is often set in reverse, asking how many watt a motor of a given horsepower consumes.

The correct answer is C, the kilowatt hour. Household electricity is billed in these units, and one kilowatt hour, popularly called one unit, is the energy consumed when an appliance of one kilowatt runs for one hour; in SI terms it equals 3.6 million joule.

Option A, the joule, is the SI unit of energy but is far too small for billing, since even a single fan uses millions of joule in an evening. Option B, the watt, measures power and not energy, so it cannot be billed at all. Option D, the erg, is the CGS unit of work and is smaller still, with ten million erg in one joule. Questions on this topic often ask for the number of joule in one kilowatt hour, so carry the figure 3.6 million along with the name.

The correct answer is B, four times. Kinetic energy is half the mass into the square of the speed, so when the speed is multiplied by two the energy is multiplied by two squared, that is four. If the speed were tripled the energy would become nine times as large.

Option A, double, would be right only if the energy varied directly with the speed, which is true of momentum, not of kinetic energy. Option C, half, describes what happens to nothing in this situation and is pure distraction. Option D, unchanged, would be true only if the speed did not change, as in uniform circular motion. This relation explains why the braking distance of a vehicle rises sharply with speed, a point road safety questions also use.

The correct answer is B, mechanical energy into electrical energy. A dynamo, also called a generator, is turned by some mechanical agency such as falling water, steam or a bicycle wheel, and the rotation of a coil in a magnetic field produces an electric current by electromagnetic induction.

Option A describes an electric motor, which is the exact reverse of a dynamo and drives fans, pumps and mixers. Option C describes a cell or battery, in which a chemical reaction pushes a current through a circuit. Option D describes a solar cell or photovoltaic cell, which turns sunlight directly into electricity. Device and conversion pairs are asked every year, so also fix the microphone as sound to electrical and the loudspeaker as electrical to sound.

The correct answer is B, kinetic energy. The work-energy theorem states that the net work done on a body equals the difference between its final and initial kinetic energies, which is why a push that speeds a body up does positive work while friction, which slows it, does negative work.

Option A, momentum, changes with impulse, that is force multiplied by the time for which it acts, a different relation altogether. Option C, potential energy, changes with the work done against a conservative force such as gravity, and the theorem is not stated in those terms. Option D, power, is a rate and cannot be equated with work, which is a quantity. A useful check is that a force doing no work, such as the centripetal force, leaves the speed and therefore the kinetic energy unchanged.

The correct answer is A, zero. The force he applies to support the load acts vertically upward, while his displacement along the platform is horizontal, so the angle between force and displacement is ninety degrees and the work done against gravity is zero, however tired he may feel.

Option B, maximum, would apply only if the force and the displacement were in the same direction, as when he climbs a staircase with the load. Option C confuses force with work; the weight of the load is a force in newton, whereas work would be that force multiplied by a vertical displacement. Option D, negative, applies when the force opposes the motion, as friction does. This question is the classic example of the difference between the ordinary and the scientific sense of the word work.

The correct answer is B, potential energy. A stone at rest at a height has no motion and therefore no kinetic energy, but it possesses gravitational potential energy equal to its mass into the acceleration due to gravity into the height of the tower.

Option A, kinetic energy, is what that potential energy becomes as the stone falls, and it is greatest at the instant the stone reaches the ground. Option C, an equal share of both, holds only at the point where it has fallen through half its height, ignoring air resistance. Option D, heat energy, appears only after the impact, when the mechanical energy is dissipated. Through the fall the sum of the two mechanical forms stays constant, which is the law of conservation of energy in its simplest illustration.

The correct answer is C, 10 million. The erg is the unit of work in the CGS system, being one dyne of force acting through one centimetre, and since one newton is one lakh dyne and one metre is a hundred centimetre, one joule works out to ten million erg, that is 10 raised to the power seven.

Option A, ten thousand, and option B, one lakh, are the partial products a candidate gets by converting only the force or only the distance, which is exactly the slip the setter expects. Option D, a hundred million, overshoots by a factor of ten. The safe method is to convert both quantities and multiply: one lakh dyne into a hundred centimetre. Keep this beside the other conversions of the chapter, one calorie as about 4.2 joule and one kilowatt hour as 3.6 million joule.