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The Vault
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The Vault
CBSE Class 9 Physics · 12 questions · 29 marks
In everyday speech you "work hard" while standing still holding a heavy bag, but in physics that counts as zero work. This chapter fixes the scientific meanings of work, energy, and power, shows how energy changes form without ever being lost, and then applies those ideas to the oldest tools humans built. Levers, pulleys, and inclined planes do not create energy — they simply let a small effort move a large load, and mechanical advantage is how you measure that bargain.
A porter carries a suitcase horizontally across a level platform at a steady speed. How much work does he do against gravity on the suitcase?
Answer
Zero, because the force of gravity is perpendicular to the displacement — the gravitational force acts vertically downward while the suitcase moves horizontally, so θ = 90° and W = F s cos 90° = 0. The porter certainly gets tired, but no work is done against gravity in the scientific sense.
The speed of a moving car is tripled. By what factor does its kinetic energy increase?
Answer
9 times — kinetic energy is Kₑ = ½mv², so it depends on the square of the speed. Replacing v by 3v gives ½m(3v)² = 9 × ½mv², which is why stopping distances grow so dramatically at higher speeds.
A crowbar is used to lift a heavy stone. The effort arm is 90 cm and the load arm is 15 cm. What is its ideal mechanical advantage?
Answer
6 — for a lever, the ideal mechanical advantage equals the ratio of effort arm to load arm, MA = 90/15 = 6. This means a load six times the applied effort can be balanced, though friction at the fulcrum makes the real advantage slightly less.
A machine does 1800 J of useful work while 2400 J of energy is supplied to it. What is its efficiency?
Answer
75% — efficiency = (useful output work / input work) × 100 = (1800/2400) × 100 = 75%. The remaining 600 J is wasted, mostly as heat and sound generated by friction in the moving parts.
Assertion (A): No simple machine can have an efficiency of 100%. Reason (R): A simple machine multiplies the effort applied to it and therefore creates extra energy at the load end.
Answer
A is true but R is false — no real machine reaches 100% efficiency, because part of the input work is always spent overcoming friction and appears as heat and sound. But the reason given is wrong: a machine never creates energy. It multiplies force only by making the effort move through a proportionally larger distance, so the output work can never exceed the input work.
State the two conditions that must be satisfied for work to be done on a body in the scientific sense.
Answer
First, a force must act on the body. Second, the body must undergo a displacement, and that displacement must have a component along the direction of the force. If either condition fails — for example a person pushing a wall that does not move, or a coolie carrying a load horizontally while gravity acts vertically — the work done is zero.
A pump lifts 400 kg of water through a height of 12 m in 40 s. Taking g = 10 m/s², find the work done and the power of the pump.
Answer
Work done against gravity = mgh = 400 × 10 × 12 = 48000 J = 48 kJ. Power = work done / time = 48000/40 = 1200 W = 1.2 kW. So the pump does 48 kJ of useful work and delivers a useful power output of 1.2 kilowatts. A real pump would need a higher input power because of losses in the pipes and motor.
A single fixed pulley has a mechanical advantage of only about 1. Why is it still widely used at wells and on flagpoles?
Answer
A single fixed pulley does not multiply the effort, since the effort applied equals the load lifted, giving MA ≈ 1. What it does is change the direction of the applied force. That makes it far more convenient to pull downwards — using one's own body weight and a comfortable stance — instead of lifting the load straight up, which is why it is used to draw water from wells and to raise flags.
A 2 kg stone is dropped from a height of 20 m. Taking g = 10 m/s², find its potential energy at the top and its kinetic energy and speed just before it hits the ground.
Answer
At the top: Pₑ = mgh = 2 × 10 × 20 = 400 J, and since the stone is dropped from rest its kinetic energy there is zero. Just before landing the height is zero, so all the potential energy has been converted into kinetic energy: Kₑ = 400 J. Speed: ½mv² = 400, so ½ × 2 × v² = 400, giving v² = 400 and v = 20 m/s. The stone strikes the ground at 20 m/s, and the total energy has stayed at 400 J throughout the fall.
(a) Define kinetic energy and derive the expression Kₑ = ½mv² for a body of mass m accelerated from rest to velocity v. (b) A 1200 kg van moving at 15 m/s is braked to a stop. Find the work the brakes must do and the average braking force if the van stops in 30 m.
Answer
(a) Kinetic energy is the energy possessed by a body because of its motion, and it is measured by the amount of work the body can do before coming to rest. Suppose a constant force F acts on a body of mass m initially at rest, giving it an acceleration a and bringing it to velocity v after a displacement s. From the third equation of motion, v² = u² + 2as with u = 0, so v² = 2as, which gives s = v²/2a. The work done by the force is W = F × s = ma × v²/2a = ½mv². This work is stored in the body as its kinetic energy, so Kₑ = ½mv². (b) Kinetic energy of the van = ½ × 1200 × (15)² = ½ × 1200 × 225 = 135000 J. To stop the van the brakes must remove all of this, so the work done by the braking force is 135000 J (negative work on the van). Using W = F × s, F = 135000/30 = 4500 N. The brakes must supply an average retarding force of 4500 N.
(a) What is a simple machine, and why can it never do more work than is put into it? (b) A drum of weight 600 N is rolled up an inclined plank 5 m long onto a truck 1.25 m high, using an effort of 180 N along the plank. Calculate the ideal mechanical advantage, the actual mechanical advantage, and the efficiency of the arrangement.
Answer
(a) A simple machine is a device that makes work easier by changing the magnitude or the direction of an applied force — levers, pulleys, inclined planes, wheel and axle, screws and wedges are the common types. A machine can never deliver more work than it receives, because it is not a source of energy; it only transfers energy. When a machine multiplies force, the effort must move through a correspondingly greater distance, so the product force × distance at the output can at best equal the input. In practice some input work is always converted into heat by friction, so the useful output is always less. (b) Ideal mechanical advantage of an inclined plane = length / height = 5/1.25 = 4. Actual mechanical advantage = load / effort = 600/180 = 3.33 (approximately). Efficiency = (actual MA / ideal MA) × 100 = (3.33/4) × 100 = 83.3% (approximately). Checking by work: useful work = 600 × 1.25 = 750 J; input work = 180 × 5 = 900 J; efficiency = (750/900) × 100 = 83.3%, which agrees. The missing 150 J is spent against friction between the drum and the plank.
Read the following and answer the questions that follow: A workshop uses a hoist to lift engine blocks. A 250 kg block is raised 3 m onto a bench in 10 s. The hoist motor is rated 1 kW. Take g = 10 m/s². (a) Calculate the useful work done in lifting the block. (b) Calculate the useful power output of the hoist. (c) Find the efficiency of the hoist and suggest where the wasted energy goes. (d) If the block is later lowered gently back to the floor, what happens to the potential energy it had gained?
Answer
(a) Useful work = mgh = 250 × 10 × 3 = 7500 J = 7.5 kJ. (b) Useful power output = work / time = 7500/10 = 750 W. (c) Efficiency = (useful output power / input power) × 100 = (750/1000) × 100 = 75%. The remaining 250 W is wasted mainly as heat in the motor windings and gearbox, as friction at the pulleys and cable, and as sound from the running machinery. (d) As the block is lowered, its gravitational potential energy of 7500 J is released. Because it descends slowly and at a nearly steady speed, it does not build up kinetic energy; instead the energy is transferred to the braking mechanism of the hoist and to friction, where it finally appears as heat. No energy is destroyed — it simply changes form, exactly as the law of conservation of energy requires.
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