Exploration Class 9 Science Chapter 7: Work, Energy, and Simple Machines — NCERT Solutions

Explanation: Follow the arrows in the figure: the striker hits the white coin, and the white coin then hits the black coin - the striker never touches the black coin. In each collision the body that strikes pushes the struck body through a distance in the direction of the push, so it does positive work and the struck body gains kinetic energy. By Newton's third law the struck body pushes back with an equal and opposite force, so it does an equal negative amount of work on the body that hit it, which is why the striker slows down after the impact and the white coin slows after passing the motion on. Energy is transferred along the chain and never created: muscular energy to striker, striker to white coin, white coin to black coin, with a little turning into sound at each click and into heat through friction with the board - which is why every piece eventually stops.

Explanation: By the work-energy theorem, the work done by the stopping force equals the kinetic energy lost by the aircraft: F x s = (1/2) m v². Work done by the wire = 367500 N x 100 m = 36750000 J. So (1/2) x 15000 x v² = 36750000, giving v² = (2 x 36750000)/15000 = 4900. Therefore v = 70 m/s, which is the aircraft's speed just before being caught by the wire.

Explanation: By conservation of mechanical energy, the potential energy at the top converts to kinetic energy at the bottom: mgh = (1/2) m v², so v = (2gh)^(1/2). (i) The speed at the bottom depends only on the vertical height h of the slide and the acceleration due to gravity g; friction would reduce it slightly. (ii) Mass cancels out of the equation, so children of different masses reach the bottom of the same slide with the same speed. (iii) In the figure the blue spiral slide, the red straight slide, and the purple wavy slide all start from the same platform, i.e. the same height, so neglecting friction every slide gives the same speed at the bottom regardless of its length or shape.

Explanation: A seesaw balances when the turning effects on both sides of the fulcrum are equal: weight1 x distance1 = weight2 x distance2. The lighter child must sit farther from the fulcrum C and the heavier child closer. Check: 15 kg x 2 m = 30 kg m and 30 kg x 1 m = 30 kg m, so the two sides balance. Since A and B are on one side of C and D and E on the other, the 15 kg child sits at A (2 m) with the 30 kg child at D (1 m), or the 15 kg child at E with the 30 kg child at B.

Explanation: (i) At a height of 1 m the ball has gravitational potential energy PE = mgh. As it falls this converts to kinetic energy, and on hitting the sand the ball does work on the sand by pushing the grains aside, forming a depression. (ii) From 2 m the ball has twice the potential energy (PE is proportional to h), so it reaches the sand with more kinetic energy and does more work on it. Hence the 2 m drop creates the deeper depression and the 1 m drop creates the shallower one.

Explanation: The truck's speed is 72 km/h = 20 m/s, so its kinetic energy is KE = (1/2) m v² = (1/2) x 10000 x 20² = 2000000 J. This energy must be used up by climbing the ramp and by working against the sand. For a ramp of length L, the vertical rise is L/2, so the gain in potential energy is mgh = 10000 x 10 x (L/2) = 50000L J, and the work done against the sand's resistive force is 50000 x L = 50000L J. Setting total energy absorbed equal to the kinetic energy: 50000L + 50000L = 2000000, so 100000L = 2000000 and L = 20 m.

Explanation: The spoon works on the principle of the lever. The rim of the can acts as the fulcrum, the effort is applied at the far end of the spoon's handle, and the load is the tightly fitted lid close to the fulcrum. Since the effort arm (rim to hand) is much longer than the load arm (rim to lid edge), the mechanical advantage = effort arm / load arm is greater than 1. A small downward effort on the handle is therefore multiplied into a large upward force on the lid, prying it open easily.

Explanation: An inclined ladder works on the principle of the inclined plane. To reach the same height h, the climber travels a longer distance along the incline than along a vertical ladder. Since work done against gravity is fixed at W = mgh, spreading it over a longer distance means the force the climber must exert at each moment is smaller; the ladder's normal reaction supports part of the body's weight. On a vertical ladder the climber's muscles must support and lift the entire body weight directly. Less required force makes the inclined climb easier, even though the total work done is the same.

Explanation: Kinetic energy is given by KE = (1/2) m v², so it is proportional to the square of the velocity. If the velocity is doubled (v -> 2v), the new kinetic energy is (1/2) m (2v)² = 4 x (1/2) m v². Hence the kinetic energy becomes four times its initial value.

Explanation: Gravitational potential energy is PE = mgh, which depends only on the object's height above the reference level. (i) In horizontal motion the height h does not change, so the potential energy remains constant; no work is done against gravity. (ii) When the object is lifted vertically, h increases, so its potential energy increases by mgh; the work done against gravity in lifting it is stored as this gain in potential energy.

Explanation: Work is done when a force acting on an object moves it through some distance. It is defined as W = F x s, where F is the applied force and s is the displacement of the object measured along the direction of the force. Its SI unit is the joule (J), where 1 J = 1 N x 1 m.

Explanation: Sample model: rest a ruler (lever arm) on a pencil placed under it (fulcrum), keep the load (a paper cup with coins) near one end and press down on the other end to lift it. Measure the load's weight and the applied effort using a rubber-band spring balance or known weights. Mechanical advantage is calculated as MA = Load / Effort. For example, if a 2 N load is lifted by applying only 0.5 N of effort, MA = 2 / 0.5 = 4, meaning the machine multiplies the applied force 4 times. Keeping the fulcrum closer to the load increases the MA; actual values will vary with your model.

Explanation: For an inclined plane, the mechanical advantage is the ratio of the length of the slope to the vertical height gained: MA = length of ramp / height of step. Here MA = 50 cm / 30 cm = 5/3, which is approximately 1.67. This means the effort needed to push the object up the ramp is only about 3/5 of the force needed to lift it straight up; the horizontal base (40 cm) is not used in the calculation.

Explanation: Work is positive when the force and the displacement are in the same direction, and negative when they are opposite. While lifting, the girl applies an upward force on the dumbbell and the dumbbell moves upward, so her force and the displacement are in the same direction and the work she does is positive. While slowly lowering it, she still pushes upward to support the dumbbell, but the dumbbell moves downward; her force is opposite to the displacement, so the work done by her on the dumbbell is negative.