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Two students are conducting experiments with identical 100 g mass simple pendulums, each raising the bob 5 m above the mean position. The graph depicting the relationship between distance from the mean position and velocities is presented in the diagram.

Two students are conducting experiments with identical 100 g mass simple pendulums, each raising the bob 5 m above the mean position. The graph depicting the relationship between distance from the mean position and velocities is presented in the diagram. Physics Competency Focused Practice Questions Class 10 Solutions.

(a) Demonstrate, using mathematical calculations, that the path followed by student 1 is devoid of friction.

(b) Does the situation involving student 2 exhibit a breach of the law of conservation of energy?

Work, Energy & Power

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Answer

(a) Given mass of simple pendulum = 100 g = 0.1 kg
Height raised = 5 m

Student 1
Potential energy: U1 = mgh
U1 = 0.1 x 10 x 5 = 5 J

Kinetic energy: K1 = 12\dfrac{1}{2} mv2
K1 = 12\dfrac{1}{2} x 0.1 x 102

K1 = 102\dfrac{10}{2}

K1 = 5 J

∴ Potential energy = Kinetic energy

Student 2
Potential energy: U2 = mgh
U2 = 0.1 x 10 x 5 = 5 J

Kinetic energy: K2 = 12\dfrac{1}{2} mv2

K2 = 12\dfrac{1}{2} mv2

K2 = 12\dfrac{1}{2} x 0.1 x 82

K2 = 6.42\dfrac{6.4}{2}

K2 = 3.2 J

∴ Potential energy > Kinetic energy

U2 - K2 = 5 J - 3.2 J = 1.8 J of energy is converted as heat energy due to friction.

(b) No, law of conservation of energy is not breached in case of student 2. The difference in the value of potential energy and kinetic energy is coming due to dissipation of energy caused by friction.
Potential energy = Kinetic energy + Degraded energy

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