Which of the following potential energy curves in Fig. 6.18 cannot possibly
[question] Question. Which of the following potential energy curves in Fig. 6.18 cannot possibly describe the elastic collision of two billiard balls? Here r is the distance between centres of the balls. [/question] [solution] solution: (i), (ii), (iii), (iv), and (vi) The potential energy of a system of two masses is inversely proportional to the separation between them. In the given case, the potential energy of the system of the two balls will decrease as they come closer to each other. It wi...
A body of mass 0.5 kg travels in a straight line with velocity
[question] Question. A body of mass $0.5 \mathrm{~kg}$ travels in a straight line with velocity $v=a x^{\frac{3}{2}}$ where $a=5 \mathrm{~m}^{-\frac{1}{2}} \mathrm{~s}^{-1}$. What is the work done by the net force during its displacement from $x=0$ to $x=2$ m? [/question] [solution] solution: Mass of the body, m = 0.5 kg Velocity of the body is governed by the equation, $v=a x^{\frac{3}{2}}$ with $a=5 \mathrm{~m}^{\frac{-1}{2}} \mathrm{~s}^{-1}$ Initial velocity, $u($ at $x=0)=0$ Final velocity ...
A body is moving unidirectionally under the influence of a source
[question] Question. A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional to (i) $t^{\frac{1}{2}}$ (ii) $t$ (iii) $t^{\frac{3}{2}}$ (iv) $t^{2}$ [/question] [solution] solution: (iii) $t^{\frac{3}{2}}$ Power is given by the relation: P = Fv $=m a v=m v \frac{d v}{d t}=$ Constant $($ say,$k)$ $\therefore v d v=\frac{k}{m} d t$ $m$ Integrating both sides: $\frac{v^{2}}{2}=\frac{k}{m} t$ For displacement $x$ of the body, we ...
A body is initially at rest. It undergoes one-dimensional motion with
[question] Question. A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to (i) $t^{\frac{1}{2}}$ (ii) $t$ (iii) $t^{\frac{3}{2}}$ (iv) $t^{2}$ [/question] [solution] solution: Answer: (ii) t Mass of the body = m Acceleration of the body = a Using Newton’s second law of motion, the force experienced by the body is given by the equation: F = ma Both m and a are constants. Hence, force F will also be a con...
Answer carefully, with reasons:
[question] Question. Answer carefully, with reasons: (a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact)? (b) Is the total linear momentum conserved during the short time of an elastic collision of two balls? (c) What are the answers to (a) and (b) for an inelastic collision? (d) If the potential energy of two billiard balls depends only on the separation distance between their ce...
State if each of the following statements is true or false. Give reasons for your answer.
[question] Question. State if each of the following statements is true or false. Give reasons for your answer. (a) In an elastic collision of two bodies, the momentum and energy of each body is conserved. (b) Total energy of a system is always conserved, no matter what internal and external forces on the body are present. (c) Work done in the motion of a body over a closed loop is zero for every force in nature. (d) In an inelastic collision, the final kinetic energy is always less than the init...
Underline the correct alternative:
[question] Question. Underline the correct alternative: (a) When a conservative force does positive work on a body, the potential energy of the body increases/decreases/remains unaltered. (b) Work done by a body against friction always results in a loss of its kinetic/potential energy. (c) The rate of change of total momentum of a many-particle system is proportional to the external force/sum of the internal forces on the system. (d) In an inelastic collision of two bodies, the quantities which ...
Answer the following:
[question] Question. (a) The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere? (b) Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet’s velocity in general. Yet the work done by the gravitational force over every complete orbit of the comet is zero. Why? (c) An artificial satellite orbiting the earth in very thin...
A body of mass 2 kg initially at rest moves under the action
[question] Question. A body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1. Compute the (a) work done by the applied force in 10 s, (b) work done by friction in 10 s, (c) work done by the net force on the body in 10 s, (d) change in kinetic energy of the body in 10 s, and interpret your results. [/question] [solution] solution: Mass of the body, m = 2 kg Applied force, F = 7 N Coefficient of kineti...
The sign of work done by a force on a body is important to understand.
[question] Question. The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative: (a) work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket. (b) work done by gravitational force in the above case, (c) work done by friction on a body sliding down an inclined plane, (d) work done by an applied force on a body moving on a rough horizontal plane with uniform velocity, (e) work done by...