07. Very Short Question Answer: Work, Energy, and Simple Machines

Q1: Define work done by a constant force on an object.

Ans: Work done on an object by a constant force is equal to the force applied multiplied by the displacement of the object in the direction of the force. Mathematically, $W = F \times s$ .

Q2: What is the SI unit of work and how is it defined?

Ans: The SI unit of work is the joule (J). One joule of work is done when a constant force of 1 newton displaces an object by 1 metre in the direction of the force, i.e., $1 J = 1 N \times 1 m$ .

Q3: When is the work done on an object equal to zero?

Ans: Work done on an object is zero when either the force acting on it is zero $(F = 0)$ , or there is no displacement of the object $(s = 0)$ , regardless of the force applied. For example, pushing a rigid wall does no work.

Q4: When is work done said to be negative?

Ans: Work done is negative when the displacement of the object is in the direction opposite to the applied force. For example, a goalkeeper stopping a football does negative work on the ball.

Q5: State the work-energy theorem.

Ans: The work-energy theorem states that the work done on an object is equal to the change in its energy, i.e., $W = Δ E$ . When positive work is done on an object, its energy increases by the same amount.

Q6: What is energy? What is its SI unit?

Ans: Energy is the capacity of an object to do work. The SI unit of energy is the joule (J), which is the same as the SI unit of work.

Q7: Define kinetic energy and give its mathematical expression.

Ans: The energy possessed by an object due to its motion is called kinetic energy. For an object of mass $m$ moving with velocity $v$ , its kinetic energy is given by $K = \frac{1}{2} m v^{2}$ .

Q8: If the velocity of an object is doubled, how does its kinetic energy change?

Ans: Since kinetic energy $K = \frac{1}{2} m v^{2}$ , doubling the velocity makes it $\frac{1}{2} m (2 v)^{2} = 4 \times \frac{1}{2} m v^{2}$ . Therefore, the kinetic energy becomes 4 times the original value.

Q9: What is potential energy?

Ans: The energy stored by an object as a result of its deformation, or in a system of objects due to their relative positions, is called potential energy. For example, a stretched rubber band and a raised object both possess potential energy.

Q10: Write the expression for the gravitational potential energy of an object and explain each term.

Ans: The gravitational potential energy of an object of mass $m$ at a height $h$ above the ground is given by $U = m g h$ , where $g$ is the acceleration due to gravity. Its unit is the joule (J).

Q11: What is mechanical energy?

Ans: The sum of the kinetic energy and the potential energy of an object is called its mechanical energy. For a freely falling object, the mechanical energy remains constant and equals $m g h$ throughout the motion.

Q12: State the law of conservation of mechanical energy.

Ans: When no external forces other than gravity act on an object, its mechanical energy remains constant. This means the lost potential energy is entirely converted into kinetic energy and vice versa.

Q13: Define power and write its mathematical expression.

Ans: Power is defined as the rate at which work is done. Mathematically, average power $P$ is given by $P = \frac{W}{t}$ , where $W$ is the work done and $t$ is the time taken.

Q14: What is the SI unit of power and how is it defined?

Ans: The SI unit of power is the watt (W). One watt is equal to 1 joule of work done per second, i.e., $1 W = 1 {J s}^{- 1}$ .

Q15: What are simple machines? Give three examples studied in this chapter.

Ans: Simple machines are devices that make work easier by changing the magnitude or direction of the force that needs to be applied, without reducing the total work. The three examples studied in this chapter are the pulley, the inclined plane, and the lever.

Q16: Define mechanical advantage of a simple machine.

Ans: Mechanical advantage is defined as the ratio of the load to the effort applied on a machine. It can be written as $Mechanical Advantage = \frac{load}{effort}$ . A value greater than 1 means the machine multiplies the applied force.

Q17: What is the mechanical advantage of a fixed pulley, and what is its main advantage?

Ans: The mechanical advantage of a fixed pulley is 1, since the effort and the load are equal in magnitude. Its main advantage is that it changes the direction of the effort, making it easier to lift a load by pulling downward instead of pushing upward.

Q18: Write the expression for the mechanical advantage of an inclined plane.

Ans: The mechanical advantage of an inclined plane is given by $Mechanical Advantage = \frac{L}{h}$ , where $L$ is the length of the inclined plane and $h$ is its height. Since $L > h$ , the mechanical advantage is always greater than 1.

Q19: Name the three parts of a lever and define each.

Ans: The three parts of a lever are: (i) Fulcrum – the fixed point about which the lever rotates; (ii) Load – the force to be overcome; and (iii) Effort – the force applied to the lever.

Q20: Write the mathematical condition for a lever to be balanced.

Ans: A lever is balanced when $effort \times effort arm = load \times load arm$ , i.e., $F_{1} \times d_{1} = F_{2} \times d_{2}$ . By increasing the effort arm, a larger force can be applied to the load with a smaller effort.