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IBDP Physics- A.3 Work, energy and power- IB Style Questions For SL Paper 1A -FA 2025

Question

A horizontal spring follows Hooke’s law and has spring constant \(k\). It is stretched by a distance \(x\) and then released from rest. The spring takes a time \(\Delta t\) to return to its natural length. What is the average power delivered by the spring during this interval?
(A) \(\frac{kx}{2\Delta t}\)
(B) \(\frac{kx}{\Delta t}\)
(C) \(\frac{kx^{2}}{2\Delta t}\)
(D) \(\frac{kx^{2}}{\Delta t}\)
▶️ Answer/Explanation
Detailed solution

1. Calculate Energy Stored:
The potential energy stored in a spring extended by \(x\) is given by \(E_p = \frac{1}{2}kx^2\).

2. Define Power:
Power is the rate at which work is done or energy is transferred.
\(P = \frac{\text{Energy}}{\text{Time}}\)

3. Calculate Average Power:
As the spring returns to its original length, it releases this stored energy over time \(\Delta t\).
\(P = \frac{\frac{1}{2}kx^2}{\Delta t} = \frac{kx^2}{2\Delta t}\).
Answer: (C)

Question

The input power of an electric motor is \(200\,\text{W}\). The motor is used to lift a mass of \(10\,\text{kg}\) vertically at a constant speed. The efficiency of the motor is \(40\%\).
Through what height is the mass raised in \(1\,\text{s}\)?
A. \(0.5\,\text{m}\)
B. \(0.8\,\text{m}\)
C. \(1.2\,\text{m}\)
D. \(2.0\,\text{m}\)
▶️ Answer / Explanation

Useful output power:
\(P_\text{useful} = \text{efficiency} \times P_\text{input}\)
\(P_\text{useful} = 0.40 \times 200 = 80\,\text{W}\)

Work done in \(1\,\text{s}\):
\(W = Pt = 80 \times 1 = 80\,\text{J}\)

This work equals the gain in gravitational potential energy:
\(W = mgh\)
\(80 = 10 \times 9.81 \times h\)
\(h \approx 0.815\,\text{m}\)

Rounded to one decimal place:
Answer: B

Question

A ball falls through air at terminal velocity. What is correct about the kinetic energy and the total energy of the ball?
 Kinetic energyTotal energy
Aconstantdecreases
Bincreasesdecreases
Cconstantconstant
Dincreasesconstant
▶️ Answer/Explanation
Detailed solution

At terminal velocity, the speed is constant, so the kinetic energy of the ball remains constant.

As the ball continues to fall, gravitational potential energy is transferred to the surroundings as thermal energy due to air resistance. So the total energy of the ball decreases.

Answer: (A)

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