Question

A body of mass 500 g is falling from rest from a height of 3.2 m from the ground. If the body reaches the ground with a velocity of 6 ms⁻¹, then the energy lost by the body due to air resistance is (Acceleration due to gravity = 10 ms⁻²)

• A. 14 J
• B. 7 J
• C. 21 J
• D. 28 J

Hint:

An alternative approach is the Work-Energy Theorem: \(W_{total} = \Delta KE\). Here, total work is done by gravity and air resistance: \(W_g + W_{air} = KE_f - KE_i\). Calculating \(W_g = mgh = 16\) J gives \(16 + W_{air} = 9 - 0\), so \(W_{air} = -7\) J. The energy lost is the magnitude of the work done by resistance, which is 7 J.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This problem involves the principle of conservation of energy. In the presence of non-conservative forces like air resistance, the total mechanical energy (potential + kinetic) of the system is not conserved. The energy "lost" is the work done by the air resistance. We can find this lost energy by comparing the initial mechanical energy of the body with its final mechanical energy.
Step 2: Key Formula or Approach:
Energy Lost = Initial Mechanical Energy (\(E_i\)) - Final Mechanical Energy (\(E_f\))
Where \(E = \text{Potential Energy (PE) + Kinetic Energy (KE)}\).
\(PE = mgh\) and \(KE = \frac{1}{2}mv^2\).
First, convert all units to SI units: mass \(m = 500\) g = 0.5 kg.
Step 3: Detailed Explanation:
Calculate Initial Energy (\(E_i\)):
At the initial position (height \(h = 3.2\) m), the body is at rest (\(u = 0\)).
Initial Potential Energy: \(PE_i = mgh = (0.5 \text{ kg}) \times (10 \text{ m/s}^2) \times (3.2 \text{ m}) = 16\) J.
Initial Kinetic Energy: \(KE_i = \frac{1}{2}mu^2 = 0\), since it starts from rest.
Total Initial Energy: \(E_i = PE_i + KE_i = 16 + 0 = 16\) J.
Calculate Final Energy (\(E_f\)):
At the final position (on the ground, \(h = 0\)), the body has a velocity \(v = 6\) m/s.
Final Potential Energy: \(PE_f = mgh = 0\), since it is at ground level.
Final Kinetic Energy: \(KE_f = \frac{1}{2}mv^2 = \frac{1}{2}(0.5 \text{ kg})(6 \text{ m/s})^2 = 0.25 \times 36 = 9\) J.
Total Final Energy: \(E_f = PE_f + KE_f = 0 + 9 = 9\) J.
Calculate Energy Lost:
The energy lost due to air resistance is the difference between the initial and final mechanical energy.
\[ \text{Energy Lost} = E_i - E_f = 16 \text{ J} - 9 \text{ J} = 7 \text{ J} \] Step 4: Final Answer:
The energy lost by the body due to air resistance is 7 J. Therefore, option (B) is the correct answer.