Question 14 of 19advanced🔧 ApplyNumerical5 marks

A bullet of mass 50 g moving with a speed of 100 m s⁻¹ enters a heavy stationary wooden block and stops after penetrating a distance of 50 cm. Estimate the stopping force acting on the bullet (assume that the bullet undergoes constant acceleration within the block).

Correct Answer

500 N

Exercise: Revise, Reflect, Refine | Q: 12 | (Page 21)
For More Understanding

Explanation

To find the stopping force, we first convert the given physical quantities into standard SI units. Then, we apply the kinematic equation v² = u² + 2as to find the constant acceleration (retardation) of the bullet as it stops. Finally, we use Newton's second law of motion, F = ma, to calculate the force. The negative sign in the calculation indicates that the stopping force acts in the opposite direction to the bullet's motion.

Solution Steps

  1. Step 1: Convert units to SI: Mass of the bullet, m = 50 g = 0.05 kg; Distance penetrated, s = 50 cm = 0.5 m.

  2. Step 2: Identify given values: Initial speed, u = 100 m s⁻¹; Final speed, v = 0 m s⁻¹ (since the bullet stops).

  3. Step 3: Calculate acceleration: Using the kinematic equation v² = u² + 2as, we get 0 = (100)² + 2 * a * 0.5. This simplifies to 0 = 10000 + a, so acceleration, a = -10000 m s⁻².

  4. Step 4: Calculate force: Using Newton's second law of motion, F = m * a, we substitute the values: F = 0.05 kg * (-10000 m s⁻²) = -500 N.

  5. Step 5: Interpret the result: The negative sign indicates the force opposes the motion. Thus, the magnitude of the stopping force is 500 N.

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