A 0.30kg soccer ball is released from the top of a 10m building. The ball strikes the ground with a speed of 12m/s. Use the conservation of energy to determine the energy lost due to the work done by air resistance.

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Question restatement: A 0.30 kg soccer ball is released from a height of 10 m. It strikes the ground with a speed of 12 m/s. Using conservation of energy, determine the energy lost to air resistance.

Option analysis:
- a) 21.6 J: This value matches the final kinetic energy of the ball at impact, calculated as KE = 1/2 m v^2 = 1/2 × 0.30 kg × (12 m/s)^2 = 0.15 × 144 = 21.6 J. However, this is not the energy lost to air resistance; it is the portion of energy remaining as kinetic energy at impact.
- b) 7.8 J: This is the energy dissipated by air resistance. Start with the initial gravitational potential energy: U_i = m g h = 0.30 kg × 9.8 m/s^2 × 10 m = 29.4 J. If there were no air resistance, all this potential energy would convert to kinetic energy at ground, K_ground = 29.4 J. But the actual kinetic energy at impact is 21.6 J, so the difference is E_lost = 29.4 J − 21.6 J = 7.8 J. This is the energy that went into overcoming air resistance (heat, sound, deformation, etc.).
- c) 13.2 J: This value does not correspond to any standard energy partition in this setup. It could arise from a miscalculation, such as taking KE_final as 16.2 J or misapplying the energy balance, but it does not match the actual energy lost to drag.
- d) 29.4 J: This would imply that all the initial potential energy was lost to air resistance, leaving zero kinetic energy at impact, which contradicts the given final speed of 12 m/s. Therefore this choice is inconsistent with the stated impact velocity.

Summary: The correct energy loss due to air resistance is the difference between the initial potential energy and the final kinetic energy, 29.4 J − 21.6 J = 7.8 J. The other options misidentify the final kinetic energy, miscalculate the energy dissipated, or ignore the nonzero final speed.

SPH4U - Physics 12 (2025-26) - A

A 0.30kg soccer ball is released from the top of a 10m building. The ball strikes the ground with a speed of 12m/s. Use the conservation of energy to determine the energy lost due to the work done by air resistance.

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