Practice Problems

1. A 5 kg object is pushed with a force of 40 N along a horizontal frictionless surface for 6 m. Find the work done and the final speed of the object if it starts from rest.

   Work done: \( W = F d = 40 \times 6 = 240 \,\text{J} \).

   Kinetic energy gained: \( KE = 240 \,\text{J} \).

   \( \tfrac{1}{2} m v^2 = 240 \implies v^2 = \tfrac{480}{5} = 96 \implies v \approx 9.8 \,\text{m/s} \).

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2. A 3 kg mass is lifted vertically at constant speed through 2.5 m. How much work is done against gravity, and what is the increase in potential energy?

   \( W = m g h = 3 \times 9.8 \times 2.5 = 73.5 \,\text{J} \).

   Increase in potential energy: \( PE = 73.5 \,\text{J} \).

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3. A motor does 6000 J of work in lifting a load in 15 seconds. Find the average power output.

   Power: \( P = \tfrac{W}{t} = \tfrac{6000}{15} = 400 \,\text{W} \).

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4. A 200 g ball is dropped from a height of 5 m. Neglecting air resistance, find its speed just before hitting the ground.

   Potential energy converts to kinetic energy.

   \( m g h = \tfrac{1}{2} m v^2 \implies v = \sqrt{2 g h} = \sqrt{2 \times 9.8 \times 5} \approx 9.9 \,\text{m/s} \).

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5. A machine requires 500 J of input energy to produce 350 J of useful work. Calculate its efficiency.

   \( \eta = \tfrac{W_{out}}{W_{in}} \times 100\% = \tfrac{350}{500} \times 100\% = 70\% \).

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