Loading a Maize Sack with a Ramp and a Wheelbarrow
A farmer needs to load a 120 kg sack of maize into a truck whose floor is 1.0 m above the ground. He has a strong plank 3.0 m long and two helpers. Lifting the sack straight up requires a force of about 1 200 N (taking 10 N per kg). Using the plank as a ramp, the ideal force is about 400 N, but because of friction the real force is 550 N. The farmer also has a single fixed pulley and a wheelbarrow. The sack is placed at the very front of the wheelbarrow, close to the wheel, and the wheelbarrow tips forward easily. A helper says, 'The longer the ramp, the less force, so a 6 m ramp would need no force at all.' The farmer wants the safest and most efficient method and asks the pupils to explain, not just calculate.
1. Calculate the work done lifting the sack straight up and using the 3.0 m ramp. Explain why the ramp reduces force but does not remove the need for work.
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Work = force × distance moved in the direction of the force. Lifting straight up: force 1 200 N × 1.0 m = 1 200 J. Using the 3.0 m ramp ideally: 400 N × 3.0 m = 1 200 J. So the ramp does not reduce the work needed in an ideal machine; it spreads the same work over a longer distance, so the force is smaller. In reality friction adds work: real force 550 N × 3.0 m = 1 650 J. The extra 450 J is used to overcome friction and becomes heat. The ramp is still useful because 550 N is less than 1 200 N, so one person can manage, but the ramp must be strong and not too steep.
2. Explain why the wheelbarrow tips forward when the sack is at the very front, close to the wheel, and state where the sack should be placed.
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A wheelbarrow is a lever with the wheel as the pivot. The load creates a turning effect, or moment, about the wheel. Moment = force × distance from pivot. If the sack is at the very front, close to the wheel, its distance from the pivot is small, so its turning effect is small and the load is stable. If the sack is placed at the back, far from the wheel, the same weight has a larger moment and can tip the barrow or make it hard to lift. The sack should be placed low and as near to the wheel as possible, with the heavy end towards the wheel. The helper's claim is about force, but stability depends on where the load is placed.
3. Evaluate the helper's claim that a 6 m ramp would need no force at all. Choose the safest and most efficient method for the farmer.
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The helper's claim is only partly true. A longer ramp does reduce the force needed, because force = work ÷ distance. A 6 m ramp would ideally need 1 200 J ÷ 6 m = 200 N, not zero. Force never becomes zero because the load still has weight and friction still acts. A very long ramp also needs more space and materials, and friction may add more work. The best choice is a ramp long enough to keep the force below what the workers can safely control, with a rough surface or a stop to prevent slipping. The fixed pulley changes the direction of the force but does not reduce it for a single fixed pulley. The ramp is the better simple machine here, and the wheelbarrow helps for short moves.