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Drag and terminal speed questions
Friction and drag are the forces the idealised problems leave out, and this topic puts them back in, qualitatively. Their defining habit is that drag grows with speed, and that single fact produces terminal speed, two-stage skydives and the top speed of every vehicle.
18 original questions · 56 marks · the drag and terminal speed notes · Mechanics
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A cyclist travels along a straight, level road. Name two resistive forces that act on the moving cyclist and state the direction in which each acts.
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Air resistance (drag) on the cyclist and bicycle (1); friction (rolling resistance) at the tyres or in the bearings (1). Each acts in the direction opposite to the motion (1).Define terminal speed.
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The constant maximum speed reached by a falling object when the resultant force on it is zero (1), so the drag, plus any upthrust, balances its weight and it stops accelerating (1).State how the drag force on an object depends on its speed, for motion through a fluid.
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Drag increases as speed increases (1); at the speeds studied it rises roughly with the square of the speed (1).State what is meant by lift.
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The component of the force exerted by a fluid on an object moving through it that acts perpendicular to the direction of flow. (1)A car travels at its maximum speed along a straight, level road. State the relationship between the driving force and the total resistive force, and state the car's acceleration.
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The driving force equals the total resistive force (1); the resultant force is therefore zero, so the acceleration is zero. (1)State one similarity and one difference between the friction between two solid surfaces and the drag on an object moving through air.
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Similarity: both are resistive forces that oppose (relative) motion (1). Difference: drag increases with speed, whereas friction between solid surfaces does not depend on speed (or: drag requires motion through a fluid). (1)A skydiver of weight 750 N falls at terminal speed. State the size and direction of the drag force on them, and explain your reasoning.
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Drag = 750 N (1)
Acting upwards (1)
At terminal speed the resultant force is zero, so the upward drag exactly balances the downward weight (1)A small sphere falls at terminal speed through a liquid. Its weight is 0.30 N and the upthrust on it is 0.05 N. Calculate the drag force on the sphere, and explain why it is not accelerating.
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At terminal speed: weight = upthrust + drag (1)
Drag = 0.30 − 0.05 (1)
Drag = 0.25 N (1)
The three forces balance, giving zero resultant force and therefore zero acceleration (1)Describe the shape of the velocity–time graph for an object dropped from rest that reaches terminal speed, and explain the changing gradient.
A raindrop of mass 65 mg falls vertically. At one instant the drag force on it is 4.2 × 10−4 N. Taking g = 9.81 m s−2, calculate the acceleration of the raindrop at this instant.
A skydiver can fall either spread out or head-first. Explain why the terminal speed is lower when the skydiver is spread out.
The engine of a car can deliver a maximum useful output power of 90 kW. At the car's top speed on a level road the total resistive force on it is 2.0 kN. (a) Calculate the top speed. (b) Explain why the car cannot travel faster than this speed.
A parachutist is falling at terminal speed when the parachute opens. Explain, in terms of the forces, why the speed decreases and how a new, lower terminal speed is reached.
Assuming the drag force is proportional to the square of the speed, an object experiences a drag of 20 N at 5.0 m s−1. Calculate the drag force at 10 m s−1.
Explain why a heavier skydiver of the same shape and size reaches a higher terminal speed than a lighter one.
A trainee parachutist of total weight 850 N must land at no more than 5.5 m s−1. With a particular canopy open, the drag force at speed v is given by D = kv2, where k = 24 kg m−1. Deduce whether this canopy is suitable.
A skydiver of mass 92 kg falls head-first with a terminal speed of 58 m s−1. Assume the drag force is proportional to the square of the speed. Taking g = 9.81 m s−2, determine the drag force and the acceleration of the skydiver at a speed of 29 m s−1.
A cyclist starts from rest on a straight, level road and pedals so that the driving force stays constant. After some time she reaches her maximum speed, and she then stops pedalling. Air resistance increases with speed. Describe and explain, in terms of the forces acting, how her velocity changes throughout.
The same practice on paper: the printable workbook for this topic, questions and a worked answer book.
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