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Ben is cycling at 5 mph on a flat road and starts to accelerate to 20 mph.

Force A has changed from 14 N to 37 N by the time he reaches 15 mph.

Force B changes from 27 N to 76 N when he starts to accelerate and stays at that value.

Force C changes from 13 N to 17 N by the time he reaches 15 mph.

a. Suggest which force is the force from the pedals. Explain your answer.

b. Work out the resultant horizontal force on the bike at 15 mph and state its direction. Ben continues to pedal with the same force, but his speed stops changing when he reaches 20 mph.

c. What is the resultant horizontal force on the bike at 20 mph? Explain your answer.

d. How big is the combined force of friction and air resistance at 20 mph? Explain your answer.

Answer :

Final answer:

Force A, which changes from 14 N to 37 N, likely represents the force from the pedals. The resultant horizontal force on the bike at 15 mph is 130 N, in the direction of acceleration. At 20 mph, the resultant horizontal force is zero and the combined force of friction and air resistance is also 37 N.

Explanation:

The force that most likely represents the force from the pedals would be Force A, as it is the only force that increases significantly as Ben accelerates, indicating that it is the force being actively controlled by Ben's pedaling. Force B remains constant, suggesting it could be a static force unrelated to pedaling effort, such as gravity acting on the bicycle's mass, or perhaps a force from rolling friction that does not vary with speed. Force C changes only slightly, indicating a minor factor in acceleration, possibly the bearing resistance in the wheel hubs or the bicycle chain.

To work out the resultant horizontal force on the bike at 15 mph, sum the forces: 37 N (Force A) + 76 N (Force B) + 17 N (Force C) = 130 N, which is the total force propelling the bike forward.

When Ben reaches 20 mph and his speed stops changing, the resultant horizontal force must be zero because the forces from pedaling and the resistive forces (friction and air resistance) are balanced and there is no net acceleration.

The combined force of friction and air resistance at 20 mph would be equal to the force being applied by the pedals when Ben's speed is no longer increasing, which is the same as Force A at 15 mph, or 37 N since no further information about changes in Force A between 15 mph and 20 mph is provided.

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