A bicyclist notes that the pedal sprocket has a radius of rp = 11 cm while the wheel sprocket has a radius of rw = 4.5 cm. The two sprockets

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A bicyclist notes that the pedal sprocket has a radius of rp = 11 cm while the wheel sprocket has a radius of rw = 4.5 cm. The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R = 64 cm. When pedaling the cyclist notes that the pedal rotates at one revolution every t = 1.2 s. When pedaling, the wheel sprocket and the wheel move at the same angular speed. Randomized Variables rp = 11 cm rw = 4.5 cm R = 64 cm t = 1.2 s show answer Correct Answer 17% Part (a) The pedal sprocket and the wheel sprocket have the same _____________________. Tangential speed at their outer edges. ✔ Correct! show answer No Attempt 17% Part (b) Calculate the angular speed of the pedal sprocket ωp, in radians per second.

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Orla Orla 5 years 2021-08-05T11:44:23+00:00 1 Answers 73 views 0

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  1. minhkhang
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    2021-08-05T11:46:10+00:00
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    Answer:

    (a) See explanation below.

    (b) ω = 5.24rad/s.

    Explanation:

    (a) The tangential speed at the outer edges of the sprocket and wheel are the same because the wheel does not slip and as a result the rotational kinetic energy delivered to/by the pedal transmitted uniformly throughout the chain and sprocket system. This energy causes the outer edges to move equal linear distances in equal time intervals.

    Let s be the distance covered in time t

    Let the tangential speed of the pedal sprocket be v1 and that of the wheel sprocket be v2

    S = v1t = v2t since the time interval is the same and the wheel does not slip.

    v1 = v2 = v

    (b)The radius of the pedal sprocket r = 11cm = 0.11m

    The pedal rotates 1 rev in every 1.2s. One revolution is equal to 2π radians.

    So the angular speed is equal to ω = 2π/1.2s = 5.24rad/s

    ω = 5.24rad/s

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