A cord is wrapped around the rim of a solid uniform wheel 0.300 m in radius and

Question

A cord is wrapped around the rim of a solid uniform wheel 0.300 m in radius and of mass 7.80 kg . A steady horizontal pull of 38.0 N to the right is exerted on the cord, pulling it off tangentially from the wheel. The wheel is mounted on frictionless bearings on a horizontal axle through its center.

Part A

Compute the angular acceleration of the wheel.

32.5

Part B

Compute the acceleration of the part of the cord that has already been pulled off the wheel.

9.74

Part C

Find the magnitude of the force that the axle exerts on the wheel.

85.4

Part D

Find the direction of the force that the axle exerts on the wheel.

Part E

Which of the answers in parts (A), (B), (C) and (D) would change if the pull were upward instead of horizontal?

32.5

Explanation / Answer

solid uniform wheel 0.300 m

radius and of mass 7.80 kg

horizontal pull of 38.0 N

  I = 1/2mr^2 = 1/2 * 7.80kg * (0.3m)2 = 0.351 kg·m²

= I = F•d

Part A

a. 0.351kg·m² * = 38N * 0.3m = 32.5 rad/s²

Part B

b. a = r = 9.74m/s

Part C

c. F = (38^2 + (7.80kg*9.8m/s²)^2) N = 85.46 = 85.5 N m/s²

Part D

d. = arctan(7.80*9.8/38) = 63.56º below horizontal

Part E

e. only d
.

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