M6 Week 11 Problem Set #11

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Mechanical Engineering

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Dec 6, 2023

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M6 Week 11 Problem Set #11 Hallstrom Problems: 2, 12, 24, 40, 42, 64 2. The gardening tool is used to pull weeds. If a 1.23-N * m torque is required to pull a given weed, what force did the weed exert on the tool? τ = r F F = τ r F = 1.23 N m 0.04 m F = 30.75 N → 30.7 N 12. When the play button is pressed, a CD accelerates uniformly from rest to 450 rev/min in 3.0 revolutions. If the CD has a radius of 6.0 cm and a mass of 17 g, what is the torque exerted on it? M = 1 2 mr 2 17 10 3 kg ¿ ( 6 10 2 m ) 2 M = 1 2 ¿ M = 3.06 10 5 ω 2 = ω 0 2 + 2 αθ ( 450 rev / min ¿ 2 π 60 rad / s 1 rev / min ) 2 = 0 2 + 2 α ( 3.0 rev 2 π rad 1 rev ) α = 58.9 rad / s 2 τ = Ma τ = 3.06 10 5 kg m 2 58.9 rad / s 2 τ = 1.8 10 3 N m
M6 Week 11 Problem Set #11 Hallstrom 24. To determine the location of her center of mass, a physics student lies on a lightweight plank supported by two scales 2.50 m apart. If the left scale reads 435 N, and the right scale reads 183 N, find (a) the student’s mass and (b) the distance from the student’s head to her center of mass. a. The student’s mass f y = f 1 + f 2 mg = 0 m = f 1 + f 2 g m = 435 N + 183 N 9.8 m / s 2 m = 63.06 kg→ 63.1 kg b. The distance from the student’s head to her center of mass τ ¿ = x 2 f 2 x cg ( mg ) = 0 x cg = x 2 f 2 mg x cg = ( 2.5 m )( 183 N ) ( 63.06 kg )( 9.8 m / s 2 ) x cg = 457.5 617.98 x cg = 0.74 m 40. A 2.85-kg bucket is attached to a rope wrapped around a disk-shaped pulley of radius 0.121 m and mass 0.742 kg. If the bucket is allowed to fall, (a) what is its linear acceleration? (b) What is the angular acceleration of the pulley? (c) How far does the bucket drop in 1.50 s? (group) a. What is its linear acceleration? For this equation: m1=bucket, m2=mass of pulley a = m 1 g 1 2 m 2 + m 1 a = ( 2.85 kg )( 9.8 m / s 2 ) 1 2 ( 0.742 kg )+( 2.85 kg ) a = 8.68 m / s 2 However, this value will be negative because the bucket is falling. a =− 8.68 m / s 2 b. What is the angular acceleration of the pulley? For the purpose of this problem, we are going to use the magnitude of the acceleration, so the positive value α = a r
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