A light rope is wrapped several times around a large wheel with a radius of 0.400 m. The wheel rotates in frictionless bearings about a stationary horizontal axis, as shown in the figure below. The free end of the rope is tied to a suitcase with a mass of 15.0 kg. The suitcase is released from rest at a height of 4.00 m above the ground. The suitcase has a speed of 3.50 m/s when it reaches the ground. Calculate:What is the linear acceleration of the suitcase as it falls? (Hint: It’s not in free fall!)What is the resulting angular acceleration of the wheel?What is the angular velocity of the wheel when the suitcase hits the ground?What is the tension in the string as the suitcase falls? (Hint: It is not equal to the weight of the case! Use Newton’s Second Law!)What is the torque caused by that tension?What is the moment of inertia of the wheel? 一个4.00 m

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Answered: A light rope is wrapped several times…

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter1: Measurement

Section: Chapter Questions

Problem 7E: Write the following quantities in standard units. (a) 0.55 Ms (b) 2.8 km (c) 12 mg (d) 100 cm

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A light rope is wrapped several times around a large wheel with a radius of 0.400 m. The wheel rotates in frictionless bearings about a stationary horizontal axis, as shown in the figure below. The free end of the rope is tied to a suitcase with a mass of 15.0 kg. The suitcase is released from rest at a height of 4.00 m above the ground. The suitcase has a speed of 3.50 m/s when it reaches the ground. Calculate:

What is the linear acceleration of the suitcase as it falls? (Hint: It’s not in free fall!)
What is the resulting angular acceleration of the wheel?
What is the angular velocity of the wheel when the suitcase hits the ground?
What is the tension in the string as the suitcase falls? (Hint: It is not equal to the weight of the case! Use Newton’s Second Law!)
What is the torque caused by that tension?
What is the moment of inertia of the wheel?

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

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