Ch 10: Dynamics of Rotational Motion

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 10: Dynamics of Rotational Motion

Problem 21c

Chapter 10, Problem 21c

A solid ball is released from rest and slides down a hillside that slopes downward at 65.0° from the horizontal. In part (a), why did we use the coefficient of static friction and not the coefficient of kinetic friction?

Verified step by step guidance

Understand the difference between static and kinetic friction: Static friction acts when an object is at rest and prevents it from starting to move, while kinetic friction acts when an object is already in motion.

Recognize that the ball is initially at rest when it is released. This means that static friction is the force that must be overcome for the ball to start sliding down the hill.

Consider the role of static friction in preventing slipping: Static friction provides the necessary force to prevent the ball from slipping as it begins to roll down the slope.

Note that once the ball starts moving, kinetic friction would be relevant. However, the problem specifically asks about the initial release, which involves overcoming static friction.

Conclude that the coefficient of static friction is used because it determines the maximum force that can be applied without causing the ball to slip, which is crucial for understanding the initial motion of the ball.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Static Friction

Static friction is the force that prevents an object from moving when it is at rest. It acts between the surfaces in contact and is generally higher than kinetic friction. In this scenario, static friction is relevant because it determines the initial resistance to motion as the ball starts sliding down the slope.

Kinetic Friction

Kinetic friction is the force that opposes the motion of an object that is already sliding. It is usually less than static friction and comes into play once the object is in motion. The question focuses on the initial phase where the ball is at rest, hence kinetic friction is not used.

Transition from Rest to Motion

The transition from rest to motion involves overcoming static friction. When an object is released from rest, static friction must be overcome for the object to start moving. This is why the coefficient of static friction is used initially, as it dictates the force needed to initiate movement down the slope.

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Related Practice

Textbook Question

A 2.20-kg hoop 1.20 m in diameter is rolling to the right without slipping on a horizontal floor at a steady 2.60 rad/s. Find the velocity vector of each of the following points, as viewed by a person at rest on the ground: (i) the highest point on the hoop; (ii) the lowest point on the hoop; (iii) a point on the right side of the hoop, midway between the top and the bottom.

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Textbook Question

A bicycle racer is going downhill at 11.0 m/s when, to his horror, one of his 2.25-kg wheels comes off as he is 75.0 m above the foot of the hill. We can model the wheel as a thin-walled cylinder 85.0 cm in diameter and ignore the small mass of the spokes. How much total kinetic energy does the wheel have when it reaches the bottom of the hill?

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Textbook Question

A playground merry-go-round has radius $2.40$\text{ m}$$ and moment of inertia $2100$\text{ kg m}$^2$ about a vertical axle through its center, and it turns with negligible friction. A child applies an $18.0$\text{ N}$$ force tangentially to the edge of the merry-go-round for $15.0$\text{ s}$$ . If the merry-go-round is initially at rest, how much work did the child do on the merry-go-round?

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Textbook Question

A 2.20-kg hoop 1.20 m in diameter is rolling to the right without slipping on a horizontal floor at a steady 2.60 rad/s. Find the velocity vector for each of the points in part (c), but this time as viewed by someone moving along with the same velocity as the hoop.

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Textbook Question

A 12.0-kg box resting on a horizontal, frictionless surface is attached to a 5.00-kg weight by a thin, light wire that passes over a frictionless pulley (Fig. E10.16). The pulley has the shape of a uniform solid disk of mass 2.00 kg and diameter 0.500 m. After the system is released, find the acceleration of the box.

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Textbook Question

A playground merry-go-round has radius $2.40 m$ and moment of inertia $2100 kg m squared$ about a vertical axle through its center, and it turns with negligible friction. A child applies an $18.0 cap N$ force tangentially to the edge of the merry-go-round for $15.0 s$ . If the merry-go-round is initially at rest, what is its angular speed after this $15.0 s$ interval?

1347

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