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Chapter 8: Problem 1

An object moves at constant speed in a circular path. Which of the following statements is true? Select two answers. (A) The velocity is changing. (B) The velocity is constant. (C) The magnitude of acceleration is constant. (D) The magnitude of acceleration is changing.

Short Answer

Expert verified
(A) The velocity is changing and (C) The magnitude of acceleration is constant are the correct statements.

Step by step solution

01

Analyze the Velocity in Circular Motion

Velocity is a vector quantity, comprising both speed and direction. When an object moves in a circular path at constant speed, its direction of motion is constantly changing at every point in the motion. Therefore, despite the constant speed, the overall velocity of the object is changing.
02

Analyze the Acceleration in Circular Motion

Circular motion is always accompanied by a centripetal (or radial) acceleration, directed towards the center of the circle. This acceleration is due to the change in direction of the velocity vector, not its magnitude. Therefore, if the speed is constant, the magnitude of this centripetal acceleration remains constant as well, though its direction constantly changes as the object moves around the circle.

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Most popular questions from this chapter

You are looking at a top view of a planet orbiting the Sun in a clockwise direction. Which of the following would describe the velocity, acceleration, and force acting on the planet due to the Sun's pull at point \(\mathrm{P}\) ? \(\begin{array}{lll}\text { (A) } v \downarrow & a \uparrow & F \uparrow\end{array}\) (B) \(v \downarrow \quad a \leftarrow \quad F \leftarrow\) (C) \(v \downarrow \quad a \rightarrow \quad F \rightarrow\) \((\mathrm{D}) v \uparrow \quad a \leftarrow \quad F \leftarrow\)

A moon of mass \(m\) orbits a planet of mass \(100 \mathrm{m}\). Let the strength of the gravitational force exerted by the planet on the moon be denoted by \(F_{1},\) and let the strength of the gravitational force exerted by the moon on the planet be \(F_{2} .\) Which of the following is true? (A) \(F_{1}=100 F_{2}\) (B) \(F_{1}=1 \mathrm{OF}_{2}\) (C) \(F_{1}=F_{2}\) (D) \(F_{2}=10 F_{1}\)

Two large bodies, Body A of mass \(m\) and Body B of mass \(4 m\), are separated by a distance \(R\). At what distance from Body A, along the line joining the bodies, would the gravitational force on an object be equal to zero? (Ignore the presence of any other bodies.) (A) \(\frac{R}{16}\) (B) \(\frac{R}{8}\) (C) \(\frac{R}{4}\) (D) \(\frac{R}{3}\)

A \(60 \mathrm{cm}\) rope is tied to the handle of a bucket which is then whirled in a vertical circle. The mass of the bucket is \(3 \mathrm{kg}\). What is the critical speed below which the rope would become slack when the bucket reaches the highest point in the circle? (A) \(\mathrm{O} .6 \mathrm{m} / \mathrm{s}\) (B) \(1.8 \mathrm{m} / \mathrm{s}\) (C) \(2.4 \mathrm{m} / \mathrm{s}\) (D) \(4.8 \mathrm{m} / \mathrm{s}\)

An object of mass \(m\) is traveling at constant speed \(v\) in a circular path of radius \(r .\) How much work is done by the centripetal force during one-half of a revolution? (A) \(\pi m v^{2}\) (B) 0 (C) \(\pi m v^{2} r\) (D) \(2 \pi m v^{2} r\)
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