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Chapter 10: Q.10 (page 256)

A 20 kg child is on a swing that hangs from 3.0-m-long chains. What is her maximum speed if she swings out to a 45° angle?

Short Answer

Expert verified

As a result, the child's maximum speed is $4.15 m / s$ .

Step by step solution

01

Introduction

The distance travelled by an object per unit time is known as its speed.

02

Explanation

Draw the child's and swing's free body diagrams.

Calculate the child's increased height.

Putting $3 m$ for ll, $0.7071$ for $\cos 45 °$ in equation $x = l \cos 45 °$

$x = (3 m) (0.7071)$

$= 2.12 m$

Putting $2.12 m$ for $x$ , and $3 m$ for $l$ in equation $h = l - x$

$h = 3 m - 2.12 m$

$= 0.88 m$

Calculate the child's maximum speed.

At the two positions depicted in the diagram, apply the law of conservation of energy.

$K E_{i} + P E_{i} = K E_{f} + P E_{f}$

$\frac{1}{2} m v_{\max}^{2} + 0 = 0 + m g h$

$v_{\max} = \sqrt{2 g h}$

Putting $9.81 m / s^{2}$ for $g$ , and $0.88 m$ for $h$ by equation.

$v_{\max} = \sqrt{2 (9.81 m / s^{2}) (0.88 m)}$

$= \sqrt{17.26 m^{2} / s^{2}}$

$= 4.15 m / s$

As a result, the child's maximum speed is $4.15 m / s$ .

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Most popular questions from this chapter

A stretched spring stores 2.0 J of energy. How much energy will be stored if the spring is stretched three times as far?

You have a ball of unknown mass, a spring with spring constant $950 N / m$ , and a meter stick. You use various compressions of the spring to launch the ball vertically, then use the meter stick to measure the ball’s maximum height above the launch point. Your data are as follows:

Use an appropriate graph of the data to determine the ball’s mass.

The spring shown in FIGURE P10.54 is compressed $50 c m$ and used to launch a $100 k g$ physics student. The track is frictionless until it starts up the incline. The student’s coefficient of kinetic friction on the $30^{o}$ incline is $0.15$ .

a. What is the student’s speed just after losing contact with the spring?

b. How far up the incline does the student go?

A particle moving along the y-axis is in a system with potential energy $U = 4 y^{3} J$ , where y is in m. What is the y-component of the force on the particle at $y = 0 m, 1 m, a n d 2 m$ ?

A $100 g$ particle experiences the one-dimensional, conservative force Fx shown in FIGURE $P 10.59$ .

a. Let the zero of potential energy be at $x = 0 m$ .

What is the potential energy at $x = 1.0, 2.0, 3.0, a n d 4.0 m$ ? Hint: Use the definition of potential energy and the geometric interpretation of work.

b. Suppose the particle is shot to the right from $x = 1.0 m$ with a speed of $25 m / s$ . Where is its turning point?

See all solutions

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