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Chapter 1: Q62P (page 1)

What is the magnitude of the acceleration of a sprinter running at10 m/s when rounding a turn of radius 25 m?

Short Answer

Expert verified

The magnitude of the acceleration $a = 4.00 m / s^{2}$

Step by step solution

01

Given data

The speed of the sprinter is v = 10 m/ s

The radius of the turn is r = 25 m

02

Understanding the concept

The sprinter is rounding a turn hence it has centripetal acceleration. Use the formula for the centripetal acceleration in terms of velocity and radius to calculate the acceleration.

Formulae:

The centripetal acceleration is $a = \frac{v^{2}}{r}$ .

03

Calculate the magnitude of the acceleration of the sprinter

The sprinter is rounding a turn; hence it has centripetal acceleration. The centripetal acceleration of the sprinter is

$a = \frac{v^{2}}{r} = \frac{{(10 m / s)}^{2}}{25 m} = 4.00 m / s^{2}$

Therefore, the magnitude of the acceleration of the sprinter is $4.00 m / s^{2}$ .

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Most popular questions from this chapter

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In the arrangement of Fig. $7 - 10$ , we gradually pull the block from $x = 0 t o x = + 3.0 c m$ , where it is stationary. Figure $7 - 35$ gives the work that our force does on the block. The scale of the figure’s vertical axis is set by $W_{s} = 1.0 J$ . We then pull the block out to $x = + 5.0 c m$ and release it from rest. How much work does the spring do on the block when the block moves from $x_{i} = + 5.0 c m$ to, (a) $x = + 4.0 c m$ (b) $x = - 2.0 c m$ , and (c) $x = - 5.0 c m$ ?

Question: A particle moves along a straight path through displacement $\vec{d} = (8.0 m) \hat{i} + c \hat{j}$ while force $\vec{F} = (2.0 N) i + (4.0 N) j$ acts on it. (Other forces also act on the particle.) What is the value of c if the work done by $\vec{F}$ on the particle is (a) zero, (b) positive, and (c) negative?

Question: Spacing in this book was generally done in units of points and picas: 12 Points = 1 pica , and 6 picas =1 inch. If a figure was misplaced in the page proofs by 0.80cm , what was the misplacement in (a) picas and (b) points?

See all solutions

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