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The masses of the javelin, discus, and shot are 0.80 kg, 2.0 kg, and 7.2 kg, respectively, and record throws in the corresponding track events are about 98 m, 74 m, and 23 m, respectively. Neglecting air resistance, (a) calculate the minimum initial kinetic energies that would produce these throws, and (b) estimate the average force exerted on each object during the throw, assuming the force acts over a distance of 2.0 m. (c) Do your results suggest that air resistance is an important factor?

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College Physics

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781285737027

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Section
BuyFindarrow_forward

College Physics

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781285737027
Chapter 5, Problem 84AP
Textbook Problem
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The masses of the javelin, discus, and shot are 0.80 kg, 2.0 kg, and 7.2 kg, respectively, and record throws in the corresponding track events are about  98 m, 74 m, and 23 m, respectively. Neglecting air resistance, (a) calculate the minimum initial kinetic energies that would produce these throws, and (b) estimate the average force exerted on each object during the throw, assuming the force acts over a distance of 2.0 m. (c) Do your results suggest that air resistance is an important factor?

(a)

To determine
The minimum initial kinetic energy of the throws.

Explanation of Solution

Given Info: The mass of the javelin is 0.80kg , the record throw in javelin is 98m .

Expression used for finding horizontal displacement of a projectile.

R=v02sin(2θ)g

  • v0 is the launching speed of the projectile
  • R is the horizontal displacement of a projectile
  • θ is the angle of the projectile with the horizontal
  • g is the acceleration due to gravity

Expression used for the maximum horizontal displacement of a projectile.

Rm=v02g

  • Rm is the maximum horizontal displacement of a projectile

Re-write the expression for the launching speed of the projectile.

v02=Rmg (I)

Expression used for a minimum kinetic energy to reach a given maximum range.

KE=12mv02 (II)

  • KE is the kinetic energy to reach a given maximum range
  • m is the mass of the projectile

Substitute equation (I) in (II) to find the minimum kinetic energy to reach a given maximum range.

KE=12mgRm

Substitute 0.80kg for m, 9.8m/s2 for g and 98m for Rm to find the minimum kinetic energy to reach a given maximum range.

KE=12(0.80kg)(9.8m/s2)(98m)=3.8×102J

Expression used to calculate the minimum kinetic energy of the discus throw.

KE=12mgRm

Substitute 2

(b)

To determine
Average force exerted on each object during the throw.

(c)

To determine
Whether the air-resistance is an important factor in the throws.

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