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Chapter 6: Problem 66

A baseball pitcher can throw a 5.00 -oz baseball with a speed measured by a radar gun to be 90.0 mph. Assuming that the force exerted by the pitcher on the ball acts over a distance of two arm lengths, each 28.0 in, what is the average force exerted by the pitcher on the ball?

Short Answer

Expert verified
Answer: The average force exerted by the pitcher on the ball is approximately 80.23 N.

Step by step solution

01

Convert units

First, let's convert the given values into the standard metric units: weight into mass (kilograms, kg) and speed into meters per second (m/s).
02

Weight to Mass Conversion

To convert the weight of the baseball (5.00 ounces) into mass (kg), use the conversion factor 1 ounce = 0.0283495 kg. Mass of the baseball (m) = 5.00 oz * 0.0283495 kg/oz = 0.141748 kg
03

Speed Conversion

To convert the speed of the baseball (90.0 mph) into meters per second (m/s), use the conversion factor 1 mph = 0.44704 m/s. Speed of the baseball (v) = 90.0 mph * 0.44704 m/s/mph = 40.2336 m/s
04

Distance Conversion

To convert the distance over which the force is exerted (28.0 inches per arm length) into meters (m), use the conversion factor 1 inch = 0.0254 m. Distance (d_arm) = 28.0 inches * 0.0254 m/inch = 0.7112 m Total distance = 2 * d_arm = 2 * 0.7112 m = 1.4224 m
05

Find initial and final kinetic energies

Before the pitcher throws the ball, its initial kinetic energy (KE_initial) is 0, since it's initially at rest. After the pitcher applies force to the ball, the final kinetic energy (KE_final) is given by the formula KE = 0.5 * m * v^2. KE_final = 0.5 * m * v^2 = 0.5 * 0.141748 kg * (40.2336 m/s)^2 ≈ 114.105 J
06

Calculate the work done

Now, we will use the work-energy principle. The equation is Work = KE_final - KE_initial. Since KE_initial is 0, we have: Work = KE_final ≈ 114.105 J
07

Find the average force exerted by the pitcher

Finally, we will find the average force (F_avg) exerted by the pitcher. To do this, we will use the equation: Work = F_avg * Distance F_avg = Work / Distance ≈ 114.105 J / 1.4224 m ≈ 80.23 N The average force exerted by the pitcher on the ball is approximately 80.23 N.

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