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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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Most popular questions from this chapter

An arrow is placed on a bow, the bowstring is pulled back, and the arrow is shot straight up into the air; the arrow then comes back down and sticks into the ground. Describe all of the changes in work and energy that occur.

A father exerts a \(2.40 \cdot 10^{2} \mathrm{~N}\) force to pull a sled with his daughter on it (combined mass of \(85.0 \mathrm{~kg}\) ) across a horizontal surface. The rope with which he pulls the sled makes an angle of \(20.0^{\circ}\) with the horizontal. The coefficient of kinetic friction is \(0.200,\) and the sled moves a distance of \(8.00 \mathrm{~m}\). Find a) the work done by the father, b) the work done by the friction force, and c) the total work done by all the forces.

A particle is moving along the \(x\) -axis subject to the potential energy function \(U(x)=1 / x+x^{2}+x-1\) a) Express the force felt by the particle as a function of \(x\). b) Plot this force and the potential energy function. c) Determine the net force on the particle at the coordinate \(x=2.00 \mathrm{~m}\)

A spring with a spring constant of \(500 . \mathrm{N} / \mathrm{m}\) is used to propel a 0.500 -kg mass up an inclined plane. The spring is compressed \(30.0 \mathrm{~cm}\) from its equilibrium position and launches the mass from rest across a horizontal surface and onto the plane. The plane has a length of \(4.00 \mathrm{~m}\) and is inclined at \(30.0^{\circ} .\) Both the plane and the horizontal surface have a coefficient of kinetic friction with the mass of \(0.350 .\) When the spring is compressed, the mass is \(1.50 \mathrm{~m}\) from the bottom of the plane. a) What is the speed of the mass as it reaches the bottom of the plane? b) What is the speed of the mass as it reaches the top of the plane? c) What is the total work done by friction from the beginning to the end of the mass's motion?

Can the kinetic energy of an object be negative? Can the potential energy of an object be negative?
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