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Chapter 5: Problem 16

(a) A baseball weighs 5.13 oz. What is the kinetic energy in joules of this baseball when it is thrown by a major-league pitcher at \(95.0 \mathrm{mph}\) ? (b) By what factor will the kinetic energy change if the speed of the baseball is decreased to \(55.0 \mathrm{mph} ?\) (c) What happens to the kinetic energy when the baseball is caught by the catcher? (d) What careful experimental measurement could (in principle) be made to confirm your answer to (c)?

Short Answer

Expert verified
The kinetic energy of a 5.13 oz baseball thrown at 95 mph is approximately 131.94 J. When the speed is decreased to 55 mph, the kinetic energy changes by a factor of about 0.328. The kinetic energy is ideally reduced to zero when caught by the catcher. A measurement to confirm this would involve tracking motion and force data to calculate the work done during the catching process, which should be equal to the initial kinetic energy.

Step by step solution

01

(a) Convert units

First, convert the weight of the baseball from ounces to kilograms: 1 oz = 0.0283495 kg, so 5.13 oz = 5.13 × 0.0283495 kg ≈ 0.145 kg. Now, convert the speed from mph to m/s: 1 mph = 0.44704 m/s, so 95 mph = 95 × 0.44704 m/s ≈ 42.47 m/s.
02

(a) Calculate kinetic energy

Now, we can calculate the kinetic energy using the formula: KE = 0.5 × m × v^2 where KE is the kinetic energy, m is the mass of the baseball (0.145 kg), and v is its speed (42.47 m/s). KE = 0.5 × 0.145 kg × (42.47 m/s)^2 ≈ 131.94 J Thus, the kinetic energy of the baseball is approximately 131.94 joules.
03

(b) Calculate new kinetic energy

First, convert the new speed from mph to m/s: 55 mph = 55 × 0.44704 m/s ≈ 24.58 m/s. Now, calculate the kinetic energy at the decreased speed: KE_new = 0.5 × 0.145 kg × (24.58 m/s)^2 ≈ 43.34 J
04

(b) Calculate change factor

Divide the new kinetic energy value by the initial kinetic energy value to determine the factor by which the kinetic energy changes: factor = 43.34 J / 131.94 J ≈ 0.328 The kinetic energy changes by a factor of approximately 0.328.
05

(c) Kinetic energy when caught

When the baseball is caught by the catcher, its speed decreases rapidly to zero. A decrease in speed results in a decrease in kinetic energy. Therefore, when the baseball is caught, the kinetic energy is ideally reduced to zero.
06

(d) Experiment to confirm answer

In principle, a careful experimental measurement to confirm the answer to (c) could involve tracking the motion and force of the baseball during and after it is caught by the catcher. This data can be used to calculate the work done by the catcher's hand and glove during the process, which should be equal to the initial kinetic energy of the baseball. If the work done is equal to the initial kinetic energy, it would confirm that the kinetic energy was indeed reduced to zero when the baseball was caught.

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Most popular questions from this chapter

(a) Why are tables of standard enthalpies of formation so useful? (b) What is the value of the standard enthalpy of formation of an element in its most stable form? (c) Write the chemical equation for the reaction whose enthalpy change is the standard enthalpy of formation of sucrose (table sugar), \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s), \Delta H_{f}^{\circ}\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right]\)

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