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Chapter 1: Problem 25

(a) Calculate the kinetic energy, in joules, of a 15-g bullet moving at $120 \mathrm{~m} / \mathrm{s}$. (b) Convert this energy to calories. (c) When the bullet is stopped by a bulletproof vest, which form of energy does the kinetic energy of the bullet convert to?

Short Answer

Expert verified
The bullet has a kinetic energy of 108 Joules or approximately 25.8 calories. When it is stopped by a bulletproof vest, the kinetic energy mainly converts to heat energy.

Step by step solution

01

Calculate the Kinetic Energy

First, we need to find the kinetic energy (KE) of the bullet. We have the mass in grams (15g), but we need it to be in kilograms for the calculation. To convert mass m from grams to kilograms, divide by 1000: m = 15g / 1000 = 0.015 kg Now we can calculate the kinetic energy using the formula: KE = (1/2)mv^2 Plug in values for mass (m) and velocity (v): KE = (1/2)(0.015 kg)(120 m/s)^2
02

Convert Joules to Calories

Now, we can find the value of the kinetic energy (KE) in Joules: KE = 108 Joules To convert this to calories, we can use the following formula: Calories = Joules / 4.184 Calories = 108 J / 4.184
03

Energy Conversion When Bullet is Stopped by a Bulletproof Vest

When the bullet is stopped by a bulletproof vest, its kinetic energy is converted to another form of energy, mainly heat energy due to the friction between the bullet and the vest's material. Some deformation of the bullet and vest material can also lead to a small amount of other internal energy being generated.
04

Summary

The kinetic energy of the bullet is 108 Joules or approximately 25.8 calories. When the bullet is stopped by a bulletproof vest, the main form of energy it is converted to is heat energy.

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Most popular questions from this chapter

In the process of attempting to characterize a substance, a chemist makes the following observations: The substance is a silvery white, lustrous metal. It melts at \(649^{\circ} \mathrm{C}\) and boils at \(1105^{\circ} \mathrm{C}\). Its density at \(20^{\circ} \mathrm{C}\) is \(1.738 \mathrm{~g} / \mathrm{cm}^{3}\). The substance burns in air, producing an intense white light. It reacts with chlorine to give a brittle white solid. The substance can be pounded into thin sheets or drawn into wires. It is a good conductor of electricity. Which of these characteristics are physical properties, and which are chemical properties?

Water has a density of \(0.997 \mathrm{~g} / \mathrm{cm}^{3}\) at $25^{\circ} \mathrm{C}\(; ice has a density of \)0.917 \mathrm{~g} / \mathrm{cm}^{3}$ at \(-10^{\circ} \mathrm{C}\). (a) If a soft-drink bottle whose volume is $1.50 \mathrm{~L}\( is completely filled with water and then frozen to \)-10^{\circ} \mathrm{C},$ what volume does the ice occupy? (b) Can the ice be contained within the bottle?

What is the number of significant figures in each of the following measured quantities? (a) \(902.5 \mathrm{~kg}\), (b) \(3 \times 10^{-6} \mathrm{~m}\), (c) \(0.0096 \mathrm{~L}\), (d) \(2.94 \times 10^{3} \mathrm{~m}^{2}\) (e) \(92.03 \mathrm{~km}\) (f) \(782.234 \mathrm{~g}\).

Perform the following conversions: (a) 5.00 days to s, (b) \(0.0550 \mathrm{mi}\) to \(\mathrm{m}\) (c) \(\$ 1.89 /\) gal to dollars per liter, (d) 0.510 in. \(/ \mathrm{ms}\) to \(\mathrm{km} / \mathrm{hr}\), (e) \(22.50 \mathrm{gal} / \mathrm{min}\) to \(\mathrm{L} / \mathrm{s}\), (f) \(0.02500 \mathrm{ft}^{3} \mathrm{to} \mathrm{cm}^{3}\)

The distance from Earth to the Moon is approximately \(240,000 \mathrm{mi}\). (a) What is this distance in meters? (b) The peregrine falcon has been measured as traveling up to \(350 \mathrm{~km} /\) hr in a dive. If this falcon could fly to the Moon at this speed, how many seconds would it take? (c) The speed of light is \(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\). How long does it take for light to travel from Earth to the Moon and back again? (d) Earth travels around the Sun at an average speed of $29.783 \mathrm{~km} / \mathrm{s}$. Convert this speed to miles per hour.
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