Select the correct answer.
A car moving with a velocity of 20 meters/second has [tex]$1.8 \times 10^5$[/tex] joules of kinetic energy. What is the mass of the car?
A. [tex]$4.6 \times 10^2$[/tex] kilograms
B. [tex]$9.0 \times 10^2$[/tex] kilograms
C. [tex]$1.0 \times 10^3$[/tex] kilograms
D. [tex]$1.2 \times 10^3$[/tex] kilograms
Answer (2)
The problem provides the kinetic energy and velocity of a car and asks for its mass.
Recall the kinetic energy formula: K E = 2 1 m v 2 .
Rearrange the formula to solve for mass: m = v 2 2 K E .
Substitute the given values and calculate: m = ( 20 ) 2 2 × ( 1.8 × 1 0 5 ) = 900 kilograms. The final answer is 9.0 × 1 0 2 kilograms.
Explanation
Problem Analysis We are given the kinetic energy and velocity of a car and asked to find its mass. We will use the formula for kinetic energy to solve for the mass.
Kinetic Energy Formula The kinetic energy (KE) of an object is given by the formula: K E = 2 1 m v 2 where:
K E is the kinetic energy in joules,
m is the mass in kilograms,
v is the velocity in meters per second.
Solving for Mass We need to rearrange the formula to solve for the mass m :
m = v 2 2 K E
Substituting Values Now, we substitute the given values into the formula. We are given that K E = 1.8 × 1 0 5 joules and v = 20 meters/second. Therefore, m = ( 20 ) 2 2 × ( 1.8 × 1 0 5 ) m = 400 3.6 × 1 0 5 m = 400 360000 m = 900
Final Answer The mass of the car is 900 kilograms, which can be written as 9.0 × 1 0 2 kilograms. Therefore, the correct answer is B.
Examples
Understanding kinetic energy is crucial in various real-world scenarios, such as designing safer vehicles. For instance, engineers use the principles of kinetic energy to calculate the impact force during a collision and design car bumpers that can absorb energy, reducing the severity of injuries. Also, in sports, understanding kinetic energy helps athletes optimize their performance, like a baseball player maximizing the kinetic energy transferred to the ball during a swing to hit it farther.
The mass of the car, calculated from its kinetic energy of 1.8 x 10^5 joules and velocity of 20 m/s, is 900 kilograms, which can also be expressed as 9.0 x 10^2 kilograms. Therefore, the correct answer is option B.
;
