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.
We use 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 the mass: m = ( 20 ) 2 2 × ( 1.8 × 1 0 5 ) = 900 kg. The final answer is 9.0 × 1 0 2 kilograms.
Explanation
Problem Analysis We are given that a car is moving with a velocity of 20 m/s and has a kinetic energy of 1.8 × 1 0 5 joules. We need to find the mass of the car.
Kinetic Energy Formula The formula for kinetic energy (KE) is given by: K E = 2 1 m v 2 where:
KE is the kinetic energy (in joules)
m is the mass (in kilograms)
v is the velocity (in meters/second)
Rearranging the Formula We are given K E = 1.8 × 1 0 5 joules and v = 20 m/s. We need to find the mass 'm'. We can rearrange the formula to solve for m: m = v 2 2 × K E
Substituting the Values Now, we substitute the given values into the formula: m = ( 20 ) 2 2 × ( 1.8 × 1 0 5 ) m = 400 2 × 180000 m = 400 360000 m = 900
Final Answer Therefore, the mass of the car is 900 kilograms, which can be written as 9.0 × 1 0 2 kilograms.
Examples
Understanding kinetic energy is crucial in various real-world scenarios. For instance, when designing vehicles, engineers must consider the kinetic energy involved in collisions to enhance safety features. The mass and velocity of a vehicle directly impact its kinetic energy, influencing the severity of an impact. By calculating and understanding these relationships, engineers can develop effective safety measures such as airbags and crumple zones to minimize injuries during accidents. This ensures vehicles are designed to protect occupants by managing and dissipating kinetic energy efficiently.
The mass of the car, calculated using the kinetic energy and velocity provided, is 900 kilograms, or 9.0 × 1 0 2 kilograms. Therefore, the correct answer is option B: 9.0 × 1 0 2 kilograms.
;
