A soccer ball is traveling at a velocity of [tex]$50 m / s$[/tex]. The kinetic energy of the ball is 500 J. What is the mass of the soccer ball?
A. 0.1 kg
B. 0.4 kg
C. 5 kg
Answer (1)
We are given the kinetic energy ( K E = 500 J ) and velocity ( v = 50 m / s ) of a soccer ball.
We use the kinetic energy formula K E = 2 1 m v 2 and rearrange it to solve for mass: m = v 2 2 K E .
Substituting the given values, we calculate the mass: m = 5 0 2 2 × 500 = 0.4 k g .
The mass of the soccer ball is 0.4 kg .
Explanation
Understanding the Problem We are given the kinetic energy ( K E ) and velocity ( v ) of a soccer ball and asked to find its mass ( m ). We know that the kinetic energy is given by the formula: K E = 2 1 m v 2 where:
K E is the kinetic energy in Joules (J)
m is the mass in kilograms (kg)
v is the velocity in meters per second (m/s)
Rearranging the Formula We need to rearrange the kinetic energy formula to solve for the mass m . Multiplying both sides of the equation by 2, we get: 2 × K E = m v 2 Now, divide both sides by v 2 to isolate m :
m = v 2 2 K E
Substituting the Values Now, we substitute the given values into the formula. We are given that K E = 500 J and v = 50 m/s . Plugging these values into the equation, we get: m = 5 0 2 2 × 500 m = 2500 1000 m = 0.4 kg
Final Answer Therefore, the mass of the soccer ball is 0.4 kg.
Examples
Understanding kinetic energy and mass calculations is crucial in sports science. For example, when designing safer helmets, engineers need to calculate the mass and impact velocity to ensure the helmet can absorb the energy and protect the athlete. Similarly, in manufacturing, knowing the kinetic energy of moving parts helps in designing efficient and safe machinery. This principle applies in various fields, from automotive safety to aerospace engineering, where understanding the relationship between mass, velocity, and energy is essential for designing safer and more efficient systems.
