A soccer ball is traveling at a velocity of $50 m / s$. The kinetic energy of the ball is 500 J. What is the mass of the soccer ball? (Formula: $K E=\frac{1}{2} m v^2$)
A. 0.1 kg
B. 0.2 kg
C. 0.4 kg
D. 0.5 kg
Answer (2)
We are given the kinetic energy K E = 500 J and velocity v = 50 m / s of a soccer ball.
We use the formula K E = 2 1 m v 2 to find the mass.
Rearrange the formula to solve for m: m = v 2 2 K E .
Substitute the given values: m = 5 0 2 2 × 500 = 0.4 k g . The mass of the soccer ball is 0.4 k g .
Explanation
Understanding the Problem We are given the kinetic energy (KE) and velocity (v) of a soccer ball, and we need to find its mass (m). We'll use the formula for kinetic energy to solve for the mass.
Rearranging the Formula The formula for kinetic energy is given by: K E = 2 1 m v 2 We need to rearrange this formula to solve for the mass (m).
Isolating the Mass To isolate m, we multiply both sides of the equation by 2 and then divide by v 2 :
2 K E = m v 2 m = v 2 2 K E
Substituting the Values Now, we substitute the given values into the formula. We have KE = 500 J and v = 50 m/s: m = 5 0 2 2 × 500 m = 2500 1000 m = 0.4
Final Answer The mass of the soccer ball is 0.4 kg.
Examples
Understanding kinetic energy is crucial in sports like soccer. When a player kicks a ball, they transfer energy to it, giving it velocity. The kinetic energy of the ball determines how far it travels and how much impact it has. Knowing the mass and velocity, we can calculate the kinetic energy, which helps in analyzing the force and motion involved in the game. For example, coaches can use this to optimize training techniques and improve players' kicking power.
The mass of the soccer ball can be calculated using the formula for kinetic energy, which gives a result of 0.4 kg. After rearranging the formula and substituting the given values, we find that the mass is 0.4 kg. Therefore, the correct answer is C.
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