If a bowling ball and a ping-pong ball both move with the same kinetic energy, can you say which has a greater speed? Explain in terms of Kinetic Energy
Answers
Because the momenta of the two balls are equal, the ball with the larger velocity has the larger kinetic energy. Being that the ping-pong ball has a smaller inertial mass, it must therefore have the larger kinetic energy. This means more work must be done on the ping-pong ball than on the bowling ball.
Answer:
The ping pong ball, the light molecules have greater speed
Explanation:
The kinetic energy of an object is defined as
K=\frac{1}{2}mv^2K=21mv2
where
m is the mass of the object
v is its speed
It follows that the speed can be written as
v=\sqrt{\frac{2K}{m}}v=m2K
In this problem, both the golf ball and the ping pong ball have kinetic energy K. However, the mass of a gold ball is larger (approx. 45 g) than that of a ping pong ball (approx. 4 g): therefore, since v is inversely proportional to the square root of the mass, it follows that the ping pong ball must have a greater speed in order to achieve the same kinetic energy of the golf ball.
The same argument can be applied to the gaseous mixture: if there are more massive molecules and light molecules, and if they all have the same kinetic energy, then this means that the light molecules must have a greater speed, as a result again of the equation
v=\sqrt{\frac{2K}{m}}v=m2K