Physics Help. Involves Kinetic energy.

Question

Describe how changing the fluid density, drag coefficient, and area of the ball affect the Kinetic energy of the ball?

Answer 1

When looking at the kinetic energy of a ball and how it changes with different variables changing, all we need to know is what happens to how fast the ball is able to move. This is because the equation for kinetic energy is...

 

KE = (1/2)*m*v^2

 

The mass of the ball is not going to change, so the only way the kinetic energy could change is by changing the velocity.

 

As a ball moves through a fluid, such as the atmosphere, that fluid gives some resistance to the object. When the density of the fluid increases, the ball has to 'push' a heavier amount of fluid out of the way. This causes the ball to slow down.

 

The second variable is the drag coefficient. The higher the drag coefficient, the more drag or resistance the object feels as it tries moving through a fluid. When you increase the drag coefficient, you add more resistance to the ball, causing it to slow down.

 

Finally, when you increase your area, you are allowing more fluid to 'run into' the ball. This is how parachutes work. When a person is falling from a plane, he is moving through the fluid (air). If he stands straight up and down, the only area the air can really hit is the bottom of his feet and he will fall very fast. If the sky-diver wants to slow down, they open up their parachute. Opening your parachute dramatically increases your area and allows a lot more of the fluid molecules to run into them, slowing them down.

Answer 2

The kinetic energy of the ball is KE = 1/2 mv² , where m is the mass and v is the velocity. Therefore when the ball is moving in air, the drag coefficient Cd decreases the velocity and subsequent kinetic energy when it increases because the amount of drag force increases and slows down the ball. The frontal area of the ball increases the drag coefficient and the drag force as it increases and reduces both velocity and kinetic energy. An example of this is an open umbrella on the back of a speed car that increase the frontal area, increases the drag force thereby reducing both its velocity and kinetic energy. When the ball is moving in fluid, the drag coefficient Cd and Drag force increase with an increase in fluid density and and the velocity and kinetic energy decrease. The general formula fir Drag force is Fd=−0.5ρv2ACdv^ notice that density ρ, frontal area A , and drag coefficient Cd are all directly proportional to the Drag Force Fd in the equation. Therefore, an increase in any of these variables will result in an increase in the drag force and subsequent decrease in kinetic energy.