Calculate Drag Force for Tennis Ball at 251 km/h

It should be 69.72 m/s. Also, make sure you are using the correct value for air viscosity. You have written it as 1.8x10-5 kg.m-1.s-1, but it should be 1.8x10-5 kg/m.s. In summary, to calculate the Drag Force acting on a tennis ball hit at a speed of 251 km/h in a match, one must first find the Reynolds number, which is equal to the product of air density, velocity, diameter of the ball, and air viscosity, divided by air viscosity. Then, a graph of drag coefficient against Reynolds number can be used to find the drag coefficient, which can then be used in the equation F
  • #1
steve978
1
0

Homework Statement



A tennis player hit a serve of 251 km.h-1 in a match. Calculate the Drag Force acting on the tennis ball. Diameter of ball is 6.5cm, density of air is 1.3 kg.m-3 and air viscosity is 1.8x10-5 kg.m-1.s-1.

Homework Equations



Drag Force is: Fd= [itex]\pi[/itex].d2.CD.pf.u2.1/4

The Attempt at a Solution



My attempt is to find Reynolds number: Rep = (pfutdp)/u = (1.3)(903,600,000)(0.065)/0.000018
and then use a graph of drag coefficient against Rep to find Cd. However my number for Re is 4.24E+13 which is far too large to be correct. Is there something i am doing wrong?
 
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  • #2
Hello steve978.

Check your conversion of km/h to m/s.
 

1. How is drag force calculated for a tennis ball at 251 km/h?

The drag force on a tennis ball can be calculated using the formula Fd = 0.5 * ρ * Cd * A * V^2, where ρ is the density of air, Cd is the drag coefficient, A is the cross-sectional area of the ball, and V is the velocity.

2. What is the density of air used in the calculation of drag force?

The density of air used in the calculation of drag force is typically 1.225 kg/m^3 at sea level and standard temperature and pressure.

3. What is the drag coefficient for a tennis ball?

The drag coefficient for a tennis ball can vary depending on the surface of the ball, but it is typically between 0.2-0.5.

4. How does the velocity of the tennis ball affect the drag force?

The drag force increases as the velocity of the tennis ball increases. This is because the formula for drag force includes the square of the velocity, meaning that a small increase in velocity can lead to a much larger increase in drag force.

5. How can the drag force on a tennis ball be reduced at 251 km/h?

The drag force on a tennis ball can be reduced by changing the surface of the ball to one with a lower drag coefficient, or by reducing the velocity of the ball. Additionally, aerodynamic designs, such as dimpled surfaces, can help reduce drag force on a tennis ball at high speeds.

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