Estimating Spin on a Soccer Ball Kicked from Corner

[ryanmeyer2003]

Homework Statement

A player kicks a ball into the goal on a free kick in soccer from the corner. We are to ultimatly estimate the spin on the ball. In part one of the question, we are to find the flight time of the ball. The ball reaches 5 meters off the ground.

Next, we assume the player kicked the ball from the exact corner of the field, which is 65 meters wide, and the ball lands exactly in the middle of the net. So the ball traveled 65 meters/2= 32.5 meters, what was the Y component of the ball's velocity?

The ball was kicked at an 85 degree angle, what was the X component of the ball's initial velocity? (Apparently, the tangent function will be useful here)

What is the accelleration in the X direction?

With the radius of the ball being .111 meters, and its mass being .425 kg, and based on the answer above, what is the magnus force? And, how fast (rev/second) was the ball spinning?

Homework Equations

T=2square root 2h/g
Vy=V0y+G(t)
Vy^2=V0y^2+2(ay)(Change in y)

The Attempt at a Solution

I have found the flight time to be 2.02 seconds, and I used that equation in the velocity in the Y direction and found the velocity in the Y direction to be 25.23 m/s. What I am stuck on is the X component of the balls initial velocity. I feel like I will be able to find the acceleration in the X direction by using the formula ax=Fx/mass.

Any help would be greatly appreciated, thank you.

 

[anathema]

Hello,

It seems like you are on the right track! To find the X component of the ball's initial velocity, you can use the tangent function as mentioned in the question. The tangent of an angle is equal to the opposite side divided by the adjacent side, so in this case it would be tan(85)=V0x/25.23. Rearranging this equation, we get V0x=25.23*tan(85)= 122.28 m/s.

To find the acceleration in the X direction, you can use the formula ax=Fx/mass, where Fx is the horizontal component of the force acting on the ball. In this case, the only force acting on the ball in the horizontal direction would be the Magnus force. To find the Magnus force, you can use the formula Fm=1/2*p*v*w*L, where p is the density of air, v is the velocity of the ball, w is the angular velocity (in radians/second) and L is the diameter of the ball. From the given information, we can find that p=1.2 kg/m^3, v=122.28 m/s, and L=0.222 m. The angular velocity, w, can be found using the formula w=V/R, where V is the linear velocity of the ball (122.28 m/s) and R is the radius of the ball (0.111 m). This gives us an angular velocity of w=1104.32 rad/s. Plugging all of these values into the formula for the Magnus force, we get Fm=1/2*1.2*122.28*1104.32*0.222=1457.77 N.

Finally, to find the speed of the ball's spin, we can use the formula w=V/R, where V is the linear velocity of the ball (122.28 m/s) and R is the radius of the ball (0.111 m). This gives us an angular velocity of w=1104.32 rad/s. To find the speed of the spin in revolutions per second, we can convert the angular velocity from radians/second to revolutions/second by dividing by 2*pi, giving us a spin speed of approximately 175.59 revolutions per second.

I hope this helps! Let me know if you have any further questions.