Find energy dissipated due to air friction in a thrown ball

[Gashouse]

A 0.40 kg ball is thrown vertically upward with a speed of 30 m/s. The ball reaches a height of 40 m. Assuming g= 9.8 m/s^2, the energy dissipated due to air friction is :


F=mgh m=0.40kg, g=10 m/s^2, h=40m, a= 30 m/s

Not sure if I set this problem up right, and since everything is given don't know how to find energy dissipated due to friction.

 

[OlderDan]

A 0.40 kg ball is thrown vertically upward with a speed of 30 m/s. The ball reaches a height of 40 m. Assuming g= 9.8 m/s^2, the energy dissipated due to air friction is :


F=mgh m=0.40kg, g=10 m/s^2, h=40m, a= 30 m/s

Not sure if I set this problem up right, and since everything is given don't know how to find energy dissipated due to friction.

Can you calculate the initial energy of the ball, and the energy it has when it reaches the highest point?

F is not mgh. mgh is potential energy.
30 m/s is not acceleration, it is the initial velocity.

 

[thepatientmental]

To calculate the energy dissipated due to air friction, we need to first calculate the work done by the force of air friction. The work done by a force is given by the formula W = Fd, where F is the force and d is the displacement.

In this case, the force of air friction is opposing the motion of the ball, so it is acting in the opposite direction of the displacement. Therefore, we need to use the negative value of the force of air friction in our calculation.

The force of air friction can be calculated using the formula F = 0.5*Cd*rho*A*v^2, where Cd is the coefficient of drag, rho is the air density, A is the cross-sectional area of the ball, and v is the velocity of the ball.

Since we are assuming that the ball is a perfect sphere, we can use the formula for the cross-sectional area of a sphere, which is A = 4*pi*r^2, where r is the radius of the ball.

The coefficient of drag for a smooth sphere is approximately 0.47, and the air density at sea level is approximately 1.2 kg/m^3.

Plugging in all the values, we get F = 0.5*0.47*1.2*4*pi*(0.20)^2*(30)^2 = 7.12 N

Now, we can calculate the work done by this force using the formula W = Fd. Since the ball is moving vertically, the displacement is equal to the height it reaches, which is 40 m.

Therefore, W = (-7.12 N)*(40 m) = -284.8 J

Since the work done by the force of air friction is negative, it means that the energy is being dissipated or lost. Therefore, the energy dissipated due to air friction in this case would be 284.8 J.