Magnitude of the average force exerted by ground on a ball.

AI Thread Summary
The discussion revolves around calculating the average force exerted by the ground on a basketball after it bounces. The basketball, with a mass of 0.625 kg and an initial speed of 3.30 m/s, loses half of its kinetic energy upon bouncing, resulting in a post-bounce speed of 2.33 m/s. Participants highlight the importance of considering gravitational force when calculating the change in velocity (Δv) for the average force equation. The correct approach involves recognizing that the initial and final velocities have opposite directions, which affects the calculation of net force. Understanding these dynamics is crucial for accurately determining the average force, which was initially miscalculated.
NinjaChachi
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Homework Statement


Just before hitting the ground, a partially inflated 0.625kg basketball has a speed of 3.30m/s. Then it loses half of its kinetic energy as it bounces. (A)What is the ball's speed immediately after it bounces?(B) If the ball is in contact with the ground for 9.25ms, what is the magnitude of the average force exerted by the ground on the ball?

Homework Equations


None of these are positive but:
KE=.5mv^2
Fav=m(Δv)/(Δt)

The Attempt at a Solution


I found part A I believe. I just found the initial KE in that being KE=.5(.625)(3.30)^2 and got KE0=3.4
then it loses half so KEf=1.7 so to find the velocity I set up 1.7=.5(.625)v^2 and found the final velocity to be 2.33m/s.

I am quite confused on part B. I have tried m(Δv)/(Δt) to find the Fav but didn't get the right answer (381N). What do I do?
 
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NinjaChachi said:
I found part A I believe. I just found the initial KE in that being KE=.5(.625)(3.30)^2 and got KE0=3.4
then it loses half so KEf=1.7 so to find the velocity I set up 1.7=.5(.625)v^2 and found the final velocity to be 2.33m/s.
Good.

NinjaChachi said:
I am quite confused on part B. I have tried m(Δv)/(Δt) to find the Fav but didn't get the right answer (381N). What do I do?
What did you use for Δv? Did you take gravity into account?
 
Doc Al said:
Good.What did you use for Δv? Did you take gravity into account?
No I didn't use gravity. I just used 3.3-2.33 and tried 2.33-3.3. How would I take gravity into account?
 
NinjaChachi said:
No I didn't use gravity. I just used 3.3-2.33 and tried 2.33-3.3.
Try that again. Realize that the final and initial velocities have different directions.

NinjaChachi said:
How would I take gravity into account?
Realize that m(Δv)/(Δt) will give you the average net force. What forces act on the ball during the collision with the ground?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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