Calculate F(net): Net Force Acting on Cyclist at Finish Line

AI Thread Summary
To calculate the net force acting on a cyclist at the finish line of a circular race, the cyclist's motion must be analyzed in terms of tangential and radial components. The net tangential force is derived from the formula (m4pi*r)/t^2, reflecting the cyclist's acceleration. Newton's second law is essential for determining the tangential force, while the radial force relates to the cyclist's speed as they cross the finish line. The total acceleration combines both tangential and radial accelerations, which are necessary for calculating the net force. Ultimately, expressing the net force in terms of radius, time, mass, and pi is crucial for solving the problem.
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"A cyclist competes in a one-lap race around a flat, circular course of radius r . Starting from rest and speeding up at a constant rate throughout the race, the cyclist covers the entire course in a time t. The mass of the bicycle (including the rider) is m. What is the magnitude of the net force acting on the bicycle as it crosses the finish line?

Find F(net), the magnitude of the net force acting on the cyclist at the finish line.

Express the net force in terms of r, t,m , and pi."


First I tried to break it down into components.

F(net) = sqrt (net tangential force^2 + net radial force^2)

net tangential force = (m4pi*r)/t^2

I know that I will need to use Newton's 2nd law to find the tangential force. But I can't figure out how to do this.

As for the net radial force I know that I somehow need to use tangential force but since I'm stuck there that's as far as I got.

Thanks.
 
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Do it step by step:
- What's the tangential acceleration? (You found it already.)
- What's the radial acceleration? (Hint: What's the speed as he passes the finish line?
- What's the total acceleration?
 
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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