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

In summary: Hint: Use Pythagoras.)In summary, a cyclist is competing in a one-lap race on a flat, circular course of radius r. Starting from rest and accelerating at a constant rate, the cyclist completes the race in time t. The mass of the bicycle and rider is m. To find the magnitude of the net force acting on the bicycle at the finish line, we need to use Newton's 2nd law to calculate the tangential force, which is equal to (m4pi*r)/t^2. Next, we need to find the radial acceleration by using the speed of the cyclist as they cross the finish line. Finally, we can use Pythagoras' theorem to find the total acceleration and thus,
  • #1
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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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  • #2
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?
 
  • #3


Hi there,

To calculate the net force acting on the cyclist at the finish line, we first need to understand the forces acting on the cyclist throughout the race.

The cyclist is starting from rest and speeding up at a constant rate, which means that there is an acceleration acting on the cyclist. This acceleration can be found using the formula a = v/t, where v is the final velocity and t is the time taken to reach that velocity.

In this case, the final velocity is equal to the circumference of the circular course divided by the time taken to complete one lap, which is t. So, v = 2πr/t.

Using Newton's second law, we can calculate the tangential force acting on the cyclist as F(t) = ma = m(v/t) = m(2πr/t^2).

Next, we need to consider the radial force acting on the cyclist. Since the race is taking place on a flat, circular course, the only radial force acting on the cyclist is the normal force from the ground. This normal force is equal in magnitude but opposite in direction to the weight of the cyclist and bicycle, which is given by mg.

Therefore, the net radial force acting on the cyclist is F(r) = mg.

Now, we can use the Pythagorean theorem to find the magnitude of the net force acting on the cyclist at the finish line:

F(net) = √(F(t)^2 + F(r)^2)

= √[(m(2πr/t^2))^2 + (mg)^2]

= √[(4π^2mr^2)/t^4 + m^2g^2]

= m√[(4π^2r^2)/t^4 + g^2]

Therefore, the magnitude of the net force acting on the cyclist at the finish line is dependent on the mass of the cyclist and bicycle, the radius of the circular course, the time taken to complete one lap, and the acceleration due to gravity.

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

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

1. What is the formula for calculating F(net)?

The formula for calculating F(net) is F(net) = ma, where F(net) is the net force, m is the mass of the object, and a is the acceleration.

2. How do you determine the direction of F(net)?

The direction of F(net) is determined by the direction of the acceleration. If the acceleration is in the same direction as the force, then the net force is positive. If the acceleration is in the opposite direction, then the net force is negative.

3. What units are used for F(net)?

The units for F(net) depend on the units used for mass and acceleration. In the SI system, the units for F(net) are Newtons (N), which is equal to kg * m/s^2.

4. Can F(net) be a negative value?

Yes, F(net) can be a negative value. This indicates that the net force is acting in the opposite direction of the acceleration. It is important to pay attention to the sign of the net force when analyzing the motion of an object.

5. How does air resistance affect F(net) for a cyclist at the finish line?

Air resistance can create a force in the opposite direction of the cyclist's motion, which would decrease the net force acting on the cyclist. This can result in a slower speed at the finish line. However, the exact impact of air resistance on F(net) would depend on factors such as the cyclist's speed, body position, and the aerodynamics of their bike and clothing.

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