How Much Force is Needed to Climb a Hill at Constant Speed with Air Resistance?

AI Thread Summary
To determine the force needed for a bicyclist to climb a 6.90-degree hill at a constant speed of 5.80 km/hr, the net force must account for gravitational pull and air resistance. The cyclist's mass is 68.0 kg, and while descending, the force of air resistance can be calculated based on the steady speed condition. The equations of motion indicate that the sum of forces in the x-direction equals the gravitational component minus the air resistance. The key is to recognize that at steady speed, the net force is zero, allowing for the deduction of air resistance from the downhill scenario to apply it to the uphill case. Understanding these dynamics is crucial for solving the problem accurately.
BMWPower06
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Homework Statement


If a bicyclist of mass 68.0 kg (including the bicycle) can coast down a 6.90 degree hill at a steady speed of 5.80 km/hr because of air resistance, how much force must be applied to climb the hill at the same speed (and the same air resistance)?


Homework Equations


The air resistance equations don't seem to apply.

F=MA as always


The Attempt at a Solution


I drew the FBD, tried to sum the forces and got:
The sum of forces in x= mgsino-Fa (force of air resistance)= ma
Sum of forces in y= N-mgcoso=0

Can anyone help me out?
Thanks
 
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BMWPower06 said:

Homework Statement


If a bicyclist of mass 68.0 kg (including the bicycle) can coast down a 6.90 degree hill at a steady speed of 5.80 km/hr because of air resistance, how much force must be applied to climb the hill at the same speed (and the same air resistance)?


Homework Equations


The air resistance equations don't seem to apply.

F=MA as always


The Attempt at a Solution


I drew the FBD, tried to sum the forces and got:
The sum of forces in x= mgsino-Fa (force of air resistance)= ma
Sum of forces in y= N-mgcoso=0

Can anyone help me out?
Thanks
What is the value of the acceleration in the x direction along the incline, if the bicyclist is moving at steady speed?
 
Use the data provided in the downhill case to figure out the magnitude of the air resistance. Then apply that to the uphill case.
 
Doc Al said:
Use the data provided in the downhill case to figure out the magnitude of the air resistance. Then apply that to the uphill case.

im confused as to which formula i use for air resistance.
 
You won't calculate the air resistance directly; instead, you'll deduce it from the fact that the bicyclist moves at a steady speed. What does that tell you about the net force on him?
 

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