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

[hemetite]

Homework Statement

A bicyclist of mass 65kg (including the bicycle) can coast down a 6 degree hill at steady speed of 6km/h because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?

The Attempt at a Solution

since it is at constant speed. the net force is zero.

therefore the

Fg (force due to mg) - Fr (air resistance force) = 0

(mg sin 6) - Fr = 0

Fr= mg sin 6 = 66.58N.

For it to climb back the hill at the same speed and same air restance?

the bicyclist have to tackle the two same force now = 66.58 + mg sin 6 = 133N.

The model answer given is 130N...but i got 133N...

any mistake i have made?

 

[Hootenanny]

Homework Statement

A bicyclist of mass 65kg (including the bicycle) can coast down a 6 degree hill at steady speed of 6km/h because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?

The Attempt at a Solution

since it is at constant speed. the net force is zero.

therefore the

Fg (force due to mg) - Fr (air resistance force) = 0

(mg sin 6) - Fr = 0

Fr= mg sin 6 = 66.58N.

For it to climb back the hill at the same speed and same air restance?

the bicyclist have to tackle the two same force now = 66.58 + mg sin 6 = 133N.

The model answer given is 130N...but i got 133N...

any mistake i have made?

You haven't made any mistakes, perhaps the model answer has rounded to 2sf?

 

[thomate1]

I would first like to commend you on your attempt to solve this problem using the principles of physics. Your approach is correct, and your calculations are accurate. The slight difference in the answer (130N vs 133N) could be due to rounding errors or slight variations in the values used for mass and air resistance. Overall, your solution is a valid and logical explanation for the amount of force required to climb the hill at the same speed and air resistance as coasting down the hill.