Question

a cyclist coasting down a 5.0 ◦ incline at a constant speed of 6.0 km/h because of air resistance. If the total mass of the bicycle + cyclist is 50 kg, how much force must be generated to climb back up the incline at the same speed (and same air resistance)?

Answer 1

`F_(net)= 85.41\ N`

Step-by-step explanation:

mass of the bicycle + cyclist = 50 kg

constant speed = 6 km/h

a cyclist coasting down a 5.0° incline

the downward velocity is constant, so net acceleration must be zero

the air drag must be equal to gravitational force downward along the ramp

`F_a = mg sin \theta`

now for upward motion

`F_(net) = mg sin \theta + air\ drag`

`F_(net) = mg sin \theta + mg sin \theta`

`F_(net) = 2 mg sin \theta`

`F_(net) = 2* 50 * 9.8 sin 5^0`

`F_(net)= 85.41\ N`