Question

A bicycle with a mass of 10.0 kg is pushed up an incline of 30 ° with respect to the horizon. Friction is assumed to be negligible. a) Draw the free body diagram. b) It determines the intensity of the force which, applied horizontally, makes the bicycle move forward at a constant speed. c) Determines the intensity of the force which, applied horizontally, moves the bicycle forward with an acceleration of 100 m / s²

Answer 1

Answer:

a) The free body diagram is drawn in the explanation section

b) The intensity of the force applied horizontally which makes the bicycle move forward at a constant speed = 49.05 N

c) The intensity of the force applied horizontally which makes the bicycle move forward with an acceleration of 100 m/s² = 1049.05N

Explanation:

The mass of the bicycle, m = 10.0 kg

Angle of inclination, θ = 30°

The free body diagram of the illustration is drawn below

The bicyce is pushed up an incline of 30°

The weight of the bicycle acts downward (because the weight of every object acts downward)

Since the bicycle is pushed up an inclined of 30°, the force has to be resolved to the vertical(mgcosθ) and horizontal(mgsinθ)

b) The net force on the bicycle is:

$\sum F=mg\sin \theta+ma$

If the bicycle moves at constant speed, the acceleration is 0 m/s²

a = 0m/s²

$\begin{gathered} \sum F=10(9.81)\sin 30+10(0) \\ \sum F=10(9.81)(0.5) \\ \sum F=49.05N \end{gathered}$

c) The intensity of the force applied horizontally which moves the bicycle forward with an acceleration of 100 m/s²

$\begin{gathered} \sum F=10(9.81)\sin 30+10(100) \\ \sum F=49.05+1000 \\ \sum F=1049.05N \end{gathered}$