Question

Your mission to Mars team needs a mars rover to slide down a frictionless ramp as shown to the right if the max acceleration that the rover can handle down the ramp before breaking apart is 0.513 m/s squared A. what is the maximum angle that the ramp can be made with the horizontal?B. Use your answer from A & the fact that Mars has a rover mass is 1025 kg to find the normal force on the inclined plane?

Answer 1

Given,

The maximum acceleration that the rover can handle, a=0.513 m/s²

(A)

The rover slides down the ramp under the influence of gravity. The component of the gravity that provides the rover with the required acceleration is the component that is along the ramp.

Thus,

`g\sin \theta=a`

Where g is the acceleration due to gravity and θ is the angle of inclination of the ramp.

On substituting the known values,

`\begin{gathered} 9.8*\sin \theta=0.513 \\ \Rightarrow\theta=\sin ^(-1)((0.513)/(9.8)) \\ =3\degree \end{gathered}`

Thus the maximum angle that the ramp can be made with the horizontal is 3°

(B)

Given, the mass of the rover, m=1025 kg

The normal force will be equal to the vertical component of the weight of the rover.

That is,

`N=mg\cos \theta`

On substituting the known values,

`\begin{gathered} N=1025*9.8*\cos 3\degree^{} \\ =10031.2\text{ N} \end{gathered}`

Thus the normal force on the rover is 10031.2 N