Question

Consider a cart of mass M that can roll on frictionless bearings. In which of the following cases will the normal force acting on the cart be less than the cart's weight? Select two answers. For each answer choice A-D, draw a free body diagram for mass M and write an equation that has Fnet and other forces in it. Explain using your equations why the two answers you chose have normal force less than weight force.

Answer 1

The normal force will be less than the cart's weight when the cart is accelerating upward or when the cart is on an inclined plane.

Step-by-step explanation:

To determine when the normal force acting on the cart will be less than the cart's weight, we need to consider the forces acting on the cart. The normal force, which is perpendicular to the surface, counteracts the force of gravity acting downward. If there are other forces acting in the upward direction that are greater than the force of gravity, then the normal force will be less than the weight. The two cases where this can occur are when the cart is accelerating upward or when the cart is on an inclined plane.

In both cases, we can write Newton's second law equation to analyze the forces:

ΣF = ma

For the case of acceleration, if the net force in the upward direction is greater than the weight, then the normal force will be less than the weight. Similarly, on an inclined plane, if the component of the weight parallel to the incline is greater than the force opposing it, then the normal force will be less than the weight.

Therefore, the two cases where the normal force will be less than the cart's weight are when the cart is accelerating upward and when the cart is on an inclined plane.

Answer 2

We will have the following:

We recall that the normal force is perpendicular to the surface, so we can see that in scenario A and scenario C the normal force will be a component of the weight of the car, and thus it will be less than the weight.

Free body diagrams:

Scenario A:

Scenario B:

Scenario C:

Scenario D:

***Equations for scenarios A and :***

Scenario A:

`\begin{gathered} \sum F_x=Ncos(\theta) \\ \\ \sum F_y=wg+Nsin(\theta) \end{gathered}`

*Scenario C:

`\begin{gathered} \sum F_x=Fcos(\theta) \\ \\ \sum F_y=mg+N+Fsin(\theta) \end{gathered}`