Calculating Magnitude of Force Exerted by Shopper

[blrdey]

I've tried doing this question in many different ways:

A person pushes a 13.8-kg shopping cart at a constant velocity for a distance of 31.7 m on a flat horizontal surface. She pushes in a direction 31.8 ° below the horizontal. A 30.6-N frictional force opposes the motion of the cart. (a) What is the magnitude of the force that the shopper exerts? Determine the work done by (b) the pushing force, (c) the frictional force, and (d) the gravitational force.

I know that I can do parts b, c, and d. I can't remember how to do part a, though. I tried saying that F=ma, but this doesn't work. F=ma(sin31.8) won't work for me either. I'm assuming that a=9.8, even though it is on a horizontal plane. I can't think of what else could be the horizontal acceleration, if there could be anything else.

 

[neutrino]

Using the components of the force is the right way to do it, but I think you've got the components mixed up. The problem states that the cart is moving at a constant velovity. What does that say about the net force acting on cart (along the direction of motion)?

 

[blrdey]

The net force is equal to zero?

 

[radou]

The net force is equal to zero?

Since velocity is constant, the net force must equal zero, yes.

 

[blrdey]

I don't understand what to do with this.

 

[radou]

I don't understand what to do with this.

Again, you know that the net force equals zero, i.e. the components of all the forces exerted on the cart in the x and y direction seprately, must equal zero. Write down the equation of equilibrium for the x-direction; what forces act in the x direction?

 

[blrdey]

I still don't understand this. I'll ask my teacher in the morning about it. I don't remember him going over a lot of this . . . Thanks for all the help, I really appreciate it.