Calculating Horizontal Force for a Shopping Cart on an Inclined Plane

[wr1015]

What formula do I use?

A shopper pushes a 7.3 kg shopping cart up a 13° incline, as shown in Figure 5-21. Find the horizontal force, F, needed to give the cart an acceleration of 1.63 m/s2.

 

[Tide]

What formula do I use?

Use $$\vec F = m \vec a$$

 

[wr1015]

Use $$\vec F = m \vec a$$

i did that and got 18.99 N but its being counted as wrong. There are some formulas in my book that show horizontal force as $$\sum\\F_{x}=F_{1},_{x}+F_{2},_{x}=F_{1}+F_{2}\cos\theta$$ but am not given any forces??

 

[Tide]

You know what the force of gravity is! It's direction is vertical but has a component parallel to the incline. The shopper applies a horizontal force which also has a component parallel to the incline. The sum of the forces parallel to the incline equals mass times acceleration along the incline.

You should be able to take it from there.