A shopper pushes a 8.0 kg shopping cart up a 13 degree incline.

Find the magnitude of the horizontal force, needed to give the cart an acceleration of 1.25 m/s^2.

ignoring friction?

force up the incline=PushingForce*cos13

= ma
solve for Pushing force

To find the magnitude of the horizontal force needed to give the cart an acceleration of 1.25 m/s^2, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.

First, we need to determine the components of the forces acting on the cart. The weight of the cart can be divided into two components: the perpendicular component (mg⊥) and the parallel component (mg∥) to the incline. The perpendicular component mg⊥ will balance the normal force exerted by the surface.

1. Determine the perpendicular component (mg⊥):
The perpendicular component of the weight is given by the formula mg⊥ = mg cos(theta), where m is the mass of the cart (8.0 kg) and theta is the angle of the incline (13 degrees).

mg⊥ = (8.0 kg) * (9.8 m/s^2) * cos(13 degrees)

2. Determine the parallel component (mg∥):
The parallel component of the weight is given by the formula mg∥ = mg sin(theta).

mg∥ = (8.0 kg) * (9.8 m/s^2) * sin(13 degrees)

3. Determine the net force (Fnet):
The net force acting on the cart is equal to the product of its mass and acceleration.

Fnet = (8.0 kg) * (1.25 m/s^2)

4. Determine the magnitude of the horizontal force (F∥):
The magnitude of the horizontal force (F∥) can be found by subtracting the parallel component (mg∥) from the net force (Fnet):

F∥ = Fnet - mg∥

Now you can calculate the magnitude of the horizontal force (F∥) by substituting the values into the equation:

F∥ = [(8.0 kg) * (1.25 m/s^2)] - [(8.0 kg) * (9.8 m/s^2) * sin(13 degrees)]