If the cart moves with constant velocity, find the friction force, the applied force in both the horizontal and vertical directions, the object's weight, and the normal force.

Question

A horse pulls a 1250 kg cart with a force of 250 N at an angle of 25 degrees. If the cart moves with constant velocity, find the friction force, the applied force in both the horizontal and vertical directions, the object's weight, and the normal force.

Answer 1

Friction Force

If the cart is moving towards the right, the Friction force is acting towards the left. And since we know the velocity is constant, that means acceleration is 0. If acceleration is 0, the net horizontal force on the cart is also 0. This means that the force towards the right has to equal the friction force towards the left. If we can figure out the force pulling the cart to the right, we will also find the friction force.

A force of 250 N is applied at an angle of 25 degrees.

250*cos(25) = the horizontal force = friction force

Weight

If you put the cart on a scale, with no vertical force, the weight of the cart would equal the normal force: Weight = mass*gravity = 1250kg*9.81m/s².

Normal Force (F_N )

There is also a vertical component to the 250N force that is pulling up on the cart and reducing the normal force.

250*sin(25) = the vertical force

Since there is a vertical force pulling up, we have to subtract that from the original normal force.

F_N = mg - F*sin(Θ) = 1250*9.81 - 250*sin(25)