How Do We Calculate Kinetic Friction and Net Force in a Donkey-Cart System?

[CINA]

Homework Statement

A 255[kg] donkey is pulling on a cart with a horizontal force of 1940[N]. The mass of the cart is 520[kg] and the cart is rolling at a constant velocity of 0.72[m/s] to the left.

Find: a) The coefficient of kinetic friction for the wheel’s bearings of the cart.
b) The NET force (magnitude and direction) exerted by the surface on the donkey

Homework Equations

Not sure about these:

X) -Fc/d + Ff = 0 <-- Friction has to be in the direction of the motion since that's what causes it to move, right?

Y) Fn-Fg = 0

I think that's it.

The Attempt at a Solution

I don't really know where to be begin. Is 1940 N the force on the whole system, donkey plus cart? Do I need a FBD for donkey and cart or just one with both? I'm lost, please help.

 

[tiny-tim]

I don't really know where to be begin. Is 1940 N the force on the whole system, donkey plus cart? Do I need a FBD for donkey and cart or just one with both?

Hi CINA!

1940 N is the force on the cart only.

For a) you need an FBD for the cart, for b) you need an FBD for the donkey.

 

[baba89]

I can provide a response to this problem by breaking down the information and applying relevant equations to find the requested values. First, we know that the donkey is pulling the cart with a horizontal force of 1940 N, and the mass of the donkey is 255 kg while the mass of the cart is 520 kg. The cart is also rolling at a constant velocity of 0.72 m/s to the left.

To find the coefficient of kinetic friction for the wheel's bearings of the cart, we can use the equation F = μkN, where F is the force of friction, μk is the coefficient of kinetic friction, and N is the normal force. In this case, the normal force is equal to the weight of the cart, which is given by mg = 520 kg * 9.8 m/s^2 = 5096 N. The force of friction, F, is equal to the horizontal force applied by the donkey, 1940 N. Therefore, we can rearrange the equation to solve for μk: μk = F/N = 1940 N / 5096 N = 0.38. This means that the coefficient of kinetic friction for the wheel's bearings of the cart is 0.38.

To find the net force exerted by the surface on the donkey, we can use the equation ΣF = ma, where ΣF is the sum of all forces acting on the donkey, m is the mass of the donkey, and a is the acceleration. In this case, the donkey is moving at a constant velocity, so its acceleration is 0. Therefore, the sum of all forces acting on the donkey is also equal to 0. We can use this to solve for the net force, which is equal to the force of gravity, Fg, minus the force of friction, Ff: ΣF = Fg - Ff = 0. Since the donkey is not accelerating, we know that Fg = ma = 255 kg * 0 = 0. Therefore, the net force exerted by the surface on the donkey is equal to the force of friction, Ff = μkN = 0.38 * 5096 N = 1933 N. This force is acting in the opposite direction of motion, or to the right.

In summary, we can find the