What is the frictional force on the horse while pulling a wagon?

[asheik234]

Homework Statement

A horse of mass M pulls a wagon of mass m so that the horse and wagon have an acceleration a. Assume the wagon wheels have frictionless bearings. Write expressions for the following in terms of m, M, and a.

(A) The horizontal frictional force that the ground exerts on the horse.

Homework Equations

F=ma

F_fr=μF_n

The Attempt at a Solution

I found the answer to be Ma-ma, but that's not right.

 

[cepheid]

If the horse has acceleration a, then it *must* have a NET force of Ma acting on it. That's just Newton's second law. This means that the vector sum of all forces acting on it must be Ma. So, what forces are acting on it, and what are their magnitudes and directions? Draw a free body diagram for the horse. Hint: one of the forces acting on the horse is because of Newton's third law.

 

[asheik234]

Yes, but then wouldn't the answer be Ma-ma, the net force subtracted by the force tension. Newton's third law is that there is an equal reaction to every action. How does that apply here?

 

[cepheid]

Yes, but then wouldn't the answer be Ma-ma, the net force subtracted by the force tension. Newton's third law is that there is an equal reaction to every action. How does that apply here?

**Did you draw the free body diagram for the horse?** I.e just the horse and the forces that act on it, with all other elements of the system removed. Step 1. What forces act on the horse? List them for me:

 

[asheik234]

**Did you draw the free body diagram for the horse?** I.e just the horse and the forces that act on it, with all other elements of the system removed. Step 1. What forces act on the horse? List them for me:

Force normal, force weight (which both cancel out), force tension, and force friction, which both point to the left, and then Ma-force friction and force tension to the right. Am I missing anything?

 

[cepheid]

Force normal, force weight (which both cancel out), force tension, and force friction, which both point to the left, and then Ma-force friction and force tension to the right. Am I missing anything?

There are only two horizontal forces. What you're calling tension, and the friction. Are you SURE that the friction points to the left? When the horse tries to walk forward, in which direction does the hoof want to slide relative to the ground? The friction force will oppose this sliding motion.

Step 2: Once you've got all the signs right, set up Newton's second law:

sum of horizontal forces = Ma.

 

[asheik234]

There are only two horizontal forces. What you're calling tension, and the friction. Are you SURE that the friction points to the left? When the horse tries to walk forward, in which direction does the hoof want to slide relative to the ground? The friction force will oppose this sliding motion.

Step 2: Once you've got all the signs right, set up Newton's second law:

sum of horizontal forces = Ma.

Ohhh I understand now, the force friction is always in the opposite direction as the force tension, thus it would be Ma+ma. Thank You!

 

[cepheid]

Ohhh I understand now, the force friction is always in the opposite direction as the force tension, thus it would be Ma+ma. Thank You!

Yup. Friction is required for walking, and a LOT of friction is required for walking while pulling a heavy load, otherwise your feet just slip.

You're welcome!