A horse is trotting along pulling a sleigh through the snow. To move the sleigh, of mass m, straight ahead at a constant speed, the horse must pull with a force of magnitude T. What is the net force acting on the sleigh? What is the coefficient of kinetic friction between the sleigh and the snow?

To find the net force acting on the sleigh, we first need to understand the forces at play.

In this scenario, there are two forces acting on the sleigh: the force of tension provided by the horse (T) and the force of kinetic friction between the sleigh and the snow (fk).

Since the sleigh is moving at a constant speed, which implies an equilibrium state (no acceleration), the net force acting on it must be zero. Therefore, the magnitude of the force of tension (T) must be equal to the magnitude of the force of kinetic friction (fk).

So, the net force acting on the sleigh is zero.

Now, let's consider the coefficient of kinetic friction (μk) between the sleigh and the snow. The force of kinetic friction can be calculated using the equation:

fk = μk * N,

where N is the normal force. In this case, the normal force is equal to the weight of the sleigh, given by N = m * g, where g is the acceleration due to gravity.

Since the sleigh is moving horizontally and not accelerating vertically, the normal force (N) is equal to the weight of the sleigh (mg). Thus, we can rewrite the equation for the force of kinetic friction as:

fk = μk * mg.

Since the magnitude of the tension force (T) is equal to the magnitude of the force of kinetic friction (fk), we can write:

T = fk.

Therefore, we have:

T = μk * mg.

From this equation, we can solve for the coefficient of kinetic friction (μk):

μk = T / (mg).

So, the coefficient of kinetic friction between the sleigh and the snow is μk = T / (mg).