Question

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 \(T.\) (a) What is the net force acting on the sleigh? (b) What is the coefficient of kinetic friction between the sleigh and the snow?

Short answer

The net force acting on the sleigh is 0. (b) Calculate the coefficient of kinetic friction between the sleigh and the snow. μ_k = T / (m * g)

Step-by-step solution

(a) Net force calculation

To find the net force acting on the sleigh, we need to consider the forces acting on it. There are two forces acting on the sleigh: tension (T) exerted by the horse and friction (f) between the sleigh and the snow. Since the sleigh is moving at a constant speed, the net force acting on the sleigh must be zero. Therefore, the tension force is equal and opposite to the friction force. Mathematically: Net force = T - f = 0 Hence, T = f The net force acting on the sleigh is 0.

(b) Coefficient of kinetic friction calculation

To find the coefficient of kinetic friction (μ_k), we need to use the friction formula: f = μ_k * N where f is the friction force, N is the normal force acting on the sleigh (which is equal to its weight), and μ_k is the coefficient of kinetic friction. Since the sleigh is moving horizontally, its normal force (N) will be equal to its gravitational force, which is given by: N = m * g where m is the mass of the sleigh and g is the gravitational acceleration (approximately 9.81 m/s^2) Since we derived earlier that the tension force equals the friction force (T = f), we can substitute f by T: T = μ_k * m * g Now, to find the coefficient of kinetic friction (μ_k), we need to rearrange the equation: μ_k = T / (m * g) By plugging the given values of tension force (T) and mass (m) into the equation, we can calculate the coefficient of kinetic friction (μ_k).