A rescue worker pulls an injured skier lying on a toboggan (with a combined mass of 127 kg) across flat snow at a constant speed. A 2.53 m rope is attached to the toboggan at ground level, and the rescuer holds the rope taut at shoulder level. If the rescuer's shoulders are 1.65 m above the ground, and the tension in the rope is 148 N, what is the coefficient of kinetic friction between the toboggan and the snow?
Fs = m*g = 127kg * 9.8N/kg = 1245 N. =
Wt. of skier and toboggan.
sin A = Y/r = 1.65/2.53 = 0.6522
A = 40.7o
Fk = u*mg-u*T*sinA
Fk = 1245u - u*148*sin40.7
Fk = 1245u - 96.5u = 1148u
148*cos40.7 - 1148u = m*a = m*0 = 0
1148u = 112.2
u = 0.098
To find the coefficient of kinetic friction between the toboggan and the snow, we need to consider the forces acting on the system.
First, let's identify the forces at play:
1. Tension force: The force exerted by the rescuer to pull the toboggan. In this case, the tension force is equal to 148 N, acting in the upward direction.
2. Weight force: The force exerted by the combined mass of the skier and the toboggan. The weight force is equal to the mass multiplied by the acceleration due to gravity (9.8 m/s^2) and acts vertically downward.
3. Normal force: The force exerted by the ground on the toboggan. It acts perpendicular to the ground and counteracts the weight force.
4. Friction force: The force opposing the motion of the toboggan, acting parallel to the ground.
Since the skier and the toboggan are moving at a constant speed, the net force acting on them is zero. This means the forces in the vertical direction must balance each other:
Tension force - Weight force = 0
148 N - (mass * 9.8 m/s^2) = 0
Now we need to find the mass of the skier and the toboggan combined. We can calculate it by dividing the weight by the acceleration due to gravity:
mass = weight / acceleration due to gravity
mass = 148 N / 9.8 m/s^2
Next, let's consider the horizontal forces. The horizontal force acting on the toboggan is the friction force. The friction force can be calculated using the equation:
Friction force = coefficient of kinetic friction * Normal force
We don't have the value of the normal force, but we can calculate it using similar triangles. The vertical distance between the rescuer's shoulders and the ground is 1.65 m, and the length of the rope is 2.53 m. So, the length of the vertical component of the rope is:
vertical component length = (1.65 m / 2.53 m) * rope length
Now, the normal force is equal to the weight force in the vertical direction, so we can calculate it using the mass we found earlier:
Normal force = mass * acceleration due to gravity
Finally, substituting the values we found into the equation for the friction force, we can solve for the coefficient of kinetic friction:
Friction force = coefficient of kinetic friction * Normal force
(coeffcient of kinetic friction) = (Friction force) / (Normal force)