Sam, whose mass is 73.0kg , takes off down a 50.0m high, 12.0∘ slope on his jet-powered skis. The skis have a thrust of 210N . Sam's speed at the bottom is 45.0m/s . What is the coefficient of kinetic friction of his skis on the snow?
energy going into his KE-energy going into friction=final KE
mg50+210*50/cos12 - mgcos12*mu=1/2 m 45^2
notice mass divides out, you are left with an expression, solve for mu.
To find the coefficient of kinetic friction of Sam's skis on the snow, we can use the following steps:
Step 1: Calculate the gravitational force acting on Sam.
The gravitational force is given by F_gravity = m * g, where m is the mass of Sam and g is the acceleration of gravity (9.8 m/s^2). Therefore, F_gravity = 73.0 kg * 9.8 m/s^2.
Step 2: Calculate the component of the gravitational force parallel to the slope.
The component of the gravitational force acting parallel to the slope is F_parallel = F_gravity * sin(theta), where theta is the angle of the slope (12.0 degrees). Therefore, F_parallel = F_gravity * sin(12.0 degrees).
Step 3: Calculate the net force acting on Sam.
The net force is the difference between the thrust force provided by the skis and the component of the gravitational force parallel to the slope. Therefore, F_net = Thrust - F_parallel, where Thrust is the thrust provided by the skis (210 N).
Step 4: Calculate the kinetic friction force.
The kinetic friction force is given by F_friction = coefficient of friction * normal force, where the normal force is the force perpendicular to the slope. In this case, the normal force is equal to the component of the gravitational force perpendicular to the slope, which is F_perpendicular = F_gravity * cos(theta). Therefore, F_friction = coefficient of friction * F_perpendicular.
Step 5: Set up the equation for Newton's second law.
Using Newton's second law (F_net = m * a), we can solve for the acceleration (a). In this case, the net force acting on Sam is equal to the sum of the kinetic friction force and the component of the gravitational force parallel to the slope.
Step 6: Calculate the coefficient of kinetic friction.
Using the acceleration (a) obtained from Step 5, we can calculate the coefficient of kinetic friction using the equation a = g * coefficient of friction * cos(theta).
By following these steps, you can find the coefficient of kinetic friction of Sam's skis on the snow.