A ski starts from rest and slides down 22 degree incline 75 m long.If the coefficient of friction is .090 what is the ski's speed at the base of incline and if the snow is level at the foot of the incline and has the same coefficient of friction,how far will the ski travel along the level
To find the ski's speed at the base of the incline, we can use the principles of mechanics. First, let's break down the forces acting on the ski.
1. The force of gravity (mg): The component of the gravitational force acting down the incline is given by mg * sin(θ), where m is the mass of the ski and θ is the angle of the incline.
2. The normal force (N): This force acts perpendicular to the incline. Its value is equal to mg * cos(θ).
3. The frictional force (f): According to the problem, the coefficient of friction is given as 0.090. The frictional force is given by f = μN, where μ is the coefficient of friction and N is the normal force.
Now, let's calculate the speed of the ski at the base of the incline:
Step 1: Calculate the net force acting on the ski.
The net force is the force parallel to the incline and is given by F_net = mg * sin(θ) - f.
Step 2: Calculate the acceleration of the ski.
The acceleration of the ski is given by a = F_net / m.
Step 3: Calculate the final velocity of the ski at the base of the incline.
The final velocity can be found using the equation v^2 = u^2 + 2as, where u is the initial velocity (0 m/s as the ski starts from rest), a is the acceleration, and s is the distance traveled down the incline (75 m).
Now, let's plug in the values and calculate:
1. The force of gravity (mg) = m * g * sin(θ) = m * 9.8 * sin(22°).
2. The normal force (N) = m * g * cos(θ) = m * 9.8 * cos(22°).
3. The frictional force (f) = μ * N = 0.090 * m * 9.8 * cos(22°).
Next, we calculate the net force and the acceleration:
F_net = mg * sin(θ) - f
a = F_net / m
Then, we calculate the final velocity using the formula v^2 = u^2 + 2as, where u = 0 (as the ski starts from rest) and s = 75 m.
Finally, we find the square root of the final velocity to get the speed at the base of the incline.
To find how far the ski will travel along the level snow at the foot of the incline, we need to consider the frictional force acting on the ski. The frictional force is given by f = μ * N, where μ is the coefficient of friction and N is the normal force.
Using the equation f = μ * N, we can calculate the frictional force acting on the ski. Then, we can use the equation F = ma (where F is the net force, m is the mass of the ski, and a is the acceleration) to find the acceleration of the ski on the level snow.
Assuming the ski starts from rest again, we can then use the kinematic equation v^2 = u^2 + 2as to find the distance traveled (s) along the level snow, where v is the final velocity of the ski at the base of the incline and u is the initial velocity (0 m/s).
Now, let's plug in the values and calculate the distance traveled along the level snow.