A loaded penguin sled weighing 60 N rests on a plane inclined at 20° to the horizontal. Between the sled and the plane the coefficient of static friction is 0.25, and the coefficient of kinetic friction is 0.18.
(a) What is the minimum magnitude of the force F, parallel to the plane, that will prevent the sled from slipping down the plane?
_________ N
(b) What is the minimum magnitude F that will start the sled moving up the plane?
__________ N
(c) What value of F is required to move the block up the plane at constant velocity?
_______ N
Break the weight of the sled into normal, and down the plane components.
Then, down the plane, you have a component of weight, opposiing it F and friction.
Now as F starts to move the sled upward, friction is now down the plane.
a is wrong.
To solve these questions, we need to understand the concepts of forces, friction, and components of forces.
(a) To determine the minimum magnitude of the force F that will prevent the sled from slipping down the plane, we need to find the maximum static friction between the sled and the plane. The formula to calculate the maximum static friction is:
F_static_max = μ_static * N
where F_static_max is the maximum static friction force, μ_static is the coefficient of static friction, and N is the normal force.
The normal force N can be calculated using the formula:
N = m * g * cos(θ)
where m is the mass of the sled, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of inclination of the plane.
Given that the weight of the sled is 60 N and the angle of inclination is 20°, we can compute:
N = 60 N * cos(20°)
Now, substituting the value of N into the equation for maximum static friction, we can find F_static_max :
F_static_max = 0.25 * N
Calculate F_static_max to get the minimum magnitude of the force F that will prevent the sled from slipping down the plane.
(b) To find the minimum magnitude of the force F that will start the sled moving up the plane, we need to determine the force required to overcome the static friction before sliding begins. This force is equal to the static friction force:
F_start = F_static_max = 0.25 * N
Using the equation for N above, we can calculate F_start.
(c) To move the block up the plane at a constant velocity, the force F needs to overcome the kinetic friction. The formula for kinetic friction is:
F_kinetic = μ_kinetic * N
where F_kinetic is the kinetic friction force and μ_kinetic is the coefficient of kinetic friction.
Substitute the given coefficient of kinetic friction (0.18) and calculate the force F_kinetic using the value of N from earlier.
This value of F_kinetic represents the force required to move the block up the plane at constant velocity.