a block slides down an angle 10 incline at a constant speed. what is the coefficient of sliding friction between the block's surface and the incline?
Since there is no acceleration, the friction force, M g u cos 10, equals the component of the weight down the plane, M g sin 10
(u is the coefficient of friction). Note than the M and g cancel, and you are left with
u cos 10 = sin 10
u = tan 10 = 0.176
To find the coefficient of sliding friction between the block and the incline, we need to use Newton's second law and the concept of force equilibrium. Here's how you can calculate it:
1. Identify the forces acting on the block: There are three forces at play in this scenario: gravitational force (mg), normal force (N), and frictional force (f).
2. Split the gravitational force into two components: One parallel to the incline and another perpendicular to the incline.
3. Set up an equation for the force equilibrium along the incline: Since the block slides down the incline at a constant speed, the sum of the forces acting parallel to the incline is zero. In this case, the only force acting parallel to the incline is the component of the gravitational force.
4. Determine the equation for the gravitational force component along the incline: The component of the gravitational force parallel to the incline is given by mg*sin(10°).
5. Write the equation for force equilibrium: The equation becomes mg*sin(10°) - f = 0.
6. Calculate the normal force: The normal force acting perpendicular to the incline can be determined using mg*cos(10°).
7. Substitute the value of the normal force into the force equilibrium equation: The equation now becomes mg*sin(10°) - μ*N = 0, where μ is the coefficient of sliding friction.
8. Solve for the coefficient of sliding friction (μ): Rearrange the equation to solve for μ: μ = (mg*sin(10°))/N.
Now, you can substitute the mass of the block (m) and the angle of the incline (10°) into the equation to find the value of the coefficient of sliding friction (μ).