A block accelerates at 3.3 m/s2 down a plane
inclined at an angle 27.0�.
m
μk
3.3 m/s2
27�
Find μk between the block and the in-
clined plane. The acceleration of gravity is
9.81 m/s2 .
To find the coefficient of kinetic friction (μk) between the block and the inclined plane, we can use the given information on the acceleration of the block and the angle of the inclined plane.
1. Start by analyzing the forces acting on the block along the inclined plane. The main forces involved are the gravitational force (mg) acting vertically downward and the frictional force (fk) acting parallel to the inclined plane.
2. Resolve the gravitational force into its components. The component of the gravitational force acting parallel to the inclined plane is mg*sin(theta), where theta is the angle of the inclined plane (27 degrees in this case). This component tends to push the block down the incline.
3. Determine the net force acting on the block. The net force is given by the equation:
Net Force = Mass * Acceleration
Since the block is accelerating down the inclined plane, the net force is in the same direction as the component of the gravitational force (mg * sin(theta)).
Therefore, Net Force = mg * sin(theta)
4. Calculate the gravitational force acting along the incline. The gravitational force is given by the equation:
Gravitational Force = Mass * Gravity
Gravitational Force = mg
In this case, gravity is given as 9.81 m/s^2.
5. Use the formula for the coefficient of kinetic friction (μk):
μk = (fk / Normal Force)
The normal force (N) is the force exerted by the inclined plane perpendicular to it. In this case, it is equal to the gravitational force acting perpendicular to the plane, which is given by:
Normal Force = mg * cos(theta)
6. Substitute the expressions for the net force and the normal force into the formula for μk:
μk = (mg * sin(theta)) / (mg * cos(theta))
7. Cancel out the mass 'm' from the equation:
μk = (sin(theta)) / (cos(theta))
8. Plug in the given angle theta (27.0 degrees) into the equation to find μk:
μk = (sin(27.0 degrees)) / (cos(27.0 degrees))
Use a scientific calculator or online calculator to evaluate this expression and find the value of μk.
gravity force down the plane=mg*sinTheta
friction force up the plane=mu*mg*cosTheta
net force=mass*a
mg(sinTheta-mu*CosTheta)=m*3.3
solve for mu