An object of mass 10kg is placed on an inclined plane at 30 degree to the horizontal, calculate the reaction between the two surfaces and the coefficient of static friction
force down the plane: mg*sin30=1/2*10*9.8
if it is not moving, this has to eqkual frection force.
friction force=mg*coefficent*cos30
or coefficent= sin30/cos30=tangent(30 deg)
I don't understand
confused
normal force: mg*cosTheta=10*9.8*1/2*sqrt3
Don't know that's why am asking
To calculate the reaction between the two surfaces and the coefficient of static friction, we need to consider the forces acting on the object. Here are the steps to find the answers:
1. Identify the forces acting on the object:
- Weight (mg): This is the force due to gravity acting vertically downward. Its magnitude is given by the equation: weight = mass × acceleration due to gravity.
In this case, weight = 10 kg × 9.8 m/s² = 98 N.
- Normal force (N): This is the perpendicular force exerted by the inclined plane on the object. It acts normal (perpendicular) to the surface of the inclined plane.
2. Resolve the weight force into components:
Since the inclined plane makes a 30-degree angle with the horizontal, we need to find the component of the weight force acting parallel and perpendicular to the plane.
- The component of the weight force acting parallel to the plane is given by the equation: weight_parallel = weight × sin(angle).
weight_parallel = 98 N × sin(30°) = 49 N.
- The component of the weight force acting perpendicular to the plane is given by the equation: weight_perpendicular = weight × cos(angle).
weight_perpendicular = 98 N × cos(30°) = 84.8528 N (approx).
3. Calculate the normal force (N):
Since the object is in equilibrium (not accelerating), the normal force is equal in magnitude and opposite in direction to the weight perpendicular component.
Therefore, N = weight_perpendicular = 84.8528 N.
4. Calculate the coefficient of static friction (μ):
The coefficient of static friction can be determined using the equation: coefficient of static friction (μ) = frictional force / normal force.
However, since the object is at rest, the coefficient of static friction is equal to the maximum static friction coefficient.
Therefore, μ = maximum static friction coefficient.
To find the maximum static friction coefficient, we can use the equation: maximum static friction coefficient (μ_s) = tan(angle).
Therefore, μ_s = tan(30°) = 0.5774 (approx).
So, the reaction between the two surfaces (normal force) is approximately 84.8528 N, and the coefficient of static friction is approximately 0.5774.