a block of wood rest on a plane incline at 35 degrees to the horizontal.if the coefficient of the static friction between the surface is 0.45.determine:
a) what is the horizontal force that must be applied to the block to initiate motion up the plane
b)the horizontal force that must be applied to the block to prevent motion down the plane
To determine the horizontal force required to initiate motion up the plane, we need to consider the forces acting on the block. The two main forces are the gravitational force (pulling the block downward), and the static friction force (opposing the motion). We'll break it down step by step:
a) To initiate motion up the plane, the applied force needs to overcome the static friction force. The formula to calculate the static friction force is:
Static Friction Force = coefficient of static friction * Normal force
The normal force is the component of the gravitational force perpendicular to the incline plane. It can be calculated as:
Normal force = mass * gravitational acceleration * cos(angle of incline)
Here, the angle of incline is 35 degrees.
Therefore, the static friction force is:
Static Friction Force = 0.45 * (mass * gravitational acceleration * cos(35))
To initiate motion, the applied force needs to be equal to or greater than the static friction force. So the horizontal force required to initiate motion up the plane is:
Horizontal Force (initiate motion) = Static Friction Force
b) To prevent motion downward, we need to consider the forces acting on the block in the opposite direction. This includes the component of the gravitational force pulling the block downward and the static friction force.
The formula for calculating the static friction force remains the same:
Static Friction Force = coefficient of static friction * Normal force
The normal force is still given by:
Normal force = mass * gravitational acceleration * cos(angle of incline)
Therefore, the static friction force is:
Static Friction Force = 0.45 * (mass * gravitational acceleration * cos(35))
To prevent motion down the plane, the applied force needs to be equal to or less than the static friction force. So the horizontal force required to prevent motion down the plane is:
Horizontal Force (prevent motion down) <= Static Friction Force