A body of mass 5kg rest on a smooth plane inclined at angle 30 degree to the horizontal. What are the magnitude of the force p applied along the plane which keeps it from sliding down and the normal reaction between the plane and the body?
To find the magnitude of the force P applied along the plane, we need to consider the forces acting on the body.
The weight of the body acts vertically downward and can be calculated using the formula:
Weight = mass * acceleration due to gravity
Weight = 5kg * 9.8m/s^2
Weight = 49N
The weight can be resolved into components parallel and perpendicular to the inclined plane. The component perpendicular to the plane is equal to the normal reaction between the plane and the body.
The component parallel to the plane is balanced by the force P. We can find the component parallel to the plane using trigonometry.
Component parallel to the plane = Weight * sin(angle)
Component parallel to the plane = 49N * sin(30°)
Component parallel to the plane = 24.5N
Thus, the magnitude of force P applied along the plane to prevent sliding down is 24.5N.
The normal reaction can be found as the component of the weight perpendicular to the inclined plane.
Normal reaction = Weight * cos(angle)
Normal reaction = 49N * cos(30°)
Normal reaction = 42.41N
Thus, the magnitude of the normal reaction between the plane and the body is 42.41N.