A body of mass 50kg lies on a rough horizontal plat form . if a horizontal force of non applied to the body through it centre of mass and slides the body on plat form.find the coefficient of limiting friction between the body and the plat form.
To find the coefficient of limiting friction between the body and the platform, you need to use Newton's second law and the equation of motion for objects on a rough horizontal surface.
1. First, find the net force acting on the body. The only force acting on the body in the horizontal direction is the applied force, F.
2. Apply Newton's second law, which states that the net force is equal to the mass of the object multiplied by its acceleration (F = m * a). In this case, since the body is sliding, the acceleration is constant.
3. Rearrange the equation to solve for the acceleration (a = F / m).
4. The frictional force can be calculated as the product of the coefficient of friction (μ) and the normal force (N) exerted on the body by the platform. In this case, the normal force is equal to the weight of the body (N = m * g), where g is the acceleration due to gravity (9.8 m/s^2).
5. The maximum or limiting frictional force is given by the equation f = μ * N.
6. Substitute the value of the normal force into the equation to get f = μ * m * g.
7. Since the applied force overcomes the maximum frictional force when the body starts moving, the maximum frictional force is equal to the applied force (f = F).
8. Substitute the known values into the equation and solve for μ: F = μ * m * g.
By rearranging the equation, you can find the coefficient of limiting friction (μ = F / (m * g)).
Note: Ensure that the units are consistent throughout the calculation. The mass should be in kilograms (kg), the force in Newtons (N), and the acceleration due to gravity in meters per second squared (m/s^2).