A body of mass 25kg by moving at 3m/s on rough horizontal floor is brought to rest sliding through a distance 2.5m on the floor.calculate the coefficent of static frict
ion( g=10m/s square).
To calculate the coefficient of static friction, we need to set up the equation that represents the forces acting on the body. This can be done by using Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = ma).
In this case, the body starts with an initial velocity of 3 m/s and comes to rest through a distance of 2.5 m. The net force acting on the body causing it to stop is due to the force of friction.
The equation for friction is given by f = μN, where f is the frictional force, μ is the coefficient of friction, and N is the normal force. In this case, since the body is moving horizontally, the normal force is equal to the weight of the body, which is given by the formula N = mg.
To solve for the coefficient of static friction, we first determine the net force acting on the body. The net force is given by the equation:
Net force (F) = ma
Since the body comes to rest, the acceleration is equal to zero. Therefore, the net force is also zero.
The force of friction is equal in magnitude and opposite in direction to the applied force, which in this case is equal to the weight of the body. Hence, we can write the equation as follows:
Force of friction (f) = Weight of the body (mg)
Substituting the equation for the force of friction and the weight of the body, we get:
μN = mg
Since N = mg, we can rewrite the equation as:
μmg = mg
Dividing both sides by mg, we get:
μ = 1
Therefore, the coefficient of static friction in this case is 1.