when a force of 0.245 newtons is applied to a body of mass 250g which is resting on a horizontal plane, the body is found to be in a limiting equilibrium. find the coefficient of friction between body and planes.
To find the coefficient of friction between the body and the plane, we can use the concept of limiting equilibrium. In this case, the applied force is balanced by the frictional force acting in the opposite direction.
Here are the steps to find the coefficient of friction:
Step 1: Convert the mass of the body from grams to kilograms.
Given mass of the body = 250 g
Converting it to kilograms: 250 g ÷ 1000 = 0.25 kg
Step 2: Draw a free-body diagram to identify the forces acting on the body.
The forces acting on the body are the applied force (0.245 N) and the force of friction (opposing the applied force).
Step 3: Calculate the normal force acting on the body.
Since the body is resting on a horizontal plane, the normal force is equal in magnitude and opposite in direction to the force of gravity. Thus, F(normal) = mg, where m is the mass of the body and g is the acceleration due to gravity.
Given m = 0.25 kg and g = 9.8 m/s^2,
F(normal) = 0.25 kg × 9.8 m/s^2 = 2.45 N
Step 4: Determine the coefficient of friction.
The frictional force (F(friction)) can be calculated using the equation F(friction) = coefficient of friction × F(normal).
In this case, the force of friction balances the applied force in limiting equilibrium. Thus, F(friction) = 0.245 N.
Plugging in the values, we have:
0.245 N = coefficient of friction × 2.45 N
Simplifying the equation:
coefficient of friction = 0.245 N ÷ 2.45 N = 0.1
Therefore, the coefficient of friction between the body and the plane is 0.1.
Keep in mind that the coefficient of friction is dimensionless and indicates the ratio of the frictional force to the normal force.