A rough wooden block of mass 4kg placed on a rough horizontal plank is applied by a force of 35n until it just starts to move calculate the coefficient of static friction (take 9=10m/s
35=mu*4kg*9.8N/kg
solve for mu.
To calculate the coefficient of static friction in this scenario, we need to utilize the concept of equilibrium. In equilibrium, the sum of the forces acting on an object is zero.
First, let's calculate the gravitational force acting on the wooden block. The gravitational force (weight) can be calculated using the formula:
Weight = mass * acceleration due to gravity
Given that the mass is 4 kg and the acceleration due to gravity is 10 m/s², we can plug in these values to get:
Weight = 4 kg * 10 m/s² = 40 N
The normal force (N) acting on the block is equal to the weight, since the block is on a horizontal surface and there is no vertical acceleration. Therefore, the normal force in this scenario is also 40 N.
Now, the maximum static friction force (F_s) can be determined using the formula:
F_s = coefficient of static friction * normal force
In this case, the applied force (35 N) just overcomes the static friction force, causing the block to start moving. So, we can write the equation for equilibrium as follows:
Applied force (F_app) - static friction force (F_s) = 0
35 N - F_s = 0
F_s = 35 N
Now, we can substitute this value into the formula for static friction force:
35 N = coefficient of static friction * 40 N
To isolate the coefficient of static friction, divide both sides of the equation by 40 N:
coefficient of static friction = 35 N / 40 N
coefficient of static friction = 0.875
Therefore, the coefficient of static friction between the rough wooden block and the rough horizontal plank is 0.875.