A 5 kg block rests on a rough horizontal table. A rope is attached to the block and is pulled with a force of 11N to the left. As a result, the block accelerates at 2 m/s2. The coefficient of kinetic friction between the block and the table is
To find the coefficient of kinetic friction between the block and the table, we need to use the equation for friction:
friction = coefficient of friction * normal force
The normal force is the force exerted by the table on the block perpendicular to the surface. In this case, since the block is resting on a horizontal table, the normal force is equal to the weight of the block:
normal force = mass * acceleration due to gravity
The weight of the block can be calculated using the formula:
weight = mass * acceleration due to gravity
Given that the mass of the block is 5 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can find the weight:
weight = 5 kg * 9.8 m/s^2 = 49 N
Now we can substitute the weight into the formula for the normal force:
normal force = 49 N
Next, we know that the block is being pulled to the left with a force of 11 N, which causes it to accelerate at 2 m/s^2. This means that the net force acting on the block is:
net force = applied force - friction
Using Newton's second law, we can relate the net force to the acceleration:
net force = mass * acceleration
Substituting the given values:
11 N - friction = 5 kg * 2 m/s^2
11 N - friction = 10 N
Now we can solve for the friction:
friction = 11 N - 10 N = 1 N
Finally, we can calculate the coefficient of kinetic friction using the equation:
friction = coefficient of friction * normal force
Substituting the values:
1 N = coefficient of friction * 49 N
Simplifying:
coefficient of friction = 1 N / 49 N
Therefore, the coefficient of kinetic friction between the block and the table is approximately equal to 0.02.