There is a 2kg block resting on a table with a 5kg block attached to the right hanging off the edge of the table and a 4 kg block attached to the left also hanging off the table find the acceleration of the 5 kg block if coefficient of static equals the coefficient of kinetic friction which is 0.10
To find the acceleration of the 5 kg block, we need to consider the forces acting on it. There are two main forces: the gravitational force pulling the block downwards (mg), and the friction force opposing its motion (frictional force).
First, let's calculate the gravitational force (mg) acting on the 5 kg block. The acceleration due to gravity is approximately 9.8 m/s², and the mass of the block is 5 kg. So, the gravitational force is:
Gravitational force (mg) = 5 kg * 9.8 m/s² = 49 N
Next, we need to calculate the maximum static frictional force. The maximum static frictional force can be determined using the equation:
Maximum static frictional force (F_smax) = coefficient of static friction * normal force
The normal force (N) is equal to the weight of the 5 kg block, which is 5 kg * 9.8 m/s² = 49 N.
Thus, the maximum static frictional force is:
F_smax = 0.10 * 49 N = 4.9 N
Since the coefficient of static friction equals the coefficient of kinetic friction, the frictional force during motion will also be 4.9 N.
Now, we can calculate the net force acting on the 5 kg block. The net force is equal to the difference between the gravitational force and the frictional force:
Net force = Gravitational force - Frictional force
= 49 N - 4.9 N
= 44.1 N
Finally, we can use Newton's second law of motion (F = ma) to find the acceleration (a) of the 5 kg block:
Net force = mass * acceleration
44.1 N = 5 kg * acceleration
So, the acceleration of the 5 kg block is:
Acceleration = 44.1 N / 5 kg
= 8.82 m/s²
Therefore, the acceleration of the 5 kg block is 8.82 m/s².