A 3kg block is resting on a table with a coefficient of friction of 0.4. It is now pushed with a force of 15n. What is the acceleration of the book?
Then friction force is M*g*mu = 11.8 n,
and the net force is
F = 15 - 11.8 = 2.2 n
Acceleration (a) can be obtained from Newton's second law:
F = m a
a = 0.73 m/s^2
To find the acceleration of the block, we need to apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
The net force acting on the block can be calculated using the formula:
Net force = Applied force - Frictional force
First, let's calculate the frictional force. The frictional force can be determined using the formula:
Frictional force = Coefficient of friction * Normal force
The normal force is the force exerted by the table on the block, which is equal to the weight of the block. To calculate the weight of the block, we use the formula:
Weight = Mass * Acceleration due to gravity
Here, the mass of the block is 3 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Weight = 3 kg * 9.8 m/s^2 = 29.4 N
Now, we can calculate the frictional force:
Frictional force = 0.4 * 29.4 N = 11.76 N
Next, we can find the net force:
Net force = Applied force - Frictional force = 15 N - 11.76 N = 3.24 N
Finally, we can use Newton's second law to determine the acceleration:
Acceleration = Net force / Mass = 3.24 N / 3 kg = 1.08 m/s^2
Therefore, the acceleration of the block is 1.08 m/s^2.