The coefficient of static friction between a block and a horizontal floor is 0.37, while the coefficient of kinetic friction is 0.10. The mass of the block is 3.8 kg and it is initially at rest.
Once the block is sliding, if you keep pushing on it with the same minimum starting force as in part a(13.78 N), what is its acceleration (in m/s2)?
To find the acceleration of the block once it starts sliding, we need to compare the applied force with the maximum frictional force.
The maximum static frictional force (Fs) can be calculated using the coefficient of static friction (μs) and the normal force (N) acting on the block, given by:
Fs = μs * N
The normal force, in this case, is equal to the weight of the block, which is given by the mass (m) multiplied by the acceleration due to gravity (g):
N = m * g
Substituting the given values, we have:
N = 3.8 kg * 9.8 m/s^2
N = 37.24 N
And substituting the coefficient of static friction:
Fs = 0.37 * 37.24 N
Fs = 13.7788 N
The applied force is equal to the maximum static friction force (Fs) required to start the block moving. Once the block starts sliding, it experiences kinetic friction, which is given by:
fk = μk * N
where μk is the coefficient of kinetic friction. Substituting the given values:
fk = 0.10 * 37.24 N
fk = 3.724 N
Since the applied force (13.78 N) is greater than the kinetic friction force (3.724 N), the block will continue to accelerate. The net force acting on the block is given by:
Fnet = Fa - fk
where Fa is the applied force. Substituting the values:
Fnet = 13.78 N - 3.724 N
Fnet = 10.056 N
To find the acceleration (a), we can use Newton's second law of motion:
Fnet = m * a
Substituting the values:
10.056 N = 3.8 kg * a
Rearranging the equation to solve for a:
a = 10.056 N / 3.8 kg
a ≈ 2.643 m/s^2
Therefore, the acceleration of the block once it starts sliding is approximately 2.643 m/s^2.
To find the acceleration of the block once it is sliding, we need to consider the forces acting on the block.
When the block is at rest, the maximum force of static friction is acting to keep it from moving. The maximum force of static friction can be calculated using the equation:
Fs_max = μs * N
Where μs is the coefficient of static friction and N is the normal force.
The normal force is equal to the weight of the block, which can be calculated using the equation:
N = m * g
Where m is the mass of the block and g is the acceleration due to gravity.
Substituting these values into the equation, we can calculate the maximum force of static friction:
Fs_max = μs * m * g
Once the block starts to slide, the force of friction changes from static friction to kinetic friction. The force of kinetic friction can be calculated using the equation:
Fk = μk * N
Where μk is the coefficient of kinetic friction and N is the normal force.
To find the acceleration of the block once sliding, we can use Newton's second law of motion:
F_net = m * a
Where F_net is the net force acting on the block and a is the acceleration.
In this case, since the block is initially at rest, the net force is equal to the force of static friction:
F_net = Fs_max
Once the block starts sliding, the net force is equal to the force of kinetic friction:
F_net = Fk
So, to find the acceleration, we can set the force of static friction equal to the force of kinetic friction:
Fs_max = Fk
Substituting the respective equations for each force, we get:
μs * m * g = μk * N
We can then substitute the equation for the normal force, N = m * g:
μs * m * g = μk * m * g
The acceleration due to gravity, g, cancels out:
μs * m = μk * m
Finally, we can solve for the acceleration:
a = μk * g
Substituting the given values for the coefficient of kinetic friction and the acceleration due to gravity:
a = 0.10 * 9.8 m/s²
a ≈ 0.98 m/s²
Therefore, the acceleration of the block once it starts sliding is approximately 0.98 m/s².