The coefficient of friction can be determined using the formula:
Coefficient of friction = Force of friction / Normal force
To find the force of friction, we can use Newton's second law:
Force of friction = Mass × Acceleration
Since the box is at rest, the acceleration is 0. Therefore, the force of friction is also 0.
The normal force is equal to the weight of the box, which can be calculated using the formula:
Weight = Mass × Gravitational acceleration
Substituting the given values:
Weight = 50 kg × 9.8 m/s^2 = 490 N
Now we can calculate the coefficient of friction:
Coefficient of friction = 0 / 490 N = 0
Therefore, the coefficient of friction is 0.
To find the maximum speed of the box, we need to calculate the acceleration first. We can use Newton's second law again:
Force = Mass × Acceleration
The net force acting on the box is the horizontal force minus the force of friction:
Net force = 110 N - 0 N = 110 N
Substituting the values:
110 N = 50 kg × Acceleration
Solving for acceleration:
Acceleration = 110 N / 50 kg = 2.2 m/s^2
Now, we can use the equation of motion to find the maximum speed:
v^2 = u^2 + 2as
Where:
v = final velocity (maximum speed)
u = initial velocity (0 m/s)
a = acceleration (2.2 m/s^2)
s = distance (1.1 m)
Substituting the values:
v^2 = 0^2 + 2 × 2.2 m/s^2 × 1.1 m
v^2 = 4.84 m^2/s^2
v = √4.84 m^2/s^2
v ≈ 2.2 m/s
Therefore, the maximum speed of the box is approximately 2.2 m/s.