Final answer:
To determine the coefficient of friction between the mass and the floor, we can analyze the forces acting on the mass. The force applied at an angle of 30° above the horizontal can be divided into two components: one perpendicular to the floor and one parallel to the floor. By calculating the parallel component of the force, we can find the force of friction and then determine the coefficient of friction using the equation F_friction = u * m * g.
Step-by-step explanation:
To determine the coefficient of friction between the mass and the floor, we need to analyze the forces acting on the mass. The force applied at an angle of 30° above the horizontal can be divided into two components: one perpendicular to the floor and one parallel to the floor. The perpendicular component does not affect the motion of the mass, so we can ignore it. The parallel component of the force is responsible for accelerating the mass.
The parallel component of the force can be found using the equation:
F_parallel = F * sin(theta)
where F is the given force and theta is the angle.
Plugging in the values, we have:
F_parallel = 50 N * sin(30°)
F_parallel = 50 N * 0.5
F_parallel = 25 N
The force of friction can be found using the equation:
F_friction = F_parallel - m * a
where m is the mass and a is the acceleration.
Plugging in the values, we have:
F_friction = 25 N - 10 kg * 2.0 m/s^2
F_friction = 25 N - 20 N
F_friction = 5 N
The coefficient of friction can be found using the equation:
F_friction = u * m * g
where u is the coefficient of friction, m is the mass, and g is the acceleration due to gravity.
Plugging in the values, we have:
5 N = u * 10 kg * 9.8 m/s^2
Solving for u, we find:
u = 5 N / (10 kg * 9.8 m/s^2)
u = 0.051
Therefore, the coefficient of friction between the mass and the floor is approximately 0.051.