A box with a mass of 40.0 kg is pulled along a level floor at a constant speed by a rope that makes an angle of 20.0o with the floor as shown below. If the force on the rope is 200 N, then coefficient of sliding friction or ) between the box and the floor is:
a) 0.58
b) 0.48
c) 0.51
d) 0.30
Fh = 200*cos20 = 187.9N.
Fv = 40*9.8 + 200*sin20,
Fv = 392 + 68.4 = 460.4N.
Since the velocity is constant, the
acceleration = 0:
Fn = ma = 0, Fn = Net force,
Fh - uFv = 0, uFv = force of friction.
187.9 - 460.4u = 0,
-460.4u = -187.9,
u = -187.9 / -460.4 = 0.408.
To find the coefficient of sliding friction between the box and the floor, we need to use Newton's second law of motion. In this case, the box is pulled along a level floor, which means the normal force and the gravitational force cancel each other out, resulting in a net force of zero in the vertical direction. Therefore, we only need to consider the horizontal forces.
Let's break down the given information:
- Mass of the box (m) = 40.0 kg
- Force on the rope (F) = 200 N
- Angle between the rope and the floor (θ) = 20.0°
First, we need to resolve the force on the rope into horizontal and vertical components. The vertical component does not affect the horizontal motion, so we only consider the horizontal component.
Horizontal component of the force on the rope (F_x) = F * cos(θ)
F_x = 200 N * cos(20.0°)
Next, we need to find the force of sliding friction (f) acting on the box. According to Newton's second law, the force of sliding friction can be calculated as:
f = μ * N
where μ is the coefficient of sliding friction and N is the normal force.
Since the box is pulled at a constant speed, the force of sliding friction is equal in magnitude but opposite in direction to the force on the rope.
f = F_x
Finally, we can find the coefficient of sliding friction:
μ = f / N = F_x / N
To find N, we need to consider the vertical forces. The normal force equals the force of gravity acting on the box.
Normal force (N) = m * g
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
N = 40.0 kg * 9.8 m/s^2
Now we have all the pieces we need to find the coefficient of sliding friction:
μ = F_x / (m * g)
Let's calculate it!
F_x = 200 N * cos(20.0°)
N = 40.0 kg * 9.8 m/s^2
μ = F_x / (m * g)
After substituting the values and evaluating the expression, we find:
μ ≈ 0.51
Therefore, the coefficient of sliding friction between the box and the floor is approximately 0.51.
So the correct answer is c) 0.51.