A 200 kg wooden crate is dragged at a constant speed by a rope through a distance of 4 m along a wooden floor . The coefficient of sliding friction is .2 . If the work done is 1568 j , and the rope is horizontal, calculate the tension in the rope
To calculate the tension in the rope, we first need to determine the net force acting on the wooden crate.
The work done on an object is given by the formula:
Work = Force * Distance * cos(θ)
where "Force" is the net force acting on the object, "Distance" is the distance over which the force is applied, and "θ" is the angle between the force vector and the displacement vector.
In this case, the work done is 1568 J, the distance is 4 m, and the angle between the force vector (tension in the rope) and the displacement vector (horizontal) is 0° (cos(0) = 1).
So we can rewrite the equation as:
1568 J = Force * 4 m
Solving for the force, we get:
Force = 1568 J / 4 m = 392 N
We know that the net force is equal to the force of friction (F_fric) acting on the crate. The force of friction can be calculated using the equation:
F_fric = μ * N
where "μ" is the coefficient of sliding friction and "N" is the normal force.
Since the crate is being dragged horizontally, the normal force is equal to the crate's weight (mg):
N = mg
where "m" is the mass of the crate (200 kg) and "g" is the acceleration due to gravity (9.8 m/s^2).
N = (200 kg) * (9.8 m/s^2) = 1960 N
Now we can calculate the force of friction:
F_fric = μ * N
F_fric = 0.2 * 1960 N = 392 N
Since the net force is the force of friction, the tension in the rope is also equal to 392 N.
Therefore, the tension in the rope is 392 N.