A horizontal rope is tied to a 90kg box on frictionless ice.What is the tension in the rope if the box is at rest?
0 N
To find the tension in the rope, we need to consider the forces acting on the box. In this scenario, there are two forces acting on the box: its weight (mg) and the tension in the rope (T).
Since the box is at rest, the net force acting on it must be zero. Therefore,
T - mg = 0,
where T is the tension in the rope and mg is the weight of the box.
We can rearrange the equation to solve for T:
T = mg.
Plugging in the given values, we have:
T = (90 kg) × (9.8 m/s^2) = 882 N.
Therefore, the tension in the rope is 882 N.
To find the tension in the rope when the box is at rest, we can apply Newton's second law of motion. The equation is:
ΣF = ma
where ΣF represents the sum of all the forces acting on the object, m is the mass of the object, and a is the acceleration of the object.
In this case, the box is at rest, so its acceleration is zero (a = 0). Therefore, the sum of all the forces acting on the box must also be zero.
The only force acting on the box is the tension in the rope. Since there is no friction or any other forces mentioned, the tension in the rope is the only horizontal force acting on the box.
So, we can set up the equation:
ΣF = T = ma = 0
T (tension) = 0
Therefore, the tension in the rope when the box is at rest is zero.