A box weighing 200 newtons is hanging from the the ceiling
If a box weighing 200 newtons is hanging from the ceiling, it means that the box is suspended from above by a rope or cable. The weight of the box is pulling downwards due to gravity, and the rope or cable is supporting the box and exerting an equal force in the opposite direction.
This situation can be represented by the force equation:
Force of tension in the rope/cable = Weight of the box
So in this case, the force of tension in the rope or cable is also 200 newtons because it needs to balance the weight of the box.
To calculate the tension in the cable supporting the box, we can use Newton's second law, which states that the sum of the forces acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the box is not accelerating, so the net force acting on it must be zero. The force of gravity is acting downwards, exerting a downward force of 200 newtons. The tension in the cable must act in the opposite direction to balance this force, so it will be 200 newtons upwards.
Therefore, the tension in the cable supporting the box is 200 newtons.
To determine the tension in the rope, we need to consider the forces acting on the box. In this scenario, there are two forces involved: the force of gravity pulling the box downwards and the tension force in the rope pulling the box upwards.
The force of gravity, also known as the weight, can be calculated by multiplying the mass of the box by the acceleration due to gravity (which is approximately 9.8 m/s²). Since weight is a force, its unit is the newton (N). So, if the box weighs 200 newtons, we can say that it experiences a force of 200 N due to gravity pulling it downwards.
Now, since the box is hanging stationary, it means that the tension force in the rope is equal in magnitude and opposite in direction to the force of gravity. Therefore, the tension force in the rope must also be 200 newtons.