A 1,500 kg crate hangs motionless from a crane cable. What is the tension in the cable? Ignore the mass of the cable.

Suppose the crane accelerates the crate upward at 1.2 m/s2. What is the tension in the cable now?

To determine the tension in the cable, we need to consider the forces acting on the crate.

In the first scenario where the crate hangs motionless, the tension in the cable is equal to the weight of the crate. The weight of an object is given by the equation:

Weight = mass * acceleration due to gravity

The acceleration due to gravity is approximately 9.8 m/s^2. Assuming that the question is asking for the tension in the cable, we can calculate it as follows:

Weight = mass * acceleration due to gravity
Tension = Weight
Tension = 1,500 kg * 9.8 m/s^2

Therefore, the tension in the cable when the crate hangs motionless is approximately 14,700 N (Newton).

In the second scenario where the crane accelerates the crate upward at 1.2 m/s^2, we need to consider the net force acting on the crate. Net force is given by the equation:

Net force = mass * acceleration

In this case, the net force acting on the crate is the difference between the tension in the cable and the weight of the crate.

Net force = Tension - Weight

Since the direction of the acceleration is upward, the net force will also be upward. Therefore,

Net force = mass * acceleration
Tension - Weight = mass * acceleration

Substituting the given values:

Tension - (mass * acceleration due to gravity) = mass * acceleration

Simplifying the equation:

Tension = mass * acceleration + (mass * acceleration due to gravity)
Tension = 1,500 kg * 1.2 m/s^2 + (1,500 kg * 9.8 m/s^2)

Therefore, the tension in the cable when the crane accelerates the crate upward at 1.2 m/s^2 is approximately 16,200 N (Newton).