A block of mass 21.5 kg supported by a vertical massless cable is initially at rest. The block is then pulled upward with a constant acceleration of 3.79 m/s2. what is the tension in the cable? what is the magnitude of the net force acting on the mass? what is the speed of the block after is has traveled 1.17m?

To find the tension in the cable, we can start by using Newton's second law of motion, which states that the sum of all forces acting on an object is equal to the mass of the object multiplied by its acceleration.

1. Tension in the cable:
- According to the problem, the block is being pulled upward with a constant acceleration of 3.79 m/s².
- Since the cable supports the block, the tension in the cable will be equal to the force required to accelerate the block upward.
- Using Newton's second law (F = m * a), we can calculate the tension in the cable as:
Tension = mass * acceleration
Tension = 21.5 kg * 3.79 m/s²

To find the magnitude of the net force acting on the mass, we need to consider the forces acting on the object.

2. Net force on the mass:
- Since the object is being pulled upward with a constant acceleration, the only force acting on it is the tension in the cable.
- The net force acting on the mass will be equal to the tension in the cable.
- Therefore, the magnitude of the net force is the same as the tension in the cable, which we already calculated.

To find the speed of the block after it has traveled 1.17m, we need to use the equation of motion.

3. Speed of the block after it has traveled 1.17m:
- We can use the equation of motion for uniformly accelerated linear motion: v² = u² + 2as.
- Here, v is the final velocity, u is the initial velocity (which is zero in this case since the block is initially at rest), a is the acceleration, and s is the distance traveled.
- Rearranging the equation, we have v = √(2as).
- Plugging in the values, we get:
v = √(2 * 3.79 m/s² * 1.17 m)

By following these steps and performing the calculations, you'll be able to find the tension in the cable, the magnitude of the net force acting on the mass, and the speed of the block after it has traveled 1.17m.