A block of mass 17.9 kg supported by a vertical massless cable is initially at rest. The block is then pulled upward with a constant acceleration of 2.01 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 it has traveled 3.47 m?

To determine the tension in the cable, you need to consider the forces acting on the block. In this case, there are two forces involved: the weight of the block and the tension in the cable.

Step 1: Calculate the weight of the block using the formula: weight = mass × acceleration due to gravity.

Given:
Mass of the block (m) = 17.9 kg
Acceleration due to gravity (g) = 9.8 m/s^2

Weight of the block (W) = mass × acceleration due to gravity

Step 2: Calculate the net force acting on the block using the formula: net force = mass × acceleration.

Given:
Mass of the block (m) = 17.9 kg
Acceleration (a) = 2.01 m/s^2

Net force (F) = mass × acceleration

Step 3: Calculate the tension in the cable.

In equilibrium, the tension in the cable is equal to the weight of the block. However, when the block is accelerated, the tension will be greater than the weight to provide the required upward force.

Tension (T) = weight of the block (W) + net force (F)

Step 4: Calculate the speed of the block after it has traveled a certain distance.

Given:
Distance traveled (d) = 3.47 m

Use the kinematic equation: v^2 = u^2 + 2 × acceleration × distance, where v is the final velocity, u is the initial velocity (0 in this case), and acceleration is 2.01 m/s^2.

Solve for v by rearranging the equation.

Speed (v) = √(u^2 + 2 × acceleration × distance)

Now, let's compute:

Step 1: Calculate the weight of the block.
W = m × g
W = 17.9 kg × 9.8 m/s^2

Step 2: Calculate the net force.
F = m × a
F = 17.9 kg × 2.01 m/s^2

Step 3: Calculate the tension in the cable.
T = W + F

Step 4: Calculate the speed of the block after it has traveled 3.47 m.
v = √(0^2 + 2 × a × d)

Please substitute the provided values into the equations to obtain the final answers.