A cable is lifting a construction worker and a crate, as the drawing shows. The weights of the worker and crate are 833 N and 1380 N, respectively. The acceleration of the cable is 0.620 m/s2, upward. What is the tension in the cable (a) below the worker and (b) above the worker?

(a) Below the worker, the tension in the cable can be found by calculating the net force acting on the system. The net force is given by the equation: net force = mass * acceleration. Since both the worker and crate are being lifted by the cable, their masses need to be added together.

Here, the mass of the worker can be found using the formula: weight = mass * gravitational acceleration. Rearranging the formula, we get: mass = weight / gravitational acceleration.

So, the mass of the worker is: mass = 833 N / 9.8 m/s^2 = 85 kg.

Similarly, the mass of the crate is: mass = 1380 N / 9.8 m/s^2 = 141 kg.

Now, let's calculate the net force on the system:
net force = (mass of worker + mass of crate) * acceleration
= (85 kg + 141 kg) * 0.620 m/s^2
= 58.22 N.

Since the net force is upward, the tension in the cable below the worker is 58.22 N, upward.

(b) The tension in the cable above the worker can be found by considering the entire system. The net force acting on the system is equal to the tension in the cable above the worker, which is also equal to the sum of the weight of the worker and the crate.

So, the tension in the cable above the worker is: tension = weight of worker + weight of crate
= 833 N + 1380 N
= 2213 N.

Therefore, the tension in the cable above the worker is 2213 N.

To find the tension in the cable, we can use Newton's second law of motion:

ΣF = ma

where ΣF is the net force acting on an object, m is the mass of the object, and a is its acceleration.

Let's calculate the masses of the worker and the crate first:

Mass of the worker = Weight of the worker / Acceleration due to gravity
= 833 N / 9.8 m/s^2
≈ 85 kg

Mass of the crate = Weight of the crate / Acceleration due to gravity
= 1380 N / 9.8 m/s^2
≈ 141 kg

Now, let's calculate the tension in the cable below the worker (T1):

T1 - Weight of the worker = Mass of the worker * Acceleration
T1 - 833 N = 85 kg * 0.620 m/s^2
T1 ≈ 885 N

So, the tension in the cable below the worker is approximately 885 N.

Next, let's calculate the tension in the cable above the worker (T2):

T2 - Weight of the worker - Weight of the crate = (Mass of the worker + Mass of the crate) * Acceleration
T2 - 833 N - 1380 N = (85 kg + 141 kg) * 0.620 m/s^2
T2 ≈ 2789 N

Therefore, the tension in the cable above the worker is approximately 2789 N.

To find the tension in the cable (a) below the worker and (b) above the worker, we need to consider the forces acting on the system.

(a) Tension below the worker:
To find the tension below the worker, we need to consider the gravitational force acting on the worker and the crate. Since the acceleration is upward, the net force acting on the system must be equal to the total mass multiplied by the acceleration.

The total mass is the sum of the worker's mass (which we can calculate by dividing 833 N by the acceleration due to gravity, g = 9.8 m/s^2) and the crate's mass (which we can calculate by dividing 1380 N by g). Let's consider the worker's mass as m1 and the crate's mass as m2.

m1 = 833 N / 9.8 m/s^2 ≈ 84.9 kg
m2 = 1380 N / 9.8 m/s^2 ≈ 140.8 kg

Now, we can calculate the total mass:

m_total = m1 + m2 ≈ 84.9 kg + 140.8 kg ≈ 225.7 kg

The net force acting on the system is given by:

Net Force = m_total * acceleration

Tension = Net Force + Weight of the worker

To find the tension below the worker, we can calculate:

Tension below the worker = (m_total * acceleration) + Weight of the worker

Tension below the worker = (225.7 kg * 0.620 m/s^2) + 833 N

Now, we can calculate the tension below the worker.

(b) Tension above the worker:
The tension above the worker is equal to the net force acting on the system minus the weight of the crate.

Tension above the worker = (m_total * acceleration) - Weight of the crate

Tension above the worker = (225.7 kg * 0.620 m/s^2) - 1380 N

Now, we can calculate the tension above the worker.

Please note that in this calculation, we assumed that the system is in equilibrium, meaning there are no other external forces acting on it.

Assume the crate is below the worker, with a cable in-between.

Mass of worker, mw = 833/9.81= 84.9 kg
mass of crate, mc = 1380/9.81=140.7 kg

Total mass = mw+mc= 225.6 kg

Tension in cable above worker
=(mw+mc)*(g+a)
=225.6*(9.81+0.62)
=2354 N

Tension in cable between worker and crate
=140.67*(9.81+0.62)
=1467 N