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) Well, if we want to calculate the tension in the cable below the worker, we have to dig deep. So deep, in fact, that we might find a mole throwing a surprise party down there!
Now, according to Newton's second law, the net force acting on an object is equal to its mass times its acceleration. In this case, the net force acting on the worker is the tension in the cable below him minus his weight.
So, let's do some math. The weight of the worker is 833 N, and the acceleration of the cable is 0.620 m/s². Therefore, the net force acting on the worker is (833 N) - (mass of worker * 0.620 m/s²).
But wait, we know that Weight = mass * gravitational acceleration. So we can rewrite that as: (mass of worker * 9.8 m/s²).
Now, my friend, we have ourselves a little equation: (833 N) - (mass of worker * 0.620 m/s²) = (mass of worker * 9.8 m/s²).
Are you still with me? Great! Let's solve this equation and find the tension below the worker. Just be careful not to get tangled up in all these numbers!
(b) Oh, my dear friend, the tension above the worker is like that secret special ingredient in a clown's joke book – it's the element of surprise!
So, let's find the tension above the worker. We already know the weight of the worker (833 N) and the weight of the crate (1380 N). When we add those two weights together, we get the total downward force on the cable.
Now, according to Newton's second law, the tension above the worker is equal to the mass of the worker plus the mass of the crate, all multiplied by the acceleration of the cable. It's like the cable is giving them a lift, both literally and metaphorically!
So, using our clown magic, we get: Tension above = (mass of worker + mass of crate) * 0.620 m/s².
That's it! We've found the tension both below and above the worker. I hope these answers didn't make your head spin like a circus carousel!
To find the tension in the cable, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the object being considered is the combined system of the worker and the crate.
Let's calculate the tension in the cable below the worker first:
(a) Tension below the worker:
1. Calculate the net force acting on the system:
Net force = (mass of worker + mass of crate) x acceleration
Mass of worker = weight of worker / acceleration due to gravity
Mass of crate = weight of crate / acceleration due to gravity
Net force = (Mass of worker x acceleration due to gravity + Mass of crate x acceleration due to gravity) x acceleration
2. Calculate the tension below the worker:
Tension below the worker = weight of the worker + net force
Now let's calculate the tension above the worker:
(b) Tension above the worker:
Since the cable is accelerating upward, the tension above the worker should be greater than the weight of the worker and the crate combined.
The tension above the worker is equal to the weight of the worker and crate combined plus the net force acting on them:
Tension above the worker = weight of the worker + weight of the crate + net force
Now we can substitute the given values and solve for the tensions:
Given:
Weight of the worker = 833 N
Weight of the crate = 1380 N
Acceleration = 0.620 m/s^2
(a) Tension below the worker:
1. Calculate the mass of the worker:
Mass of worker = Weight of worker / Acceleration due to gravity
Acceleration due to gravity = 9.8 m/s^2 (approximate value)
Mass of worker = 833 N / 9.8 m/s^2
2. Calculate the mass of the crate:
Mass of crate = Weight of crate / Acceleration due to gravity
Mass of crate = 1380 N / 9.8 m/s^2
3. Calculate the net force on the system:
Net force = (Mass of worker x acceleration due to gravity) + (Mass of crate x acceleration due to gravity) x acceleration
4. Calculate the tension below the worker:
Tension below the worker = Weight of the worker + Net force
(b) Tension above the worker:
Tension above the worker = Weight of the worker + Weight of the crate + Net force
By substituting the given values, you can calculate the tensions below and above the worker.
To find the tension in the cable, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's analyze the forces acting on the worker. The worker is being lifted, so there are two forces acting on the worker: the tension force in the cable pulling upward and the weight of the worker pulling downward. Since the worker's weight is given as 833 N, we can say that:
Force downward = 833 N
Using Newton's second law, the net force acting on the worker can be expressed as:
Net force = Mass of the worker x Acceleration
Next, we'll find the mass of the worker using the formula:
Weight = Mass x Acceleration due to gravity
Mass of the worker = Weight of the worker / Acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2.
So, the mass of the worker can be calculated as:
Mass of the worker = 833 N / 9.8 m/s^2
Similarly, we can repeat these steps to determine the net force and mass for the crate.
Once the masses of the worker and the crate are known, we can calculate the tension in the cable below and above the worker.
(a) Tension below the worker:
In this case, the tension in the cable must be equal to the net force acting on the worker. So:
Tension below the worker = Net force on the worker
(b) Tension above the worker:
In this case, the tension in the cable must be equal to the net force acting on the worker plus the weight of the crate. So:
Tension above the worker = Net force on the worker + Weight of the crate
By following these steps and calculations, you will be able to find the tension in the cable below and above the worker.