A cable is lifting a construction worker and a crate, as the drawing shows. The weights of the worker and crate are 961 and 1540 N, respectively. The acceleration of the cable is 0.620 m/s2, upward.
(a) What is the tension in the cable below the worker?
(b) What is the tension in the cable above the worker?
tension= totalmass*acceleration+weight
= totalmass(a+g)
b) I don't have the drawing. But tension above the worker has to support massbelow*g, and provide mass*a to accelerate.
To find the tension in the cable below the worker, we need to consider the forces acting on the cable system. The forces acting on the system are the tension force in the cable below the worker, the tension force in the cable above the worker, the weight of the worker, and the weight of the crate.
(a) The tension in the cable below the worker can be found by considering the net force acting on the system. The net force is given by Newton's second law, which states that the net force is equal to the mass of the system multiplied by the acceleration of the system. Therefore, the net force is:
Net force = (mass of the worker + mass of the crate) × acceleration
The mass of an object is equal to its weight divided by the acceleration due to gravity. In this case, we can rewrite the equation as:
Net force = (weight of the worker + weight of the crate) ÷ acceleration due to gravity × acceleration
Substituting the given values:
Net force = (961 N + 1540 N) ÷ acceleration due to gravity × acceleration
= (2501 N) ÷ acceleration due to gravity × acceleration
Now, the tension in the cable below the worker is equal to the weight of the worker plus the net force acting downwards. Mathematically, it can be expressed as:
Tension below = weight of the worker + net force
Tension below = weight of the worker + (weight of the worker + weight of the crate) ÷ acceleration due to gravity × acceleration
Substituting the given values:
Tension below = 961 N + (961 N + 1540 N) ÷ acceleration due to gravity × acceleration
(b) The tension in the cable above the worker can be found by considering the net force acting on the system. The net force is given by Newton's second law, which states that the net force is equal to the mass of the system multiplied by the acceleration of the system. Therefore, the net force is:
Net force = (mass of the worker + mass of the crate) × acceleration
Substituting the given values:
Net force = (weight of the worker + weight of the crate) ÷ acceleration due to gravity × acceleration
Now, the tension in the cable above the worker is equal to the weight of the crate minus the net force acting upwards. Mathematically, it can be expressed as:
Tension above = weight of the crate - net force
Tension above = weight of the crate - (weight of the worker + weight of the crate) ÷ acceleration due to gravity × acceleration
Substituting the given values:
Tension above = 1540 N - (961 N + 1540 N) ÷ acceleration due to gravity × acceleration
Please provide the value of the acceleration due to gravity so that we can complete the calculations.
To find the tension in the cable below the worker, we need to consider the forces acting on the system.
(a) Tension below the worker:
Step 1: Find the net force acting on the system.
The net force is equal to the sum of all the forces acting on the system. In this case, the forces involved are the weights of the worker and the crate.
Net force = weight of worker + weight of crate
Step 2: Calculate the net force.
Weight is equal to mass times the acceleration due to gravity. Since the acceleration is given in Newtons, we can use the equation:
weight = mass x acceleration due to gravity
In this case, we're given the weights of the worker and the crate (961 N and 1540 N, respectively), so we can calculate the total weight.
Total weight = 961 N + 1540 N = 2501 N
Step 3: Determine the tension in the cable below the worker.
Since the system is in equilibrium (the acceleration is zero), the net force is zero. Therefore, the tension in the cable below the worker is equal to the weight of the worker plus the weight of the crate.
Tension below the worker = weight of worker + weight of crate = 961 N + 1540 N = 2501 N
Therefore, the tension in the cable below the worker is 2501 N.
(b) Tension above the worker:
To find the tension in the cable above the worker, we can use the same reasoning as in part (a). Since the system is in equilibrium, the net force acting on the system is zero.
The tension in the cable above the worker is equal to the weight of the worker, which is 961 N.
Therefore, the tension in the cable above the worker is 961 N.