Final answer:
To calculate the tension on the cable, subtract the force due to the acceleration (2133 N) from the gravitational force (7742 N) on the 790 kg mass. The resulting tension is 5609 N.
Step-by-step explanation:
The question involves calculating the tension in the cable as a 790 kg mass is being lowered by a crane with an acceleration of 2.7 m/s2. To find the tension in the cable, we use the formula T = mg - ma, where T is the tension, m is the mass, g is the acceleration due to gravity (9.8 m/s2), and a is the acceleration of the mass. Since the mass is accelerating downwards, the gravitational force and the force due to the acceleration are in the same direction, thus the tension in the cable is reduced by the force due to acceleration.
The calculation for the tension in the cable is performed as follows:
- Determine the gravitational force acting on the mass: Fg = mg = (790 kg)(9.8 m/s2) = 7742 N.
- Determine the force due to acceleration: Fa = ma = (790 kg)(2.7 m/s2) = 2133 N.
- Calculate the tension in the cable by subtracting the force due to acceleration from the gravitational force: T = Fg - Fa = 7742 N - 2133 N = 5609 N.
Therefore, the tension on the cable while the mass is being lowered at an acceleration of 2.7 m/s2 is 5609 N.