Final answer:
To calculate the tension in the rope for a 23 kg box accelerating upwards at 7.0 m/s², use the formula T = mg + ma. The calculated tension is 385.4 Newtons.
Step-by-step explanation:
The question is asking for the tension in the rope from which a 23 kg box hangs. The box is moving with a vertical velocity (vy) of 7.0 m/s and accelerating upwards at 7.0 m/s2. To find the tension, we need to use the formula T = mg + ma, where T is the tension in the rope, m is the mass of the box, g is the acceleration due to gravity (9.8 m/s2), and a is the acceleration of the box.
For the given problem:
- Mass, m = 23 kg
- Acceleration due to gravity, g = 9.8 m/s2
- Acceleration of the box, a = 7.0 m/s2
We calculate the tension in the rope as follows:
T = mg + ma
T = (23 kg)(9.8 m/s2) + (23 kg)(7.0 m/s2)
T = 224.4 N + 161 N
T = 385.4 N
Therefore, the tension in the rope is 385.4 Newtons.