Final answer:
The tension needed to lift an 8 kg crate with an upward acceleration of 2 m/s² would be 94.4 N, accounting for both the acceleration and the gravitational force acting on the crate.
Step-by-step explanation:
The tension required to lift an 8 kg crate with an upward acceleration of 2 m/s2 can be calculated using Newton's second law of motion, which states that the force needed to accelerate an object is equal to the mass of the object multiplied by the acceleration (F=ma). In addition to the force needed to accelerate the crate, we must also overcome the force of gravity acting on the crate, which is the weight of the crate (W=mg, where g is the acceleration due to gravity, approximately 9.8 m/s2).
The total tension (T) in the rope needed is the sum of the force required for the upward acceleration and the weight of the crate. Thus, the tension can be calculated as:
T = ma + mg
T = m(a + g)
T = 8 kg (2 m/s2 + 9.8 m/s2)
T = 8 kg (11.8 m/s2)
T = 94.4 N