Final answer:
The tension in the cable is 1398.4 N, which is calculated by subtracting the force due to the crate's acceleration from its weight.
Step-by-step explanation:
To find the tension in the elevator cable, we need to consider the forces acting on the crate and apply Newton's second law of motion. This law states that the acceleration (a) of an object is directly proportional to the net force (F) acting on it and inversely proportional to its mass (m), which can be written as F=ma.
Firstly, let's find the gravitational force acting on the crate, which is its weight (W). The weight is calculated by multiplying the mass of the crate (m) by the acceleration due to gravity (g), which is approximately 9.8 m/s2. For a 152 kg crate, W = m*g = 152 kg * 9.8 m/s2 = 1489.6 N.
Next, since the crate is accelerating downward, the net force acting on it is the weight (W) minus the upward force from the cable (T), which equals the mass of the crate times its acceleration. We can write this as W - T = m*a. To find the tension, we rearrange the formula to T = W - m*a.
Substituting the numbers in, we get T = 1489.6 N - 152 kg * 0.6 m/s2 = 1489.6 N - 91.2 N = 1398.4 N. So, the force of the cable on the elevator is 1398.4 N.