A cable is lifting a construction worker and a crate, as the drawing shows. The weights of the worker and crate are 968 and 1550 N, respectively. The acceleration of the cable is 0.620 m/s2, upward.
Is there a question here?
To solve this problem, we need to consider the forces acting on the system and apply Newton's second law of motion.
First, let's establish the positive direction as upward. Therefore, the weight of the worker and the crate will act downward, and the tension in the cable will act upward.
1. Start by calculating the net force acting on the system:
Net force = Force of tension - Weight of worker - Weight of crate
2. Determine the weight of the worker and the crate:
Weight of worker = mass of worker × acceleration due to gravity
Weight of crate = mass of crate × acceleration due to gravity
3. Calculate the net force:
Net force = Force of tension - Weight of worker - Weight of crate
For easier calculations, let's express the forces in terms of magnitude:
Force of tension = T (unknown)
Weight of worker = 968 N
Weight of crate = 1550 N
4. Use Newton's second law to establish the equation of motion:
Net force = mass × acceleration
(T - 968 N - 1550 N) = (mass of worker + mass of crate) × acceleration
5. Rearrange the equation to solve for T (force of tension):
T - 968 N - 1550 N = (mass of worker + mass of crate) × acceleration
T = (mass of worker + mass of crate) × acceleration + 2518 N
By plugging in the given values for mass of worker, mass of crate, and acceleration, you can calculate the force of tension acting on the cable.