The pulley system shown in the figure is used to lift a 52-{\rm kg} crate. Note that one chain connects the upper pulley to the ceiling and a second chain connects the lower pulley to the crate. The crate is rising with an acceleration of 2.5 m/s^2.
Determine the tension in the upper chain.
310
To determine the tension in the upper chain, we need to consider the forces acting on the system.
1. Gravitational force: The weight of the crate is acting vertically downwards. We can find it using the formula:
weight (W) = mass (m) × acceleration due to gravity (g)
W = 52 kg × 9.8 m/s^2 = 509.6 N
2. Tension in the lower chain: Since the crate is rising with an acceleration of 2.5 m/s^2, we can use Newton's second law to find the tension in the lower chain:
Tension (T) = Mass (m) × (acceleration due to gravity (g) + acceleration (a))
T = 52 kg × (9.8 m/s^2 + 2.5 m/s^2) = 52 kg × 12.3 m/s^2 = 639.6 N
3. Tension in the upper chain: Since the upper and lower chains are connected, the tensions in both chains will be the same. Therefore, the tension in the upper chain is also 639.6 N.
So, the tension in the upper chain is 639.6 N.
To determine the tension in the upper chain, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
In this case, the net force is the tension in the upper chain. The mass of the crate is given as 52 kg, and the acceleration is given as 2.5 m/s^2.
So, we can use the formula:
Net force = mass x acceleration
Tension in upper chain = mass of crate x acceleration
Substituting the given values:
Tension in upper chain = 52 kg x 2.5 m/s^2
Tension in upper chain = 130 N
Therefore, the tension in the upper chain is 130 Newtons.