A 70 kg person stands on a 30 kg platform and pulls on a massless rope with a force of 400 N. The rope passes around a pulley attached to a support (roof), and then around a second pulley attached to the platform before being anchored to the support (roof). All sections of the rope are vertical. Both pulleys are massless and frictionless.

What is the acceleration of the system? What is the person's apparent weight?

answer is 840 N (CONFIRMED)

To find the acceleration of the system, we can use Newton's second law of motion, which states that the total force acting on an object is equal to the mass of the object multiplied by its acceleration.

In this case, the system consists of the person and the platform, so the total mass of the system is the sum of their masses: 70 kg + 30 kg = 100 kg.

The total force acting on the system can be determined by considering the tension in the rope. The person exerts a pulling force of 400 N on the rope. Since the rope is vertical, the tension in the rope is the same throughout. Therefore, the total force acting on the system is also 400 N.

Applying Newton's second law, we have:

Total force = mass × acceleration

400 N = 100 kg × acceleration

Solving for acceleration, we find:

acceleration = 400 N / 100 kg = 4 m/s^2

So, the acceleration of the system is 4 m/s^2.

To determine the person's apparent weight, we can use the concept of apparent weight, which is the force experienced by an object due to the acceleration of its reference frame.

The person's actual weight is given by the force of gravity acting on them, which is given by the formula:

Weight = mass × gravitational acceleration

Weight = 70 kg × 9.8 m/s^2 ≈ 686 N

However, the person is also experiencing an upward force due to the acceleration of the system. This additional force is equal to the person's mass multiplied by the acceleration of the system:

Additional force = mass × acceleration

Additional force = 70 kg × 4 m/s^2 = 280 N

The person's apparent weight is the sum of the actual weight and the additional force:

Apparent weight = Weight + Additional force

Apparent weight = 686 N + 280 N ≈ 966 N

So, the person's apparent weight is approximately 966 N.

apparent weight=620N