Elevator weighing 5000N is ascending with an acceleration of 3m/s2 .during ascent its weight is 700N is standing on the scales placed on the floor. Scale reading? Total tension in the cables of elevator

To determine the scale reading when the elevator is ascending and to find the total tension in the cables, we need to analyze the forces acting on both the elevator and the person standing inside it. Let's break this down step by step.

Understanding Forces in the Elevator

When the elevator ascends, it experiences two main forces: its weight and the tension in the cables. The weight of the elevator is given as 5000 N, and it is moving upward with an acceleration of 3 m/s². The person inside the elevator has a weight of 700 N.

Calculating the Total Forces

Using Newton's second law, we can express the net force acting on the elevator:

Net Force (F_net) = T - W_elevator

Where:

• T = tension in the cables
• W_elevator = weight of the elevator (5000 N)

Since the elevator is accelerating upwards, we can write:

F_net = m * a

Here, m is the mass of the elevator, and a is the acceleration (3 m/s²). First, we need to find the mass of the elevator:

Weight (W) = m * g

Where g is the acceleration due to gravity (approximately 9.81 m/s²). So, we have:

m = W / g = 5000 N / 9.81 m/s² ≈ 509.8 kg

Finding the Tension in the Cables

Now we can substitute the mass into our earlier equation for net force:

F_net = 509.8 kg * 3 m/s² = 1529.4 N

Now, substituting this back into the net force equation:

1529.4 N = T - 5000 N

Solving for T gives:

T = 1529.4 N + 5000 N ≈ 6529.4 N

Scale Reading for the Person Inside the Elevator

The scale reading reflects the apparent weight of the person standing on it. When the elevator is accelerating upwards, the scale will read more than the actual weight of the person due to the additional force from the elevator's acceleration. The apparent weight can be calculated as follows:

Apparent Weight = W_person + m_person * a

To find the mass of the person:

m_person = W_person / g = 700 N / 9.81 m/s² ≈ 71.3 kg

Now, we can calculate the apparent weight:

Apparent Weight = 700 N + (71.3 kg * 3 m/s²) = 700 N + 213.9 N ≈ 913.9 N

Final Results

To summarize:

• The total tension in the cables of the elevator is approximately 6529.4 N.
• The scale reading for the person standing inside the elevator is approximately 913.9 N.

This analysis shows how forces interact in an accelerating system and how they affect measurements like weight on a scale. If you have any further questions or need clarification, feel free to ask!