Two 20kg weights are hung from light strings that pass over frictionless pulleys. The ends of the strings are connected to a small, light spring balance, S,
calibrated in kg. The pulley axes are mounted on the wall of a lift in a 50-storey
building.
What is the reading on the spring balance when the lift is at rest?
Make a qualitative sketch of the variation with time of the reading on S as the lift
makes a round trip, delivering passengers from the ground floor to the top floor and
then returning to the ground floor.
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To find the reading on the spring balance when the lift is at rest, we need to consider the forces acting on the system. Since the pulleys are frictionless, the tension in the strings will be the same on both sides.
Let's assume the lift is at rest, so there is no acceleration. In this case, the net force acting on the system is zero. The weight of the weights on one side will be balanced by the tension in the string on that side.
Since each weight is 20 kg, the total weight on one side is 40 kg. Therefore, the tension in each string will be 40 kg (or 400 N) to balance the weight.
Since the spring balance is connected to both strings, the reading on the spring balance will be the sum of the tensions in both strings. Therefore, the reading on the spring balance when the lift is at rest will be:
Reading = 2 * Tension = 2 * 400 N = 800 N
So, the reading on the spring balance when the lift is at rest is 800 N.
Now, let's consider the qualitative sketch of the variation with time of the reading on the spring balance as the lift makes a round trip. Starting from the ground floor, as the lift moves upward, the tension in the strings will increase gradually. This is because the weight of the weights on one side will need to overcome the force of gravity acting on them, resulting in an increase in tension.
When the lift reaches the top floor, the tension in the strings will be at its maximum, which is twice the weight of the weights (800 N in this case). As the lift starts descending, the tension in the strings will decrease gradually until it reaches zero when the lift returns to the ground floor.
So, the sketch of the variation with time of the reading on the spring balance will be a gradual increase from zero to a maximum value of 800 N, followed by a gradual decrease back to zero.