This exercise is part of a series of problems aimed at modeling a situation by progressively refining our model to take into account more and more parameters. This progressive approach is very close to what professional scientists do! Context We want to lower a suspended load in a controlled way, so that it hits the ground with a speed whose modulus is not too great. To do this, the suspended load (B) is connected by a rope passing through a pulley to another mass (A), which can move on a horizontal surface. To slow down the descent, we added a spring behind the mass (A). Information The masses of the charges A and B are known. The mass of the rope itself is negligible (very small compared to the loads). The pulley has negligible mass and can rotate without friction. The charge B is initially stationary and is at a known height h. The surface on which mass A is placed is horizontal. There is no friction between mass A and the surface on which it is placed. The string attached to mass A is perfectly parallel to the surface on which the mass is resting, as is the spring. The spring is initially at its natural length and has a known spring constant k. Schematization Represent the initial and final states of the system, identifying an upward y+ axis for each object. Modelization Create a model for the modulus of the speed with which the load B will hit the ground as a function of the value of the masses A and B, the initial block height B, and the spring constant of the spring. What will be the final stretch of the spring? Then test your model with the following values Mass of charge A : 95 kg Mass of suspended load (B): 73 kg Initial height of suspended mass (h): 3.1 m Spring spring constant (k): 117.8 N/m
This exercise is part of a series of problems aimed at modeling a situation by progressively refining our model to take into account more and more parameters. This progressive approach is very close to what professional scientists do!
Context
We want to lower a suspended load in a controlled way, so that it hits the ground with a speed whose modulus is not too great. To do this, the suspended load (B) is connected by a rope passing through a pulley to another mass (A), which can move on a horizontal surface. To slow down the descent, we added a spring behind the mass (A).
Information
The masses of the charges A and B are known.
The mass of the rope itself is negligible (very small compared to the loads).
The pulley has negligible mass and can rotate without friction.
The charge B is initially stationary and is at a known height h.
The surface on which mass A is placed is horizontal.
There is no friction between mass A and the surface on which it is placed.
The string attached to mass A is perfectly parallel to the surface on which the mass is resting, as is the spring.
The spring is initially at its natural length and has a known spring constant k.
Schematization
Represent the initial and final states of the system, identifying an upward y+ axis for each object.
Modelization
Create a model for the modulus of the speed with which the load B will hit the ground as a function of the value of the masses A and B, the initial block height B, and the spring constant of the spring. What will be the final stretch of the spring?
Then test your model with the following values
Mass of charge A : 95 kg
Mass of suspended load (B): 73 kg
Initial height of suspended mass (h): 3.1 m
Spring spring constant (k): 117.8 N/m
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