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 what do 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 slow down the descent, we added a resort behind the mass (A), La suspended load (B) is connected by a rope passing through a pulley to another mass (A), which slides on a horizontal surface with friction. Information The masses of loads 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. Load B is initially stationary and is at a known height h. The surface on which mass A is placed is horizontal. There is friction under mass A: the kinetic friction coefficient u, is known. The rope attached to mass A is perfectly parallel to the surface on which the mass is placed, just like the spring. The resort is initially at its natural length and has a known spring constant k. Schematization Represents the initial and final states of the system, identifying a y+-axis upwards for each object. Modelization Create a model for the velocity modulus with which load B will hit the ground based on known parameters only. Do not integrate Then test your model with the following values Mass of load A: 80kg; Mass of the suspended load (B): 65kg The initial height of the suspended mass (h): 2 7m Coefficient of friction under the mass A : 0 21 Spring constant: 78 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
what do 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 slow down the descent, we added a resort behind the mass (A), La
suspended load (B) is connected by a rope passing through a pulley to another mass (A), which slides on a horizontal surface with friction.
Information
The masses of loads 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.
Load B is initially stationary and is at a known height h.
The surface on which mass A is placed is horizontal.
There is friction under mass A: the kinetic friction coefficient u, is known.
The rope attached to mass A is perfectly parallel to the surface on which the mass is placed, just like the spring.
The resort is initially at its natural length and has a known spring constant k.
Schematization
Represents the initial and final states of the system, identifying a y+-axis
upwards for each object.
Modelization
Create a model for the velocity modulus with which load B will hit the ground based on known parameters only. Do not integrate
Then test your model with the following values
Mass of load A: 80kg;
Mass of the suspended load (B): 65kg
The initial height of the suspended mass (h): 2 7m
Coefficient of friction under the mass A : 0 21
Spring constant: 78 N/m
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