Drop-load (III) 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 slides on a surface. 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 sits is tilted upwards at a known angle theta from the horizontal. There is friction under mass A: the kinetic friction coefficient is known. The string attached to mass A is perfectly parallel to the surface on which the mass rests. Schematization Draw a diagram of each object that interests us. Draw your x- and y-axes for each object. Draw and name each force experienced by each object that interests us. Modelization Creates a model for the modulus of the velocity at which the load B will hit the ground as a function of the value of the masses A and B, along with the block's initial height B, the kinetic friction coefficient, and the angle d inclination of the surface on which the mass A is resting only. Then test your model with the following values: Mass of the load A : 95kg Mass of suspended load (B): 65kg Initial height of suspended mass (h): 3.7m Coefficient of friction under mass A: 0.27 Angle of inclination of the surface on which the mass A is placed: 14.5 degrees
Drop-load (III)
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 slides on a surface.
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 sits is tilted upwards at a known angle theta from the horizontal.
There is friction under mass A: the kinetic friction coefficient is known.
The string attached to mass A is perfectly parallel to the surface on which the mass rests.
Schematization
Draw a diagram of each object that interests us. Draw your x- and y-axes for each object. Draw and name each force experienced by each object that interests us.
Modelization
Creates a model for the modulus of the velocity at which the load B will hit the ground as a function of the value of the masses A and B, along with the block's initial height B, the kinetic friction coefficient, and the angle d inclination of the surface on which the mass A is resting only.
Then test your model with the following values:
Mass of the load A : 95kg
Mass of suspended load (B): 65kg
Initial height of suspended mass (h): 3.7m
Coefficient of friction under mass A: 0.27
Angle of inclination of the surface on which the mass A is placed: 14.5 degrees
Step by step
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