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 an inclined plane. A spring is attached to mass A to slow down the motion. Information The masses of the charges A and B are known. The pulley is a disc (a solid cylinder) of mass mp and radius R that can rotate without friction. The angle delta of the inclined plane is known. There is friction between mass A and the surface it sits on, the coefficient of friction is uc. The string attached to mass A is parallel to the inclined plane. The spring is parallel to the inclined plane, initially unstretched and its spring constant is known. Schematization Represent the initial and final states of the system, identifying an upward y+ axis for each object in translation. Modelization Create a model for the modulus of the velocity of mass B when it hits the ground, given the known parameters of the problem that are relevant. Then test your model with the following values Mass of charge A : 80 kg Mass of suspended load (B): 92 kg Pulley mass (mp): 50 kg Pulley radius: 0.59 m Coefficient of friction: 0.16 Initial block height B: 0.8 m Spring constant: 75 N/m Inclined plane angle: 13.2 degrees
Drop-load (IV)
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 an inclined plane. A spring is attached to mass A to slow down the motion.
Information
The masses of the charges A and B are known.
The pulley is a disc (a solid cylinder) of mass mp and radius R that can rotate without friction.
The angle delta of the inclined plane is known.
There is friction between mass A and the surface it sits on, the coefficient of friction is uc.
The string attached to mass A is parallel to the inclined plane.
The spring is parallel to the inclined plane, initially unstretched and its spring constant is known.
Schematization
Represent the initial and final states of the system, identifying an upward y+ axis for each object in translation.
Modelization
Create a model for the modulus of the velocity of mass B when it hits the ground, given the known parameters of the problem that are relevant.
Then test your model with the following values
Mass of charge A : 80 kg
Mass of suspended load (B): 92 kg
Pulley mass (mp): 50 kg
Pulley radius: 0.59 m
Coefficient of friction: 0.16
Initial block height B: 0.8 m
Spring constant: 75 N/m
Inclined plane angle: 13.2 degrees
Step by step
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