Big celebration
An inseparable part of all big celebrations is the entertainment, during which the participants try to pull off the tablecloth from the set table so that nothing falls from the table on the ground. Let us look at this trick up close.
We will start from Newton's second law, which can be written as F=ma
The law can be understood in two ways:
If on a body with mass m acts a resultant force of magnitude F, the body will accelerate with an acceleration of magnitude a in the direction consistent with the direction of the acting force, if the base accelerates with acceleration a in the frame connected with the base, an inertial force of magnitude F acts on all objects on the base in the direction opposite to the direction of the acceleration a.
Here the role of the base will be played by the tablecloth. On it is placed a plate with a mass of m = 300 g. The coefficient of friction between the plate and the tablecloth equals f = 0.2. Adam pulled the tablecloth such that it began to move with acceleration a1=1 m⋅s−2. To his surprise, the plate began to move along with the tablecloth. Draw a picture into which with arrows mark the forces acting on the plate. Calculate the resultant force which acted on the plate in the frame connected with the tablecloth. Calculate what the smallest acceleration a2 must be, so that the inertial force overcomes the friction force, and the plate begins to move with respect to the tablecloth.
Borek therefore pulled the tablecloth in such a way that he accelerated with acceleration 3a2. Determine the magnitude and direction of the acceleration a3 of the plate in the frame connected with the tablecloth. Even though Borek pulled the tablecloth with sufficient force, the plate also began to move relative to the table. Calculate the magnitude and direction of this acceleration a3. If you calculated correctly, the acceleration a3 came out independent of the acceleration a2. That should, however, mean that for successful pulling off the tablecloth it suffices to overcome the acceleration a2. Why is it, however, better to pull off the tablecloth with the greatest possible force (with the greatest acceleration)?
We will start from Newton's second law, which can be written as F=ma
The law can be understood in two ways:
If on a body with mass m acts a resultant force of magnitude F, the body will accelerate with an acceleration of magnitude a in the direction consistent with the direction of the acting force, if the base accelerates with acceleration a in the frame connected with the base, an inertial force of magnitude F acts on all objects on the base in the direction opposite to the direction of the acceleration a.
Here the role of the base will be played by the tablecloth. On it is placed a plate with a mass of m = 300 g. The coefficient of friction between the plate and the tablecloth equals f = 0.2. Adam pulled the tablecloth such that it began to move with acceleration a1=1 m⋅s−2. To his surprise, the plate began to move along with the tablecloth. Draw a picture into which with arrows mark the forces acting on the plate. Calculate the resultant force which acted on the plate in the frame connected with the tablecloth. Calculate what the smallest acceleration a2 must be, so that the inertial force overcomes the friction force, and the plate begins to move with respect to the tablecloth.
Borek therefore pulled the tablecloth in such a way that he accelerated with acceleration 3a2. Determine the magnitude and direction of the acceleration a3 of the plate in the frame connected with the tablecloth. Even though Borek pulled the tablecloth with sufficient force, the plate also began to move relative to the table. Calculate the magnitude and direction of this acceleration a3. If you calculated correctly, the acceleration a3 came out independent of the acceleration a2. That should, however, mean that for successful pulling off the tablecloth it suffices to overcome the acceleration a2. Why is it, however, better to pull off the tablecloth with the greatest possible force (with the greatest acceleration)?
Final Answer:
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