Newton's second and third law questions

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Newton's second law states that an object will accelerate if a net force acts on it, meaning that multiple forces can result in acceleration depending on their vector sum. In the scenario of a father and daughter pushing off each other, both experience equal force magnitudes, but the daughter accelerates more due to her smaller mass. Newton's third law explains that while forces are equal and opposite, they do not cancel out in the case of a massive crate because the crate's inertia prevents it from moving. The scale readings in an elevator indicate acceleration; a reading of 75 N suggests downward acceleration, while 120 N indicates upward acceleration. Understanding these principles is crucial for grasping the fundamentals of physics.
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HW Help!

I have no idea how to answer these questions!:confused:

1) Newton's second law indicates that when a net force acts on an object, it must accelerate. Does this mean that when two or more forces are applied to an object simultaneously, it must accleerate? Explain.

2) A father and his seven-year-old daughter are facing each other on ice skates. With thei hands, they push off against one another. (a) Compare the magnitudes of the pushing forces that the experience. (b) Which one, if either, experiences the larger acceleration? Acocount for your answers.

3) According to Newton's third law, when you push on an object, the object pushes back on you with an oppositely directed force of equal magnitude. If the object is a massive crate resting on the floor, it will probably not move. Some people think that the reason the crate does not move is that the two opposite directed pushing forces cancel. Explain why this logic is faulty and why the crate does not move.

4) A 10-kg suitcase is placed on a scale that is in an elevator. Is the elevator accelerating up or down when the scale reads (a) 75 N and (b) 120 N? Justify your answers.
 
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Please write your thoughts regarding the answers to these questions.

But consider:

1. Forces are vectors. Two opposing vectors of equal magnitude will produce a null result. Otherwise, the sum of two or more vectors has a magnitude and direction.

2. Equal forces - different masses.

3. What's the significance of friction? Static. Dynamic.

4. If one has stood in an elevator which acclerates down, one feels light. If the elevator accelerates upward, one feels heavier. Gravity is always pulling matter (mass) down.
 
1. Think of a ball lying on the floor. It is experiencing at least two forces - its weight downwards and the upwards supporting force of the floor. When someone kicks it into the air it also experiences two forces - its weight downwards and the force from the boot of the player.

2. This is a demonstration of Newton's third law. The daughter pushes her father just as hard as he pushes her, the action-reaction forces are the same size, but in opposite directions. One cannot push harder than the other, no matter who is the strongest! Their acceleration will differ though since their mass is not the same. The daughter will experience a much higher acceleration due to her smaller mass.

A friendly warning though. If you do not think about these concepts and try to understand them you will find that physics will become much more unpleasant and difficult to understand. In which case we will hear much more from you in the future about problems of this nature.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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