Gauss’ law: a. Relates the surface charge density to the electric field.b. Relates the electric field at points on a closed surf
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Answer:
- Problem 1: because, by the third law of Newton, the second time, the reaction force of the desk on the hand is stronger.
- Problem 2: See the figure attached
- Problem 3: See the figure attached
- Problem 4: 8N
- Problem 5: 10N
- Problem 6: 0.0033 m/s²
- Problem 7: 0.39 m/s² backwards
Explanation:
<em>1. You hit your hand on a desk and it doesn't hurt that much. The next day you are carrying a heavy backpack in your hand and you hit the same desk. This time your hand hurts a lot when you hit the desk. Explain why your hand hurt the second time using concepts discussed in class.</em>
When you hit the desk the first day, you were able to control the force with which you did it, thus you exerted a low force on the desk. By the third law of Newton, law of action and reaction, the force that the desk exerted on your hand is the same that your hand exerted on the desk, a low force.
The next day, the force with which you hit the desk is stronger because the heavy backpack pulled your hand toward the desk, thus you exerted a stronger force on the desk than the day before and, by the third law of Newton, the force that the desk exerted on you hand is also stronger.
In conclusion, your hand received a stronger hit back from the desk.
<em>2. You are holding an apple over your head. Draw a free-body-diagram. A free-body-diagram is when you draw all the forces acting on individually objects that are free floating in space not touching anything else.</em>
To draw the free-body-diagram, FBD, you replace the apple by a point, your hand by an arrow pointing upward, and the force that the Earth exerts on the apple (the weight of the apple) by an arrow pointing downward.
The apple is at rest on your hand, meaning that the two forces, the force of gravity and the force of your hand are balanced, making the net force zero. Thus, the size of the two arrows should be equal.
In the figure attached, the arrow pointing upward is labled H, and the arrow pointing downward Fg, for force of gravity.
See the FBD attached.
<em>3. After a while, your hand/arm gets tired so you let go of the apple. Now the apple is falling through the air. Draw the free-body-diagram (and all the forces that are acting on the apple now).</em>
After you let go of the apple, the apple starts falling through the air, at first the only force acting on the apple is the force of gravity, but at it moves down the air exerts a drag force. Many times this force is neglected, but that depends on the conditions of the problem.
For an apple falling down from your hand the drag force is usually neglected and it is said that the apple is in free fall.
Since, the problem states to include all the forces acting on the apple, your FBD must include the drag force, as an arrow pointing upward. This time the arrow pointing upward is shorter than the arrow pointing downward, because the drag force is less than the gravity force.
See the second figure attached.
<em>4. If the apple has a mass of 0.8 kg, calculate the force due to gravity of the apple while it is falling through the air.</em>
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The magnitude of the <em>force due to gravity</em> on an object is equal to the product of the mass of the object and the acceleration of gravity. This force is what the weight of an object is.
The calculations are:
Formula:
- Fg = mass × acceleration
Compute:
- Fg = 0.8kg × 9.8m/s² = 7.84 N
Thus, rounding to one significant figure the force due to gravity is 8 newtons and is the wieght of the apple.
<em>5. A box with mass (m) = 2 kg) has an acceleration of 5 m/sec². Calculate the total force acting on the box.</em>
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This time you must use the second law of Newton.
The second law of Newton states that the net force acting on an object is equal to the product of the mass and the acceleration.
Equation:
- Net force = mass × acceleration
Substitute and compute:
- Net force = 2kg × 5m/s² = 10N
Thus, the magnitud of the total force is 10 newtons.
<em>6. Suppose that an astronaut outside pushes on a spaceship. The astronaut creates a force of 36N. If the mass of the spaceship is ms = 11,000kg, calculate the acceleration of the spaceship.</em>
The physical law that rules this problem is the second law of Newton.
- Net force = mass × acceleration
You must solve for the acceleration:
- Acceleration = Net force / mass
Substitute and compute:
- Acceleration = 36N / 11,000kg = 0.0033 m/s²
<em>7. The astronaut forgot about Newton's 3rd law. The moment they push on the spaceship, they start to accelerate backwards. If the astronaut has a mass of ma = 92 kg, calculate the acceleration of the astronaut using information from the previous problem.</em>
The third law of Newton is the law of action and reaction. The force that the astronaut exert on the spaceship is equal in magnitude to the force the spaceship exterts on the astronaut but backwards.
Then, using the second law of Newton with the same force and the mass of the astronaut you can calculate the acceleration of the astronaut.
- acceleration = net force / mass
- acceleration = 36N / 92kg = 0.39m/s² backwards
