A circuit contains an EMF source, a resistor R, a capacitor C, and an open switch in series. The capacitor initially carries zer
1 answer:
Answer:
t = 1.098*RC
Explanation:
In order to calculate the time that the capacitor takes to reach 2/3 of its maximum charge, you use the following formula for the charge of the capacitor:
(1)
Qmax: maximum charge capacity of the capacitor
t: time
R: resistor of the circuit
C: capacitance of the circuit
When the capacitor has 2/3 of its maximum charge, you have that
Q=(2/3)Qmax
You replace the previous expression for Q in the equation (1), and use properties of logarithms to solve for t:
The charge in the capacitor reaches 2/3 of its maximum charge in a time equal to 1.098RC
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Answer:
System D --> System C --> System A --> System B
Explanation:
The gravitational force between two masses m1, m2 separated by a distance r is given by:
where G is the gravitational constant. Let's apply this formula to each case now to calculate the relative force for each system:
System A has masses m and m separated by a distance r:
system B has masses m and 2m separated by a distance 2r:
system C has masses 2m and 3m separated by a distance 2r:
system D has masses 4m and 5m separated by a distance 3r:
Now, by looking at the 4 different forces, we can rank them from the greatest to the smallest force, and we find:
System D --> System C --> System A --> System B
1. A person's weight will change if they move from the Earth to the moon.
In fact, the weight of a person is given by:
where m is the mass of the person and g is the gravitational acceleration. The mass of the person, m, is the same on the Earth and on the moon, but the value of g is different on the Moon (about 1/6 of the Earth's value), so the weight also changes.
2. An astronaut is launched into space. The mass of the astronaut did not change. This is measured in Kg.
The mass of an object (or of a person, as in this case) is an intrinsec property of the object, that depends on the amount of matter inside the object: therefore, this quantity does not depend on the location of the object, so it is the same on the Earth, on the Moon and in space.
3. What is the weight of a ring tailed lemur that has a mass of 10 kg? -98 N
The weight of the lemur is given by:
where m=10 kg is the lemur's mass and g=-9.8 m/s^2 is the gravitational acceleration. Using these numbers, we find
and the negative sign simply means that the direction of the weight is downward.
4. What is the mass of the lemur from the previous question if it was on the International Space Station? 10 kg
As we said in question 1), the mass of an object does not depend on the location, so the mass of the lemur is still 10 kg, as in the previous exercise.
5. A rocket being thrust upward as the force of the fuel being burned pushes downward is an example of which of Newton's laws? Third's Newton Law
Third's Newton Law states that:
"When an object A exerts a force on an object B, then object B exerts an equal and opposite force on object A".
Applied to this case, the two objects are the fuel and the rocket. The fuel is pushed backward by the rocket, so the fuel exerts an equal and opposite force on the rocket, which then moves forward.
6. When a cannon is fired, the projectile moves forward. According to Newton's 3rd law, the cannon will want to travel backward.
Third's Newton Law states that:
"When an object A exerts a force on an object B, then object B exerts an equal and opposite force on object A".
Applied to this case, the two objects are the cannon and the projectile.The projectile is pushed forward by the cannon, so the projectile exerts an equal and opposite force on the cannon, which moves backward.
7. An object has a weight of 21,532 N on Earth. What is the mass of the object? 2,197 kg
The weight of the object is given by:
If we re-arrange the formula and we use W=21,532 N, we can find the mass of the object:
8. What is the mass of the object from the previous question if we put it on the moon? The force of gravity on the moon is 1.62 m/s2. 2,197 kg
As we said in question 4), the mass of an object does not change if we move it to another location, so its mass is still 2,197 kg.
9. How much force is exerted if a 250 kg object has an acceleration of 750 m/s2 ? 187,500 N
The force exerted on the object is given by Newton's second law:
where F is the force, m=250 kg is the mass and a=750 m/s^2 is the acceleration. By using these numbers, we find
10. A resting soccer ball moving after it is kicked is an example of which of Newton's laws? Newton's second law
Newton's second law states that when an object is acted upon unbalanced force, the object has an acceleration, given by the law
So, in this case, the ball is kicked and so an unbalanced force is applied to it, and for this reason the ball has an acceleration (in fact, it starts from rest, but then its velocity increases since it starts moving).