- Messages
- 227
- Reaction score
- 571
- Points
- 103
19)
Take the load on the right-hand side string. Since that load is in equilibrium, the tension force on it has to be equal to it's weight, which we are given is 100 Newtons.
Now take the scale on the right. The scale will tell us how hard the string is pulling on it, which is the definition of the tension in the string. So the tension in the left-hand string is given to us by the reading on the scale. Since this is 20 Newtons, the tension in the left-hand side string is also 20 Newtons.
Whenever the disc rotates a little, it loses energy because the tension in the string does a little work on the disc - take the right-hand string. The disc rotates in an anti-clockwise direction, such that the point of contact with the right-hand string moves upwards (Imagine it - the disc rotates, so the point on the right moves a little bit up). Since the force of tension acts downwards, the work done by the force is negative (because force and displacement are in the opposite direction, F.s becomes negative).
The work done by the force in 1 second is the (Magnitude of Force) * (distance traveled). The distance traveled by the point where the string contacts the disc is equal to 50 revolutions (every second, it goes around 50 times). This distance = 50 * 2πr.
We are told that circumference = 0.30 meters. Since circumference = 2πr, we can say that 2πr = 0.3 meters.
So distance = 50 * 0.3 = 15 meters.
Therefore, the work done by this 100 Newton force = - 100 * 15 = - 1500 Joules per Second. = -1500 Watts.
On the other side, the tension in the left-hand side string does positive work (because it acts downwards, and the point in contact with the string also moves downwards with the rotation). The distance traveled is the same, 15 meters, but the work done is positive because both the distance and force are in the same direction (downwards).
This work = + 20 Newtons * 15 meters = 300 Joules per Second = 300 Watts.
Therefore, the net power by external force = -1500 + 300 = -1200 Watts.
Since the disc keeps spinning at a constant rate and is not slowing down, the motor has to provide this much power per second to counter the effects of the external force. Therefore, the power of the motor is 1200 Watts = 1.2 kW = B.
38)
I'm actually not too sure about this - either ways, this is my best guess:
Charge has to be conserved, so taking the nucleus as the system, we can see that initially the charge of the "system" is +28 units (28 protons; neutrons don't provide charge to system, so we don't count them).
When we add an electron to the system, the charge has to decrease by 1 unit, since the charge of an electron is -1 unit. Therefore, the new charge of the system has to be +27 units.
This is also the final state of the system (since no other process occurs to balance the number we have got, etc). Therefore, if the final charge of the nucleus has to be +27 units, the only possible answers are B or C.
One guess we can make (concerning the absorption process involved) is that one proton combines with the electron to produce a neutron - this results in 28 protons becoming 27, which is correct according to what we have established. But what this also results in is an extra neutron. Therefore, in the final nucleus, we have one less proton and one more neutron than the original nucleus.
The original nucleus had 28 protons and (59 - 28) = 31 neutrons.
The final nucleus should have 27 protons and 32 neutrons.
Thus the mass number should be 27 + 32 = 59, and the proton number should be 27. The only option that has both of these criteria is C, which is our final answer.
Hope this helped!
Good Luck for all your exams!
what are u talking about??
