You're looking for the flow speed in the needle (which differs from the speed in the syringe body), so the diameter should be 0.25mm. Otherwise, it's correct.
dV/dt is rate of volume flow, which is not flow speed (which is in m/s). In a non-viscous fluid, the rate of volume flow must be constant, which is proportional to the flow speed and the area of the flow path.
Hence, dV/dt = A1v1 = A2v2 (V = volume, A= area, v = velocity).
That's it. Because initially, both the mass and the heights are the same, the GPE has to be equal. By conservation of energy, GPE = rot. KE + translational KE.
Since I is different, rot KE. has to be different (and by extension angular speed), and since the total energy for the two is equal...
Again, no. Conservation of energy states that initial energy = final energy. What form is the initial energy in? What are the final states of energy? Are the total energy for the two objects similar?
No, you see, angular speed is related to the rotational kinetic energy of the object, which are not equal. Now, examine what is similar for these two objects, there's mass and there's the starting height. These two describe a certain physical quantity, what is it?
It would be helpful if you could state the exact meaning of the variables, especially that of I, V and k, though I think I know what they mean...
I also have a feeling that k is a constant describing loss of power to the surroundings, but I can't be sure until you provide more info.
Yes, but imagine this, the dog tries to swim at a velocity (and hence a route) perpendicular to the bank, but the stream has a velocity parallel to the bank, pushing it downstream as it swims. Wouldn't it be moving at an angle?
I'm sorry if I wasn't clear earlier, for a), your equation is...
a) The first part is on Pascal's Principle. We know that the pressure exerted by the nurse must be equal to the pressure required to push the serum into the blood. (Hint: Do check out what 140 - 100 means, it's very important)
b) Fluid flow rate must always be...?
c) What is the condition for the conservation of angular momentum? Does it hold in this case?
d) Compare the rotational KE of the system before and after the rod is placed on the turntable.
2nd paper Q5: The amount of rotational KE an object has depends on the object's moment of inertia, hence that cannot be an answer. (Hint: Think conservation of energy, what is always the same of two objects of the same mass going down the same height?)
Otherwise, well done!
To determine the direction of friction, it is worth recalling that friction always acts in the opposite direction of the motion of the object. In which direction is the block "trying" to move? Also, the block is stationary: what does this tell you about the magnitude of friction?
It would help if you draw the free body diagram for the forces acting on the pendulum at the equil. point, and the two maximum points.
It is worth remembering though, that a pendulum is moving is a circular motion, and there must be a net centripetal force (which is a resultant force, and...
a) Velocity = displacement/time, therefore, time = ?. To find velocity, simply add the velocity of the stream and the dog. (Note: Recall that velocity is a vector). For this part, we are interested in the component of velocity perpendicular to the bank.
b) Well, from a), you'll realise that...
These should be correct...
L = I(omega) is correct, but you are using the wrong I. 2/5mr^2 is the moment of inertia of a sphere about an axis through its centre. However, the bob is not rotating about its centre, but rather about a vertical axis at the centre of its circular motion...
The speed of sound in a gas is generally affected by the heat capacity ratio of the gas, the temperature and the its molar mass, none of which is related to the gravitational acceleration. Hence, the frequency of a standing wave should not change if the experiment is carried out on the moon...
Now that we have the vector part aside. Recall the reasoning I have made above:
First, equate the horizontal components of T1 and T2. It should be something like:
T2cos30 = T1cos60
Can you see why?
Yes, for the block to be moving at a constant velocity (by Newton's 1st Law), friction = force applied on block. Hence your answer is absolutely correct.
OK, now I see where all the confusion is arising from. So, about force vectors...
Any force can be resolved into components. Think of a force as a line that is the hypo. of a right angle triangle, where its magnitude is represented by the length of that line. The hypo. can be broken down into...
OK, you might want to draw the free-body diagram for the object in the first case. You know that the object is moving with an acceleration, so there is a net horizontal force acting on the object. What does this tell you about the magnitudes of the forces acting on the object?
In the second...
No, their HORIZONTAL components must be equal, which is not equal their magnitudes. The horizontal component of a force is analogous to the base of a right angle triangle, where the force itself is the hypo. This is where the trig kicks in.
So, we have now establised that the sum of the horizontal forces must equal to zero. Where do we go from here?
There are only two forces that have components in the horizontal direction, T1 and T2, and we know that the magnitudes of these two components must be equal.
If you understand...
Ok, then. We shall begin from the basics...
1) This is a statics problem, i.e. the system is in equilibrium. For translational equilibrium, the sum of forces in any direction must equal to zero. Hence, we can say that the sum of the forces in the horizontal component must equal zero. (I chose...
I see your problem:
"The atomic mass unit is 1 u = 931.5 MeV/c2"
This equation converts mass in units of u directly to MeV. Hence you may directly multiply u with 931.5 to find the energy in MeV.
I'm so sorry, but I forgot to read the fine print...
OK, first, should you be taking the horizonatal or vertical components of the forces? Remember that the mass is unknown, and hence weight is unknown...
PS: It's almost 4am here, so excuse the less-than-alertness...
Almost the exact same way you normally rationalise the denominator. The difference is that this time you multiply both top and bottom with the conjugate of the numerator.
From the electric field direction, can you determine the relative potential of the two plates, and determine their "sign" (i.e. the plate with the higher potential is positive, and vice versa)?