I have a question from motors and gens (from the Surfing book)
A metal bar, mass 0.04kg, resistance 4 ohms, and length 0.5m, is placed on two frictionless conducting rails in a magnetic field of 0.3T. The bar is connected to a 36 V power source.
a) Calculate the current in the bar (ans: 9A)
b) Calculate the magnitude of the force which acts on the bar (ans: 1.35 N)
c) If the bar is free to move, and the force is in the appropriate direction, calculate how far it will move along the rails in 0.25 s. (ans: 1.05m)
Thanks in advance
P.s. I can't say for sure if the answers are correct on the book because some of the answers we get from questions can be really dodgy.
Hello Cajama:
I am a year 12 student currently undertaking physics and I am more than happy to help you out here. In regards to questions like these, a lot of people get stuck on it because of how abstract the question is (after all, we cant really see the magnetic field and whoever made this question is so time-poor that they wouldnt even bother giving us a diagram). A lot of my friends are in the same situation and what I recommend to do is to draw a simple 2D diagram just to make life easier. In a HSC exam, questions like these would often be accompanied by a 3D diagram, and similarly what I would recommend for you to do is to draw a 2D diagram which allows you to observe whats happening much more clearly.
Ok so recommendations aside, lets get into the question.
N.B. In the 2D diagram I have attached, I have assumed the direction of the magnetic field vectors and the negative and positive terminals on the voltage supplier. Now, you will soon discover that even if the magnetic field direction reverses, or if the negative and positive terminals reverse, the current will still be travelling in a direction that is perpendicular to the direction of the magnetic field. Hence in this case I am allowed to assume these directions. The importance of this will be discussed later on in part B.
a) This question is rather simple. After you manage to draw out your 2D diagram, you will see thats it's simply an application of Ohm's Law, something we learnt back in year 11 in the "Electricity at homes" module.
Ohm's law states that R = V/I. In this question, our R = 4 ohms, V = 36V and hence when we substitute these values into the formula, we get an answer of 9A currents (R = V/I, I = V/R, I = 36/4, I = 9A)
b) Usually in a question that is divided into several parts, the outcome of the previous part will usually relate to solving the second part. In part a), we were demanded to calculate the current flowing through the metal bar. Recall all the formulae you have learnt in Motors and Generators module, there are two formulae that heavily relate to the concept of force: F = BILsin(theta) and F=qvBsin(theta). If we think about F=qvBsin(theta), we will soon discover that we dont exactly have a value for q, and nor do we have a value for v. Hence F=qvB would be unsuitable for solving part b). Let's consider F =BIL sin(theta). We calculated the current flowing through the bar in part a), which we found out to be 9A. We are also provided with the length of the bar which is 0.5m and the magnitude of the magnetic field which is 0.3T.
But, what about theta? Clearly we are NOT provided with the value of theta. BUT THROUGH DRAWING A 2D DIAGRAM, we can find out what theta is. Lets go back to the first principles and define what this theta is, in the equation F = BILsin(theta). This theta is defined as the angle between the direction of the current and the magnetic field vector. So, when you consider the 2D diagram, it becomes apparent that the current is travelling in a direction that is perpendicular to the magnetic field direction. Therefore, the value of theta is 90 degrees.
Now let's substitute everything into the equation F= BILsin(theta). B = 0.3T, I = 9A, L = 0.5m and theta = 90 degrees. Hence
F = 0.3 x 0.5 x 9 x sin(90) = 1.35 N which is the magnitude of the force. The direction of the force here cannot be calculated because we are not provided with the direction of the magnetic field, we only know that the direction of the magnetic field, whether to the right or to the left, will be perpendicular to the current flow within the metal bar.
c) Ok so this is perhaps the most tricky part of the question because it combined the knowledge from TWO MODULES!! The way I figured out this question is through observing which part of the question I havent used yet. So far, we have used resistance, voltage, length and magnetic field values provided by the question. So now we are left with 0.04kg mass, and like what I said beforehand, the previous part in a question will usually relate to its subsequent part. In part b) we found out the magnitude of force which is 1.35N, hence using Newton's 2nd law F=ma, we discover that 1.35 = 0.04(a), hence a=33.75 ms^-2. Sweet, now we have acceleration, but we were asked to find the displacement of the bar. A convenient way to figure out what to do is to just skim through the formula sheet, finding out the equation that relate acceleration and displacement together. Hence in this case it would be appropriate to use the formula y = ut + 1/2 at^2, because we have all the necessary details to figure out displacement (y). Initially, velocity of the bar is 0, hence u= 0 ms^-1. The acceleration we have worked out is 33.75 ms^-2 and the time in this case is provided (t = 0.25s). Everything after this step now is easy, substitute in all the values, we will obtain that y = 0(0.25) + 1/2 (33.75) (0.25)^2 and throw this into the calculator will will obtain an answer of 1.05m (2.d.p.).