All you wanted to know about Formulae and Graphs (but were afraid to ask!)

Transcription

1 All you wanted to know about Forulae and Graphs (but were afraid to ask!) o be able to carry out practical investigations in Physics you ust understand the following: 1. What variables are you investigating 2. How the forula relates to the variables you are investigating 3. How the forula relates to a y = x + c graph 4. How to process the variables and draw a linear graph 5. What the linear graph actually tells you Soeties you are asked to investigate two variables fro a forula that ight also be exained in the external exas. Soeties the forula ay be just for the practical assessent you are doing. Exaple 1: Ai: o find the force, F, applied to a spring and the extension, x, of the spring. Step 1: What variables are you investigating? force extension Forula: F = kx Step 2: How the forula relates to the variables you are investigating F = force, x = extension, k = spring constant Step 3: How the forula relates to a y = x + c graph Since y = x + c and F = kx (You ight have to rearrange the equation at this point) he y = x + c graph is a straight line graph and so F = kx should be too providing you plot F on the y-axis and x on the x-axis y F (N) = k c x c = 0 x () If you plot F on the y axis and x on the x-axis this should give you an intercept of 0 (since you could write the equation as F = kx + 0) and the gradient,, should be equal to the spring constant, k. In this exaple there is no step 4 and 5 because this is a linear relationship. he assessed investigations are non-linear so it ay not always be as straightforward as to what you do.

2 Exaple 2: Ai: o find the atheatical distance travelled, d, and the tie taken, t, for a basketball to fall fro rest towards the ground. Step 1: What variables are you investigating? distance tie Forula: d = ½ g t 2 Step 2: How the forula relates to the variables you are investigating d = distance, g = acceleration due to gravity and t = tie Step 3: How the forula relates to a y = x + c graph Since y = x + c and d = ½ g t 2 (You ight have to rearrange the equation at this point) he y = x + c graph should a straight line graph and so should d = ½ g t 2 on the y-axis and t 2 on the x-axis).. providing you plot d y d () = ½ g c x c = 0 t 2 (s 2 ) Providing you plot d on the y-axis and t 2 on the x-axis this should give you an intercept of 0 and the gradient,, should be equal to ½ g, the acceleration due to gravity, g. Step 4: How to process the variables and draw a linear graph Now you understand that the graph is d versus t 2, calculate values for t 2 (units of s 2 ) and plot the graph. Step 5: What the linear graph actually tells you You should be able to write a atheatical forula for your graph e.g. d = 4.8t 2 (again based upon y = x + c where c = 0). In this case, the gradient of your d versus t 2 graph should be about 5 since it is the sae as ½ g.

3 Coplete the following: 1. Ai: o find the atheatical kinetic energy, E k, and the velocity, v, for a car involved in a crash. Forula: E k = ½ v 2 velocity, v kinetic energy, E k E k (J) v 2 ( 2 s -2 ) (gradient) = ½ 2. Ai: o find the atheatical velocity, v, of a ball when it hits the ground, and the height, h, it is dropped fro. Forula: v = 2gh 3. Ai: o find the atheatical ass,, of an object and its acceleration, a, for a constant force. Forula: F = a 4. Ai: o find the atheatical force exerted on a wire,f, by a current, I, flowing in a constant agnetic field, B. Forula: F = BIL *Why wouldn t you get this as an assessent?*

4 5. Ai: o find the atheatical current, I, flowing in a circuit and the resistance, R. Forula: V = IR 6. Ai: o find the atheatical ie period,, of a pendulu and its length, l. Forula: = 2π l g 7. Ai: o find the atheatical tie period,, of a spring-ass syste and its ass,. Forula: = 2π k 8. Ai: o find the relationship between the distance, S i, and the focal length, f, of a convex lens Forula: S i S o = f 2

5 Answers forula independent variable dependent variable y-axis x-axis gradient 1. E k = ½ v 2 v E k E k (J) v 2 ( 2 s -2 ) ½ 2. v = 2gh h v v (s -1 ) h ( ½ ) 2g 3. F = a (a=f/) a a (s -2 ) 1/ (kg -1 ) F 4. F = BIL I F F (N) I (A) BL * You would not get F=BIL in an assessent as this is a linear atheatical relationship. 5. V = IR (I=V/R) R I I (A) 1/R (Ω -1 ) V 6. = 2π l g l (s) l ( ½ ) 2π / g 7. = 2π k (s) (kg ½ ) 2π / k 8. S i S o = f 2 (f 2 =S i S o ) S i f f 2 ( 2 ) S i () S o