#Physics graphical analysis how to
#Physics graphical analysis plus

Only one right-angled triangle is actually necessary the two shown in the diagram are identical. The x and y components of A, A x and A y are found by drawing right-angled triangles, as shown. A vector, which we will call A, has a length of 5.00 cm and points at an angle of 25.0В° above the negative x-axis, as shown in the diagram. Splitting a vector into its components involves nothing more complicated than the trigonometry associated with a right-angled triangle.Д¬onsider the following example. The easiest way to add or subtract vectors, which is often required in physics, is to add or subtract components. Added together, the two components give the original vector. A scalar, like the magnitude of the vector, will not be in bold face (e.g., A).ДЄ vector pointing in a random direction in the x-y plane has x and y components: it can be split into two vectors, one entirely in the x-direction (the x-component) and one entirely in the y-direction (the y-component). Note that a vector will normally be written in bold, like this : A. With a vector, the negative sign can always be incorporated into the direction.

A velocity of -20 km/hr east also means that you're traveling at a speed of 20 km/hr, but in the direction opposite to east : 20 km/hr west, in other words. If you're traveling with a velocity of 20 km/hr east, it means you're traveling east, and your speed is 20 km/hr. With a vector the sign simply tells you the direction of the vector.

#Physics graphical analysis plus

A scalar with a negative sign means something very different from a scalar with a plus sign +30вЊ feels an awful lot different than -30вЊ, for example. One crucial difference between scalars and vectors involves the use of plus and minus signs. Velocity is a combination of a scalar (speed, 20 km/hr) and a direction (east).Д®xamples of scalars : mass, temperature, speed, distanceД®xamples of vectors : displacement, velocity, acceleration, force If you came to campus on the T today, at some point you may have been traveling 20 km/hr east. A vector has both a number and a direction, like velocity. A scalar is something that's just a number with a unit, like mass ( 200 g ) or temperature ( -30вЊ). It's critical now to distinguish between two kinds of quantities, scalars and vectors. We'll move on from looking at motion in one dimension to motion in two or three dimensions. This is positive but steadily decreasing on the way up, zero at the very top, and then becomes more and more negative on the way down. The slope of the position graph gives the instantaneous velocity. The graph of position as a function of time is a plot of the equation: This is correct, as the ball returns to its starting point.

The positive and negative areas cancel each other out, meaning the net displacement is zero.

Again, this agrees with the maximum height calculated previously. The area is just a triangle, with a a base T/2 = 1.2245 s and height of 12 m/s.

Calculating the area under the curve for the ball on the way up (the positive area on the graph) gives the maximum displacement.

For this example of a ball going up and then back down, the graph confirms that the time taken on the way up equals the time taken on the way down.

The slope of the velocity graph is the acceleration, while the area under the curve is the displacement.

The velocity graph can give all sorts of information: Plugging in the initial velocity and acceleration here gives v = 12.0 -9.8t What about the velocity graph? The equation for velocity is: T = -24.0 / -9.8 = 2.45 s, agreeing with what we calculated previously. If the time T represents the time when the ball returns to your hand, the area under the curve must equal -24.0 m/s, because we know the velocity changes from 12.0 m/s to -12.0 m/s. This acceleration is constant, so it's easy to plot on a graph. The only acceleration we have to worry about is the acceleration due to gravity, 9.8 m/s 2 down. Let's return to our last example, a ball thrown vertically upward with an initial speed of 12 m/s.

#Physics graphical analysis how to

Learning how to interpret these pictures can really help you understand physics. Graphs are basically pictures of equations.

We also usually need equations to find numerical solutions. It's amazing how much information you can get from a diagram. Graphical analysis and Vectors Graphical analysis and VectorsДrawing good pictures can be the secret to solving physics problems.