Review, Concepts 1-10. (And little other stuff..)
1. The S.I. units for length, time, mass, force, work, energy power, are as follows: meter, second, kilogram, Newton, joule, watt.
2. To find the vector sum of two or more vectors, you can use the tip-to-tail method or the component method. I prefer the component method, where you break down a vector into its x and y components by multiplying by cosine theta for x, by sine theta for y. Using the tip to tail method requires drawing, first choosing an initial vector, then drawing the next vector at its tip, then for the resultant connecting the initial’s tail to the last vectors tip.
3. Vectors have direction and magnitude, such as force and velocity. Scalars only have a magnitude, no direction, such as mass time and temperature.
4. The rules of scientific notation are that you must have only one digit before the decimal place, like so 3.0, and that you must multiply by a power of ten, such as 3.0 x 10^4. Significant figures in a calculation are only as accurate to the least accurate number in the operation. Example: 4.0 * 100 only has two significant figures.
5. Velocity is speed with direction, displacement is the distance displaced from original position, acceleration is the rate of change in velocity. The two essential kinematics equations are v^2=v0^2 + 2a(d) and x-x0=v0t + 1/2at^2. To calculate the horizontal displacement of a projectile, it would be Dh = Vh*t. You can find the vertical displacement by finding the vertical component’s velocity and then putting it into y= v0*t + ½*g*t^2. To calculate the horizontal displacement of a projectile given an angle, you would find the x component of that angle and then multiply it by time. You can find the vertical displacement by finding the vertical component’s velocity and then putting it into y= v0*t + ½*g*t^2.
6. Newton’s laws are as follow, Every body continues in its state of rest or of uniform speed in a straight line unless acted on by a nonzero net force. The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object. And of course, whenever one object exerts a force on a second object, the second exerts an equal and opposite force on the first.
7. Newton’s universal law of gravitation. Every particle in the universe attracts every other particle with a force that is proportional to the product of their masse and inversely proportional to the square of the distance between them. This force acts along the line joining the two particles. F = G(m1*m2)/r^2, r being the distance between m1 and m2. The relationship between mass and weight is that weight is mass*gravity.
8. Work is a scalar quantity. It is describes what is accomplished by the action of force when it acts on an object as the object moves through a distance. The unit of work is the joule. Energy is the ability to do work, this is also measured in joules.
9. Kinematics and uniformly accelerated rotational motion can be related simply by letting a = alpha, v = omega, and x = theta. Thus w=w0+alpha(t), theta = wot + ½(alpha)t^2. w^2 =w0^2 + 2(alpha)(theta). ave. w = ( w + wo )/2
10. The law of conservation of momentum states that the before momentum is equal to the momentum after. m1v1+m2v2 = m1v1`+m2v2`. A 5kg duck waddles 5m/s into a 4 kg chicken which is initially at rest. The duck ends up moving at a speed of 1m/s in it’s original direction. m1v1+m2v2 = m1v1`+m2v2`. 5*5 + 0 = 5*1 + 4v2`. 20/4 = v2` = 5m/s. The law of conservation of angular momentum states that the total angular momentum of a rotating body remains constant if the net torque acting on it is zero. This means as long as no external forces are being applied, the total angular momentum will remain the same.
11. In order for an object to be in equilibrium when concurrent forces are acting upon it, the components of the force vectors must sum to 0. Thus net force x = 0, net force y = 0, and net force in all = 0. For an object to be in equilibrium when parallel forces are acting on it, the net torques must sum to 0. Sum of torque clockwise will equal sum of torque counterclockwise. It is thus important to choose a fulcrum.
12. Periodic motion: used to describe a vibration or an oscillation that repeats itself over the same path.. Displacement: The position of an object. Amplitude: The maximum displacement. Period: The time in seconds required for one complete cycle. Frequency: The number of cycles, per second. Simple Harmonic Motion: Sinusoidal motion of a single frequency. The equation for the period of a spring is T = 2pi*sqrt(m/k). For example, how long does it take for a spring with a hanging mass of 5 kg and spring constant 10N/m to exhibit one complete cycle? T = 2pi*sqrt(5/10). T = 2pi*sqrt(1/2).
13. A transverse wave refers to a wave that causes the particles of the medium it travels in to move a direction perpendicular to the motion of the wave itself. On the other hand, in a longitudinal wave, the vibration of the particles of the medium is along the same direction as the motion of the wave. Reflection is when a wave strikes an obstacle, or comes to the end of a medium it is traveling in. A part of the wave is reflected back. Superposition is referring to the algebraic sum of waves interfering with each other. Standing waves are created when the medium is vibrating at the correct frequency. This frequency is obtained when clear nodes are formed where there is no motion, the points of destructive interference, and antinodes, the points of constructive interference. Harmonics are the frequencies where standing waves are formed. The fundamental frequency can be found by the equation v/2L or v/lambda.
14. Sound, form of energy vibration. The medium that the sound wave travels through, determines the speed. The energy is transmitted by waves. Sound waves need a medium to propagate. Sound waves are p-waves, longitudinal waves.
15. The fundamental harmonic, also known as the first harmonic of an open tube, can be found via f = v/2L, where v is the speed of the medium and f is the frequency. For a one end closed tube, it is found via f = v/4L. To find the overtones of a closed tube, you multiply the fundamental frequency by 3, 5, 7.. etc. For an open tube, it is simply 2,3,4,5.. etc