Vectors, Force and Momentum (Coursework Sample)

Vectors, Force and Momentum
Name:
Institution:
Two vectors A and B have the same magnitude of 100N (they represent forces of equal strength). We can carry out the following calculations based on the two vectors.
* What is the magnitude of the resultant vector of A and B if they are parallel and pointing in opposite direction?
The two forces are of equal magnitude but acting in opposite direction. Clearly, vectors have magnitude and direction, where in this case we can assume A to be acting to the right with 100N and B to the left with -100N. Thus, they cancel each other and hence the resultant force is zero.
-100N +100N
Resultant force = -100N + 100N = 0
* What is the magnitude of the resultant vector of A and B if they are parallel and pointing in the same direction?
The two forces are of equal magnitude and acting in the same direction. In this case, the two vectors are acting in the same direction (assume to the right) which means they have the same sign. Thus, we can represent them with +100N each to the right. Applying head-tail vector addition, we will have the forces represented by the vector diagram as
+100N +100N
Resultant force = (+100 N) + (+100 N) = 200N to the right
* If A and B are at right angles, is the magnitude of their resultant vector less 100N, exactly 100N or more than 100N?
Suppose A is acting due North while B is acting due East. The vectors form a right-angled triangle of a head-tail vector diagram as shown below.
100N 100 N
100N
The resultant force is found by calculating the length of the hypotenuse using Pythagorean Theorem since the two vectors make a right angle to each other.
Resultant force = (1002+1002 ) N = 141.42 N North-East
Therefore, the resultant force is more than 100N.
* Explain conservation of momentum. Give an example where it can be applied.
The law of conservation of momentum states that for a collision occurring between two objects or bodies in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. In this case, suppose we have two objects, object A and object B. If the two objects collide, then the momentum lost by A is equal to the momentum gained by B. what this simply implies is that the total momentum of the collection of the two bodies (a system) is conserved, that is, the total momentum is constant or unchanged. For instance, if A loses 75 units of momentum, then B gains 75 units of momentum. However, the total momentum of the two objects A and B is the as before and after the collision. Momentum, p, is the product of mass of the body, m, and its velocity, v. The SI unit for momentum is kgms. The law of conservation of momentum is applied in physics labs in ticker tape analysis. s
Momentum = mass x velocity, P=mv
Collisions occur commonly in sports, for example in football, racket, bat sports (baseball, golf, tennis, etc.). Consider a collision between a fullback and a linebacker during a line stand. The fullback plunges across the goal line and collides in midair with the linebacker. The linebacker and the fullback hold each other and move together after the collision. Suppose the linebacker possesses a momentum of 80 kgms to the right while the fullback possesses a momentum of 95 kgms to the left before the collision. Therefore, the total momentum of the system before collision is 15 kgms to the left. This also implies that the total momentum after collision is also 15 kgms to the left according to the law of conservation of momentum.
* Which Newton’s law involves acceleration? Explain.
Newton’s second law involves acceleration and it therefore states that the acceleration of a body is directly proportional to, and in the same direction as, the net force acting on the body and inversely proportional to its mass. Alternatively, when a force acts on an object, it will cause the object to accelerate. The second law of motion gives the exact relationship between force, mass and acceleration. The larger the mass of the body the greater the force needed to cause acceleration. The law can be expressed as a mathematical equation:
F=ma , where F =force, m = mass and a = acceleration
example: Mike’s motorbike, which weighs 100kg, is out of fuel. He decides to push his motorbike to a petrol station to refuel it with an acceleration of 0.5m/s2 . Then the force applied can be calculated as:
Force = mass x acceleration, F = (100 x 0.5) N = 50 N
* Why is speed considered a scalar and velocity a vector?
Scalar quantity has magnitude/size but has no direction while a vector quantity has both magnitude and direction. Speed has only magnitude and no direction, thus is a scalar quantity while velocity has both magnitude and direction and hence a vector quantity.
* If you place a box on an inclined plane, it gains momentum as it slides down. What is responsible for this increase in momentum?
The increase in momentum is clearly explained by Newton’s law of universal gravitation, which gives an equation of gravitational force acting on two massive bodies. The equation is given by
F=GMm/r2 -------------------------------------- (1)
, where F = gravitational force, G = gravitational constant, M = mass of one body, m = mass of the other body and r = distance between their centers of mass. Now, suppose M is the mass of the Earth and m the mass of the box. Newton’s second law relates the force acting on a massive body/object to its resultant acceleration.
F=ma ------------------------------------------------ (2)
Rearranging the equation for acceleration, we obtain
a=Fm ---------------------------------------------- (3a)
In this case, if we let F to be the gravitational fo...