PHY 102 1st EditionExam # 2 Study GuideLecture 10 (September 18)Position: the magnitude and direction from an arbitrary location- Difference between distance and displacement – distance is the track along which something travels and the displacement is the straight line distance between the beginning and end point.- Example: blue is distance and black is displacementVector: magnitude and direction- Measurements include velocity, acceleration, displacement, momentum, force, change in momentumVelocity: speed & direction- Important equations to note:o V = ½ (v1 + vt)Acceleration: rate in change of velocity (speed or direction)- Relationships in positive and negative accelerationo If +v and +a, the object goes faster in the + directiono If +v and -a, the object goes slower in the + directiono If –v and +a, the object goes slower in the – directiono If -v and -a, the object goes faster in the - direction- Acceleration is in the same direction as the force- Remember that negative acceleration does not necessarily mean slowing down. Do not use the term “deceleration”.One example from this lecture:a. A vehicle accelerates from rest to 22 m/s in 4 s.A = ?V0 = 0 m/sV = 22 m/sT = 4sV = v0 + atv-v0 = ata = v-v0 /ta = (22 m/s -0)/4a = 5.5 m/s2Newton’s First Law: A body at rest will stay at rest, and a body in motion will stay in motion withconstant velocity along a straight line when not acted upon by external forces, i.e. friction. The first law is also a specific case of the second law, in which the acceleration is 0.- Important misconception: objects do not need a constant source of force to keep them in the same state of motion unless in the presence of frictiono Forces that act upon an object in motion: External Friction Sound loss- Example questions:o When an object is moving with a fixed velocity, is it accelerating? A: No.o When an object is moving with a fixed speed, is it accelerating? A: Maybe. If there is a change in direction, then the answer is yes.o If a car is moving at a constant speed of 60 mph as it turns a corner, is it accelerating? A: Yes.Aristotle’s Mistakes:- Motion is a natural state for a body, not just rest.- The air is carried along with the spinning earth- Concepts of Projectile motion o A projectile is not left behind because it has forward motion of its owno When something is moving forward, it shares in the forward motionMomentum (p): p = mv (units typically in Newtons or kg*m/s)- Conservation of momentum – the momentum is the same before and after a collisiono EXAMPLE: Two carts are placed on a track, and will collide in between two monitors of each cart’s velocityMomentum before: 1 kg + 3 m/s and p = mv so M = 3 kg m/sMomentum after: m1 + m2 = 2 kg and Vf = 1.5 m/s and p = mv so M = 3 kg m/s- Inertia is proportional to mass, not a numerical value.- Most important to remember: Pi=Pf (initial momentum equals final momentum)o EXAMPLE: A truck with a mass of 3,000 kg and a velocity of 20 m/s collides head on with a car of 1500 kg and a velocity of -20 m/s. If the vehicles stick together, what is the resulting motion of the pair?We know: pi = pf(m1 + m2 )VV =m1∗v 1+m2∗v 2m1+m2¿(3000 kg)(20 ms)+(1500 kg)(−20 ms)3000 kg+1500 kg30,000 m/s/4500Newton’s Second Law: The net instantaneous force acting upon an object is precisely the instantaneous change of its momentum per unit of time. The second law is written as:F=∆ P∆ T- Important concepts to note:o Acceleration is proportional to force.o Acceleration is inversely proportional to mass. (F = ma)- Equations to represent Newton’s Second Law:o F = ∆ P∆ To F = ∆ mv /∆ to F = m*∆ v /∆ to F = mao∑F=ma- EXAMPLE: A car with the mass of 1500 kg accelerates at a rate of -2 m/s2 under a constant force. What are the magnitude and direction of that force?∑F=maForce = ?M = 1500 kgA = -2 m/s2F = 1500 kg * -2 m/s2 = -3000 N N = kg*m/s2- Another example:o A force of 7 N is applied to a 3.5 kg mass for 2 seconds. What is the change of velocity?F = maF = 7 N F = m * ∆ v∆ t∆ v=?M = 3.5 kg∆ v=(7.0 N )(2 s)3.5 kgT = 2 s 4 m/sNewton’s Third Law: If an object A exerts a force Fab on an object B, then object B exerts a force Fba on object A such that Fab = -Fba. The sum of the two forces (vectors) have to be 0 because the object is not accelerating. In this event of a collision, the masses of the vehicles are very different but the forces will be equal.Large mass small massThe change in velocity will be less in the large truck because it has a larger mass so the passenger will likely survive. A greater mass for a given force gives lesser acceleration– the sameforce applied to two different masses gives different results.Forces are equal in the event of a collisionWeight: the force of gravity upon an object. Remember that the acceleration of gravity in free fall is -9.81 m/s2. Here is a demonstration of Newton’s Third Law in relation to weight:-740 N Weight of the person740 N Force of the earth on the personExample theory question: Does the weight of an object at rest change? Yes. The mass is constant but the force of gravity