* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Newton`s Second Law (PowerPoint)
Coriolis force wikipedia , lookup
Specific impulse wikipedia , lookup
Atomic theory wikipedia , lookup
Classical mechanics wikipedia , lookup
Equations of motion wikipedia , lookup
Jerk (physics) wikipedia , lookup
Classical central-force problem wikipedia , lookup
Inertial frame of reference wikipedia , lookup
Fictitious force wikipedia , lookup
Work (physics) wikipedia , lookup
Electromagnetic mass wikipedia , lookup
Rigid body dynamics wikipedia , lookup
Centripetal force wikipedia , lookup
Equivalence principle wikipedia , lookup
Seismometer wikipedia , lookup
Relativistic mechanics wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Newton’s Second Law Why do objects of different mass and therefore different weights fall at the same rate (g) in the absence of air resistance? g g The more mass an object has the greater its inertia or resistance to a change in motion. The more mass an object has the greater the force of gravity acting on that mass. We know that an object’s ability to change its motion is related to both inertia and unbalanced force by……. Fg = m g M m g g g = Fg = Fg m M Fg Fg The bigger mass has more inertia but proportionally more force acting upon it so will fall at the same rate. Putting it all together…… The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. a = FNET / m or FNET = m a The direction of the acceleration is in the direction of the applied force. The net force in this case is: 275 N + 395 N – 560 N = +110 N and is directed along the + x axis of the coordinate system. If the mass of the car is 1850 kg then, by Newton’s second law, the acceleration is FNet 110 N 2 a 0.059 m s 1850 kg m Inertial Mass Inertial mass is the property of an object that determines how it responds to a given force Different masses have different accelerations when a force acts on them Inertial mass, M(i) = F / a Gravitational Mass Gravitational mass is the property of an object that determines how much gravitational force it feels near another object Different masses have different gravitational forces acting between them Gravitational force M(g) Gravitational Mass and Inertial Mass Inertial mass and gravitational mass are very different. The surprise is that they turn out to be equivalent. In other words, an object’s gravitational mass is equal to its inertial mass. The fact that different objects have the same value for free-fall acceleration shows this. Compound Systems A system consists of two or more interacting objects. A compound system is composed of two or more objects that are restrained so that they have to move together. Forces are external if they act on the system and internal if they act within the system Rules: 1. Treat the two connected objects as one object in order to determine the change in motion (acceleration) of the system and/or any external forces acting on the system 2. Look at each individual object separately (FBD) in order to determine any internal forces A 4000 kg airplane accelerates down the runway pulling a 1000 kg glider with a towing cable. The forward thrust provided by the planes propellers is 20000 N. i) What is the acceleration of the glider down the runway ii) What is the tension in the towing cable - + 4000kg 1000kg FT i) mp = 4000kg mg = 10000kg FE = 20000 N a = ? FT 20000N ii) Look at just the glider Fnet = mT a a = 4 m/s2 FE = mT a Fnet = mg a a = FE / mT FT = mg a = (1000kg) (4 m/s2) a = 20000N / (4000kg+1000kg) a = 4 m/s2 FT = ? = 4000N Check: Look at just the airplane Fnet = mp a FE - FT = mp a FT = FE - mp a FT = 20000N - (4000kg)(4m/s2) = 4000N Write an expression for the acceleration of the cart/weight system shown below and the tension in the string Mc FT FT mH mH g Fnet = mH g Looking just at the cart a = Fnet / mT a = mH g / (Mc + mH) FT = MC a If MC mH Looking just at the hanging mass a = mH g / (mH) = g If mH MC a = mH g / (Mc) Fnet,C = MC a Fnet,H = mH a mH g - FT = mH a = 0 FT = mH g - mH a = mH (g - a) A 500 g cart on a horizontal surface is being pulled by a 200 g hanging mass. What is its acceleration and tension in the connecting string? mH = 0.2 kg Mc = 0.5 kg g = 9.8 m/s2 a = mH g / (Mc + mH) a = (0.2kg)(9.8 m/s2) / (0.5kg+0.2kg) a = 2.8 m/s2 Looking just at the cart Looking just at the hanging mass Fnet,C = MC a FT = mH (g - a) FT = MC a FT = (0.2kg) (9.8N/kg - 2.8N/kg) FT = (0.5kg)(2.8N/kg) = 1.4 N FT = 1.4 N