# Newton's 2nd Law of Motion - Eastern Illinois University Newtons 2nd Law of Motion Force and Acceleration Newton 2 Slide 1 Mass and Acceleration Mass resists acceleration, this is the principle of inertia We call this relationship inversely proportional Acceleration ~ 1/mass Newton 2 Slide 2 Newtons 2nd Law Newton-2 The acceleration produced by a net force acting on an object is directly proportional to the magnitude of the net force and in the same direction as the net force, and the acceleration is inversely proportional to

the mass of the object. Acceleration = net force/mass a=Fnet/m Physics 3050: Lecture 5, Slide 3 The Unit Newton Newtons 2nd law says a = Fnet / m So Fnet = ma by algebra 1N 1kg m / s 2 1 Newton of force is the amount of force necessary to accelerate 1 kg at 1 m/s/s This is why 1 kg weighs 9.8 N on Earth, because the acceleration due to gravity on earth (g) is 9.8 m/s/s Physics 3050: Lecture 5, Slide 4 Pressure Pressure = Force/Area

Pressure is directly proportional to force but is not the same thing as force 10 N of force exerted by pushing on someone with the palm of your hand 10 N of force exerted by pushing on someone with a pin P F P A Physics 3050: Lecture 5, Slide 5 F A

Which has the smaller surface area -- point of pin or palm of hand? Pin has smaller area and larger pressure Pressure Units SI: N/m2 = Pascal = Pa Named for Blaise Pascal (1623 1662) s s e l s s e pr French mathemetician & physicist

e r s u s le e s s pr equal e urweights mo r pre e ssu re e re r u o m es s

pr More Pressure Information & Examp les e e or sur m es pr Physics 3050: Lecture 5, Slide 6 less pre ss ure Finding Acceleration Kinematics > > v

a t Dynamics Physics 3050: Lecture 5, Slide 7 > Fnet a m d at 1 2 2 Two Ways to Find Net Force Fnet = Vector Sum FNET = F

Newton 2 FNET = m a Physics 3050: Lecture 5, Slide 8 Example: Pushing a Box on Ice. A skater is pushing a heavy box (mass m = 100 kg) across a sheet of ice (horizontal & frictionless). He applies a force of 50 N toward the right. If the box starts at rest, what is its speed v after being pushed for a time v=? t = 5 s ? F = 50 N m d=? Physics 3050: Lecture 5, Slide 9

t=5s a=? Example: Pushing a Box on Ice... Start with F = ma. net a = Fnet / m. a = (50 N)/(100 kg) = 0.5 N/kg = (0.5 kg m/s2)/kg a = 0.5 m/s2 Recall that vf = vi+ at (from definition of a) v = 2.5 m/s So v = (0.5 m/s2) (5 s) v = 2.5 m/s F = 50 N m

Physics 3050: Lecture 5, Slide 10 d=? t=5s a = 0.5 m/s2 Example: Pushing a Box on Ice... Now, what distance will the block travel during the 5 seconds? d = a t2 d = (0.5)(0.5m/s2)(5 s)2 d = 6.25 m v = 2.5 m/s F = 50 N m Physics 3050: Lecture 5, Slide 11

d=? t=5s a = 0.5 m/s2 Force and acceleration A force F acting on a mass m1 results in an acceleration a1. The same force acting on a different mass m2 results in an acceleration a2 = 2a1. m1 F F a1 m2 a2 = 2a1

If m1 and m2 are glued together and the same force F acts on this combination, what is the resulting acceleration? F (a) 2/3 a1 Physics 3050: Lecture 5, Slide 12 m1 m2 (b) 3/2 a1 a=? (c) 3/4 a1

Force and acceleration F m1 m2 a = F / (m1+ m2) Since a2 = 2a1 for the same applied force, m2 = (1/2)m1 m1 + m2 = 3m1 /2 but F/m1 = a1 So a = (2/3)F / m1 a = 2/3 a1 (a) 2/3 a1

Physics 3050: Lecture 5, Slide 13 (b) 3/2 a1 (c) 3/4 a1 Friction: force that resists motion force between the surfaces of two objects Examples: sliding friction, air resistance Friction acts in the direction opposite to motion Physics 3050: Lecture 5, Slide 14 Friction Example A force of 5 N is used to drag a 1 kg object across the lecture table at a constant velocity of 1 m/s. What is the

friction force opposing the motion? What is the acceleration of the object? Velocity constant acceleration = 0 What is the net force on the object? Acceleration = 0 Fnet = 0 What is the force of friction opposing the FN = 10 N motion? 5N 5N 5 N Physics 3050: Lecture 5, Slide 15 Fg = 10 N Friction Example A force of 5 N is used to drag a 1 kg object across the lecture table at a constant velocity of 1 m/s. What is the

friction force opposing the motion? What is the force of friction opposing the motion? 5 N Now a force of 13 N is applied to the object. What is its acceleration? FN = 10 N 5N Fnet = 13 N 5 N = 8 N a = Fnet/m = 8 N/1 kg = 8 m/s2 Physics 3050: Lecture 5, Slide 16 13 N Fg = 10 N

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