Chapter 11 Force

Newton’s First Law An object at rest will remain at rest and an object in motion will continue in motion at a constant velocity unless acted upon by a net force

Newton’s First Law of Motion “Law of Inertia” tendency of an object to resist any change in its motion increases as mass increases

Inertia Inertia is the tendency to resist change in motion Change in motion is always caused by a force An object will keep doing what it’s doing until a force acts on it

Mass and Inertia Massive objects resist change in motion Objects with more mass need larger forces to change their motion

Newton’s 1st Law An object at rest (still) will stay at rest until a force acts on it. An object in motion will stay in motion until a force acts on it.

Newton’s 1st Law You aren’t wearing a seatbelt while driving (NOT a good idea). You run your car into a wall. Your car stops, but you remain in motion, so you fly through the windshield. If you’re wearing your seatbelt, you slow down with the car. Airbags can reduce the force of the impact.

Force, Mass, and Acceleration Exerting a larger force on an object causes a greater change in velocity. A greater change in velocity means there is greater acceleration.

F = ma Newton’s Second Law of Motion The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. AKA-When mass goes up, acceleration goes down, and when force goes up, acceleration goes up F = ma

Force, Mass, and Acceleration If the same force is exerted on a more massive and a less massive object, the more massive object can’t accelerate as much. The more massive object will have a lower velocity.

F = ma F m a F m F: force (N) m: mass (kg) a: accel (m/s2) Newton’s Second Law m F a F m F = ma F: force (N) m: mass (kg) a: accel (m/s2) 1 N = 1 kg ·m/s2

force of attraction between any two objects in the universe Gravity Gravity force of attraction between any two objects in the universe increases as... mass increases (one or both objects) distance decreases

Who experiences more gravity - the astronaut or the politician? Which exerts more gravity - the Earth or the moon? more mass less distance

W = mg Weight the force of gravity on an object MASS WEIGHT Gravity W: weight (N) m: mass (kg) g: acceleration due to gravity (m/s2) MASS always the same (kg) WEIGHT depends on gravity (N)

Would you weigh more on Earth or Jupiter? Gravity Would you weigh more on Earth or Jupiter? Jupiter because... greater mass greater gravity greater weight

Animation from “Multimedia Physics Studios.” Gravity Accel. due to gravity (g) In the absence of air resistance, all falling objects have the same acceleration! On Earth: g = 9.8 m/s2 elephant feather Animation from “Multimedia Physics Studios.”

a F m F = ? F = ma m = 40 kg F = (40 kg)(4 m/s2) a = 4 m/s2 F = 160 N Calculations What force would be required to accelerate a 40 kg mass by 4 m/s2? GIVEN: F = ? m = 40 kg a = 4 m/s2 WORK: F = ma F = (40 kg)(4 m/s2) F = 160 N m F a

a F m m = 4.0 kg a = F ÷ m F = 30 N a = (30 N) ÷ (4.0 kg) a = ? Calculations A 4.0 kg shotput is thrown with 30 N of force. What is its acceleration? GIVEN: m = 4.0 kg F = 30 N a = ? WORK: a = F ÷ m a = (30 N) ÷ (4.0 kg) a = 7.5 m/s2 m F a

a F m F(W) = 572 N m = F ÷ a m = ? m = (572 N) ÷ (9.8 m/s2) Calculations Mrs. Ellis weighs 572 N. What is her mass? GIVEN: F(W) = 572 N m = ? a(g) = 9.8 m/s2 WORK: m = F ÷ a m = (572 N) ÷ (9.8 m/s2) m = 58.4 kg m F a

ConcepTest Is the following statement true or false? An astronaut has less mass on the moon since the moon exerts a weaker gravitational force. False! Mass does not depend on gravity, weight does. The astronaut has less weight on the moon.

when an object is influenced only by the force of gravity Free-Fall Free-Fall when an object is influenced only by the force of gravity Weightlessness sensation produced when an object and its surroundings are in free-fall object is not weightless! CUP DEMO

Free-Fall Weightlessness surroundings are falling at the same rate so they don’t exert a force on the object

Space Shuttle Missions NASA’s KC-135 - “The Vomit Comet” Free-Fall Space Shuttle Missions Go to Space Settlement Video Library. NASA’s KC-135 - “The Vomit Comet” Go to CNN.com. Go to NASA.

ConcepTest 1 TRUE or FALSE: An astronaut on the Space Shuttle feels weightless because there is no gravity in space. FALSE! There is gravity which is causing the Shuttle to free-fall towards the Earth. She feels weightless because she’s free-falling at the same rate.

Newton’s Third Law Newton’s Third Law of Motion When one object exerts a force on a second object, the second object exerts an equal but opposite force on the first.

Newton’s Third Law One object exerts a force on the second object The second exerts a force back that is equal in strength, but opposite in direction

Aren’t these “balanced forces” resulting in no acceleration? Newton’s Third Law Problem: How can a horse pull a cart if the cart is pulling back on the horse with an equal but opposite force? Aren’t these “balanced forces” resulting in no acceleration? NO!!!

forces are equal and opposite but act on different objects Newton’s Third Law Explanation: forces are equal and opposite but act on different objects they are not “balanced forces” the movement of the horse depends on the forces acting on the horse

Newton’s Third Law Action and Reaction forces do not cancel – they can act on different objects or spread in different directions

Action-Reaction Pairs Newton’s Third Law Action-Reaction Pairs The hammer exerts a force on the nail to the right. The nail exerts an equal but opposite force on the hammer to the left.

Action-Reaction Pairs Newton’s Third Law Action-Reaction Pairs The rocket exerts a downward force on the exhaust gases. The gases exert an equal but opposite upward force on the rocket. FG FR

F m Action-Reaction Pairs Both objects accelerate. Newton’s Third Law Action-Reaction Pairs Both objects accelerate. The amount of acceleration depends on the mass of the object. F m Small mass  more acceleration Large mass  less acceleration

p = mv v p m Momentum quantity of motion p: momentum (kg ·m/s) m: mass (kg) v: velocity (m/s)

Momentum: inertia in motion when you’re moving, momentum keeps you moving an object with lots of momentum is hard to stop

v p m Momentum: p = momentum (in kg m/s) m = mass (in kg) p = mv p = momentum (in kg m/s) m = mass (in kg) v = velocity (in m/s) momentum is a vector quantity, so a complete answer will include magnitude and direction

Is it possible for a motorcycle and a large truck to have the same momentum? m = 400 kg m = 40,000 kg

v p m p = ? p = mv m = 280 kg p = (280 kg)(3.2 m/s) v = 3.2 m/s Momentum Find the momentum of a bumper car if it has a total mass of 280 kg and a velocity of 3.2 m/s. GIVEN: p = ? m = 280 kg v = 3.2 m/s WORK: p = mv p = (280 kg)(3.2 m/s) p = 896 kg·m/s m p v

v p m p = 675 kg·m/s v = p ÷ m m = 300 kg v = (675 kg·m/s)÷(300 kg) Momentum The momentum of a second bumper car is 675 kg·m/s. What is its velocity if its total mass is 300 kg? GIVEN: p = 675 kg·m/s m = 300 kg v = ? WORK: v = p ÷ m v = (675 kg·m/s)÷(300 kg) v = 2.25 m/s m p v

Example: What is the momentum of a 150 kg defensive tackle at 5 m/s north towards the end zone?

Example: What is the momentum of a 325 pound defensive tackle at 5 m/s north towards the end zone? m = 150 kg) v = 5 m/s north p = mv momentum p = (150 kg) (5 m/s) p = 750 kg m/s north

To change the momentum of an object, you must change… mass and/or velocity usually velocity changes change in velocity is acceleration to make an object accelerate, a force is required So a force causes a change in the momentum of an object. Size of force and the time the force acts both affect change in momentum.

The Importance of “Following Through” in Sports The follow-through increases the time of collision and thus increases the change in momentum, making the ball have a higher velocity!

t Δv I F I m Impulse: what changes the momentum Impulse = Ft Depends on force and time of collision Impulse = Ft Impulse = change of momentum units for impulse are same as units for momentum Impulse = Δp OR Ft = m(Δv) m I Δv

Example: A hockey player applies an average force of 80. 0 N to a 0 Example: A hockey player applies an average force of 80.0 N to a 0.25 kg hockey puck for a time of 0.10 seconds. Determine the impulse experienced by the hockey puck.

Example: A hockey player applies an average force of 80. 0 N to a 0 Example: A hockey player applies an average force of 80.0 N to a 0.25 kg hockey puck for a time of 0.10 seconds. Determine the impulse experienced by the hockey puck. F = 80.0 N t = 0.10 s Impulse = Ft impulse Impulse = (80.0 N) (0.1 s) Impulse = 8 N s Impulse = 8 kg m/s F I t kg m/s2 N

Δv I m I = ? I = m Δ v m = 950 kg I = (950 kg)(9m/s) Δv = 40-31 m/s Example #2 What is the change in momentum (impulse) of a 950 kg car that travels from 40 m/s to 31 m/s? GIVEN: I = ? m = 950 kg Δv = 40-31 m/s = 9 m/s WORK: I = m Δ v I = (950 kg)(9m/s) I = 8550 kg·m/s m I Δv

t I F I = 8550 kg* m/s F= I÷ t F = ? N F = (8550)÷ (30) t= 30 s Example #3 If the from the last problem had an impulse of 8550 kg*m/s, and it took 30 seconds to change speeds, then what force caused the change? GIVEN: I = 8550 kg* m/s F = ? N t= 30 s WORK: F= I÷ t F = (8550)÷ (30) F = 285 N F I t

The Effect of Collision Time upon the Force Impulse (kg m/s) Time (s) Force (N) 100 1 2 50 4 25 10 1000 0.1 F I t

Time and force are ________ proportional. inversely For an object in a collision, to decrease the effect of the force, the time must be increased To Increase the effect of the force, the time must be decreased.

Air Bags Air bags increase the time allowed to stop the momentum of the driver and passenger, decreasing the force of impact. Time increases 100 times! Force decreases 100 times!

Use of Mats in Sports Mats increase the time allowed to stop the momentum of the athlete, decreasing the force of impact.

“Riding the Punch” When a boxer recognizes that he will be hit in the head by his opponent, the boxer often relaxes his neck and allows his head to move backwards upon impact. “Riding the punch” increases the time the force is applied, decreasing the force of impact.

Conservation of Momentum Law of Conservation of Momentum The total momentum in a group of objects doesn’t change unless outside forces act on the objects. pbefore = pafter

Conservation of Momentum Elastic Collision KE is conserved Inelastic Collision KE is not conserved

Conservation of Momentum A 5-kg cart traveling at 1.2 m/s strikes a stationary 2-kg cart and they connect. Find their speed after the collision. BEFORE Cart 1: m = 5 kg v = 4.2 m/s Cart 2 : m = 2 kg v = 0 m/s AFTER Cart 1 + 2: m = 7 kg v = ? p = 21 kg·m/s m p v p = 0 v = p ÷ m v = (21 kg·m/s) ÷ (7 kg) v = 3 m/s pbefore = 21 kg·m/s pafter = 21 kg·m/s

Conservation of Momentum A 50-kg clown is shot out of a 250-kg cannon at a speed of 20 m/s. What is the recoil speed of the cannon? BEFORE Clown: m = 50 kg v = 0 m/s Cannon: m = 250 kg AFTER Clown: m = 50 kg v = 20 m/s Cannon: m = 250 kg v = ? m/s p = 0 p = 1000 kg·m/s p = 0 p = -1000 kg·m/s pbefore = 0 pafter = 0

Conservation of Momentum So…now we can solve for velocity. GIVEN: p = -1000 kg·m/s m = 250 kg v = ? WORK: v = p ÷ m v = (-1000 kg·m/s)÷(250 kg) v = - 4 m/s (4 m/s backwards) m p v