Chapter 11 Forces

Laws of Motion Force and motion are connected. Force and motion are connected. –An object will have greater acceleration if a greater force is applied to it. –The mass of an object and the force applied to it affect acceleration. Newton’s second law of motion connects force, mass, and acceleration in the equation acceleration equals net force divided by mass Newton’s second law of motion connects force, mass, and acceleration in the equation acceleration equals net force divided by mass

Laws of Motion Friction—force that opposes motion between two surfaces that are touching each other Friction—force that opposes motion between two surfaces that are touching each other –Microwelds, areas where surface bumpers stick together, are the source of friction. –Friction between two surfaces that are not moving past each other is called static friction. –Sliding friction—force that opposes the motion of two surfaces sliding past each other –Friction between a rolling object and the surface it rolls on is called rolling friction.

Laws of Motion Air resistance that opposes the force of gravity. Air resistance that opposes the force of gravity. –The amount of air resistance depends on an object’s shape, size, and speed. –Terminal velocity—forces on a falling object are balanced and the object falls with constant speed

Air Resistance Air Resistance Air Resistance –a.k.a. “fluid friction” or “drag” –force that air exerts on a moving object to oppose its motion –depends on: speed speed surface area surface area shape shape density of fluid density of fluid

Air Resistance Terminal Velocity Terminal Velocity –maximum velocity reached by a falling object –reached when… F grav = F air F air F grav –no net force  no acceleration  constant velocity

Air Resistance Falling with air resistance Falling with air resistance F grav = F air Animation from “Multimedia Physics Studios.”Multimedia Physics Studios –heavier objects fall faster because they accelerate to higher speeds before reaching terminal velocity –larger F grav  need larger F air  need higher speed

Gravity Weight Weight –the force of gravity on an object MASS always the same (kg) WEIGHT depends on gravity (N) W = mg W:weight (N) m:mass (kg) g:acceleration due to gravity (m/s 2 )

Gravity Accel. due to gravity (g) Accel. due to gravity (g) –In the absence of air resistance, all falling objects have the same acceleration! –On Earth: g = 9.8 m/s 2 elephant feather Animation from “Multimedia Physics Studios.”Multimedia Physics Studios

Gravity Law of gravitation—any two masses exert an attractive force on each other Law of gravitation—any two masses exert an attractive force on each other –Gravity is one of the four basic forces that also include the electromagnetic force, the strong nuclear force, and the weak nuclear force. –Gravity is a long-range force that gives the universe its structure. Due to inertia, all objects fall with the same acceleration regardless of mass. Due to inertia, all objects fall with the same acceleration regardless of mass.

Weight—gravitational force exerted on an object Weight—gravitational force exerted on an object –Weight decreases as an object moves away from Earth. –Weight results from a force; mass is a measure of how much matter an object contains. Objects in the space shuttle float because they have no force supporting them. Objects in the space shuttle float because they have no force supporting them. Projectiles have horizontal and vertical velocities due to gravity, and follow a curved path. Projectiles have horizontal and vertical velocities due to gravity, and follow a curved path. Acceleration toward the center of a curved path is called centripetal acceleration; it is caused by centripetal force, an unbalanced force. Acceleration toward the center of a curved path is called centripetal acceleration; it is caused by centripetal force, an unbalanced force. Gravity

Gravity Gravity Gravity –force of attraction between any two objects in the universe –increases as... mass increases mass increases distance decreases distance decreases

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

Newton’s Third Law Newton’s third law of motion—to every action force there is an equal and opposite reaction force Newton’s third law of motion—to every action force there is an equal and opposite reaction force –Action-reaction forces act on different objects and differ from balanced forces. –Rocket propulsion is based on Newton’s third law of motion. Before it was discovered, the existence of the planet Neptune was predicted based on gravitational forces and Newton’s laws. Before it was discovered, the existence of the planet Neptune was predicted based on gravitational forces and Newton’s laws.

Momentum—related to how much force is needed to change an object’s motion; momentum equals mass times velocity. Momentum—related to how much force is needed to change an object’s motion; momentum equals mass times velocity. Law of conservation of momentum— momentum can be transferred between objects; momentum is not lost or gained in the transfer. Law of conservation of momentum— momentum can be transferred between objects; momentum is not lost or gained in the transfer. Newton’s Third Law

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

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. 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

Momentum The momentum of a second bumper car is 675 kg·m/s. What is its velocity if its total mass is 300 kg? 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

Conservation of Momentum Law of 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. p before = p after

Conservation of Momentum Elastic Collision Elastic Collision –KE is conserved Inelastic Collision 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. 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 p = 0 p before = 21 kg·m/sp after = 21 kg·m/s m p v v = p ÷ m v = (21 kg·m/s) ÷ (7 kg) v = 3 m/s

Conservation of Momentum A clown is shot out of a 250 kg cannon at 20 m/s. If the cannon moves backwards at 2 m/s, how much does the clown weigh? A clown is shot out of a 250 kg cannon at 20 m/s. If the cannon moves backwards at 2 m/s, how much does the clown weigh? Given: Clown: m = ? v = 20 m/s Cannon: m = 250 kg v = -2 m/s

Conservation of Momentum So…now we can solve for velocity. So…now we can solve for velocity. GIVEN: p = 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