Newton’s Second Law of Motion

Force & Acceleration Larger the net force, greater the acceleration Double the Force Triple the Force Half the Force implies Double the Acceleration Triple the Acceleration Half the Acceleration implies Acceleration “goes as” Force Force “goes as” Acceleration. Think about Cars and Motors

Check Yourself You push on a crate with 100 Newtons of force. If the friction force is 100 Newtons, does the crate accelerate? No, because net force is zero. Does that mean that the crate is not moving? No, just that its velocity is constant.

Check Yourself (cont.) Now push with 150 N; friction is still 100 N. Does the crate accelerate? Yes, because net force is now 50 Newtons. A friend helps push with an additional 150 N. By how much does acceleration increase? Net force is now = 200 N. This is FOUR times larger so acceleration increases by a factor of four.

Mass & Acceleration For a given force, greater mass, smaller the acceleration Double the Mass Triple the Mass Half the Mass implies Half the Acceleration Third of the Acceleration Double the Acceleration implies Acceleration goes as the inverse of mass. Think about a shopping cart

Check Yourself ????? NO FRICTION

Newton’s Second Law of Motion The acceleration of an object is directly proportional to the net Force applied to the object and inversely proportional to the mass of the object. (Acceleration) = (Net Force) (Mass) Mathematically written A = F/M F = M x A M = F/A

Try it… Zoo keepers lift a stretcher that holds a sedated lion. The total mass of the lion and stretcher is 175 kg, and the upward acceleration of the lion and stretcher is m/s 2. What force is needed to produce this acceleration of the lion and the stretcher? Known:m = 175 kgEquation: F=ma a = m/s 2 Work: F = (175) (0.657)Answer: 115 N

Let’s see what you know… What force is needed to accelerate a 1.6 x 10 3 kg forward at 2.0 m/s 2 Known:m = 1600 kgEquation: F=ma a = 2.0 m/s 2 Work: F = (1600) (2.0)Answer: 3200 N The net force on the propeller of a 3.2 kg model airplane is 7.0 N. What is the acceleration of the airplane? Known:m = 3.2 kgEquation: a=F/m F= 7.0 N Work: a = 7.0/3.2Answer: 2.2 m/s 2

Last chance… A baseball accelerates downward at 9.8 m/s 2. If the gravitational force is the only force acting on the baseball and is 1.4 N, what is the baseball’s mass? Known:F = 1.4 NEquation: m=F/a a = 9.8 m/s 2 Work: m = 1.4/9.8Answer: 0.14 kg

Weight on Earth Acceleration of gravity on Earth is = 9.8 m/s 2 From Newton’s Second Law, (Force) = (Mass) X (Acceleration) For example, weight (force of gravity) for 1 kg is ( 9.8 Newtons ) = ( 1 kg ) X ( 9.8 m/s 2 )

Free Fall Acceleration Newton’s Second Law explains why all objects fall with same acceleration. Ratio of weight/mass always the same since weight depends on mass.

Falling in a Vacuum Feather falls slowly due to air resistance force. If we remove the air (create a vacuum) then feather and coin fall with same acceleration.

Air Resistance (Drag) Origin of drag is molecules of gas (or liquid) striking a moving object. (Friction in the air!) Drag force depends on: Size (area) of the object Speed of the object Larger the size or speed, larger the drag. Also depends on shape of object, density of gas or liquid, etc.

Terminal Velocity Speed of falling objects increases until drag force balances weight. When forces balance, zero acceleration so constant velocity. Speed for which air resistance balances weight called terminal speed. High terminal speed (better open the chute!) Low terminal speed (large area of chute)

Can a Penny kill you if dropped of the Empire State Building