AP Physics C I.B Newton’s Laws of Motion

Note: the net force is the sum of the forces acting on an object, as well as ma.

An object may accelerate in one dimension or two. ΣF x = ma x or ΣF y = ma y

Free body diagrams

Ex. Two cases for a 0.20 kg hockey puck on a frictionless surface. Find the horizontal acceleration when a) F 1 = 4.0 N b) F 2 = 2.0 N and F 3 = 1.0 N at 30.0º below the horizontal.

Ex. Three students pull on a ring with the forces shown. The ring doesn’t move. What is the magnitude and direction of F B ?

Weight and Mass

The normal force – the force a surface exerts on an object, perpendicular to the surface.

Tension – forces exerted by strings, ropes, chains, cables etc. Since these devices can only pull on an object and not push, the force of tension is always away from the object.

Which string experiences the most tension? 2m2mm

Newton’s Third Law – When two bodies interact, the forces are always equal in magnitude but opposite in direction. This is true whether the objects are stationary, moving at a constant velocity or accelerating.

Ex. For the system of blocks shown a) draw a free body diagram on each block b) find the acceleration of the hanging block c) and the tension in the rope.

Ex. For the hanging block shown, find the tension in each rope.

Ex. For the block shown find a) the tension in the rope and b) the normal force on the block.

Ex. Apparent weight of a 72 kg person in an elevator given by the scale reading (normal force). Find the apparent weight when a) the elevator is at rest or moving at a constant velocity b) accelerating upward at 3.20 m/s 2 and c) accelerating downward at 3.20 m/s 2.

Ex. For the blocks shown find a) the acceleration of the blocks and b) the force on block B by block A.

Friction – the book on the table The book is pushed and released The book is pushed across the table at a constant velocity Pushing a stack of books

The direction of friction

Causes of friction and a couple of equations

Ex. In 1960, the longest recorded skid marks (290 m) on a public road, the MI highway in England, were made by a Jaguar. How fast was the car moving at the moment it began skidding?

Ex. A woman uses a rope to pull a loaded sled with a mass of 75 kg along a horizontal patch of ice at a constant velocity. The coefficient of kinetic friction between the sled runners and ice is 0.10 and the rope makes an angle of 42º with the horizontal. What is the tension in the rope?

Ex. A coin rests on a book. When the book makes an angle of 13º with the table, the coin just begins to slip. What is the maximum coefficient of static friction between the coin and book?

For blocks that are sliding without slipping, treat them as a system. That is, they accelerate together. For blocks that are slipping, treat them separately. They are not accelerating together. Draw an FBD to identify the frictional force on each block.

Ex. Will the block slide if the applied force is 12 N, the coefficient of friction between the block and wall is 0.60 and the weight of the block is 5.0 N? FaFa

maa m m B = 3.0 kg m A = 1.0 kg F a = 12.0 N Ex. Find the force on block B by block A.