FORCES

Pulleys and Tension To understand and correctly use the terms “pulley” and “tension.” To set up and solve word problems involving pulleys and/or tension.

Tension The pulling force exerted on a rope, cable, etc. (Symbol: T, FT).

Pulley A wheel used to change the direction of tension on a rope.

Problems with Pulleys Find the acceleration of blocks m1 and m2. (Assume that the pulley has negligible mass and the surface and pulley are frictionless.)

Free-body Diagrams for the Two Masses FN FT FT Fg Fg

Therefore FT ia the net force on m1. For m1, Fnet= m1a For m2, gravity and tension are pulling in opposite directions. The net force is therefore Fnet= Fg- FT = m2a The blocks are connected so, FT and a are the same for both blocks.

Sample Problem 1 Suppose we had the following situation: Calculate the acceleration of the pair of blocks. 5 kg 2 kg

Youtube Video How to solve pulley problems in physics (AP Problems may not have values) https://youtu.be/Z_d1uQh_DBg

Answer For the block on the table: Fnet= FT = m1a = (5)(a) = 5a For the block hanging from the pulley: Fnet= Fg- FT = m2a = (2)(a) (2)(10) - FT = 2a 20 - FT = 2a Substitute FT = 5a into the second equation. 20 - 5a = 2a 20 = 7a a = 20/7 = 2.9 m/s2

Sample Problem 2 Two masses, m and M, are connected by an ideal (massless) rope over an ideal pulley (massless and frictionless). What is the acceleration of the larger mass, in terms of m, M, and g? m1 is m and m2 is M

Solution Substitute (2) in (1) Mg - (ma + mg) = Ma Mg - ma - mg = Ma Mg - mg = Ma + ma g(M - m) = a(M + m) (M + m) (M + m) Solution For mass, M: Fnet = Fg - T = Ma = Mg - T = Ma (1) For mass, m: Fnet = T - Fg = ma = T - mg = ma T = ma + mg (2)

Atwood’s Machine AP Physics Atwood Machine https://youtu.be/a0KVxh8iPP4

Classwork/ Homework Complete the Pulleys and Tension Worksheet

Friction To calculate the frictional force on an object and to calculate net force in problems involving friction.

Demo Drag a heavy object attached to a spring scale.

Friction Between Individuals Rub your hands together. Faster. Are they heating up? What causes this heat? We can rub each other the wrong way and “friction” will be the result. Matt 5: 9 says blessed are those who work for peace. Peace is also a fruit of the Spirit.

Friction It is a contact force caused by the roughness of the materials in contact, deformations in the materials, and molecular attractions between materials. Frictional forces are always parallel to the plane of contact between two surfaces, and opposite to the direction of motion or applied force.

Static Friction The friction acting on an object at rest that resists its ability to start moving. Push or pull is not large enough to move the object.

Kinetic Friction Friction that is resisting the motion of an object. In most situations static friction is a stronger force than kinetic friction.

Coefficient of Friction It relates the frictional force to the normal force. It is represented by the Greek letter μ (mu). It is a ratio of two forces. Therefore, is dimensionless so it has no units.

Coefficient of Static and Kinetic Friction Coefficient of Static Friction, μs represents the coefficient of friction for an object that is stationary (not moving). Coefficient of kinetic Friction, μk represents the coefficient of friction for an object that is stationary (not moving).

Note Static friction is a inequality. A stationary object the force frictional force (resisting sliding) = applied force. However, once Force Applied > μsN, the object will start to move and the equation for kinetic friction is applied.

More About Friction Its direction is opposite to the direction of motion. But the direction of the friction vector is opposite to the force that is trying to cause motion. It is perpendicular to the normal force but the normal force will not tell you the direction of friction. To determine if the friction is positive or negative, use the force applied or the direction of the motion. Remember, negative is about direction, NOT value.

Solving Simple Friction Problems Friction is constant so all friction problems involve friction in addition to some other (usually externally applied) force. To calculate the force friction, you need to Calculate the force of gravity. On Earth, Weight, Fg=m(9.8) Calculate the normal force. If the object is on a flat (horizontal) surface (most of the time) the normal force is usually equal to gravity. FN Ff Fg

Solving Simple Friction Problems 3. Determine if friction is static (stationary) or kinetic (moving). 4. Calculate the force of friction. Ff ≤ μsFN or Ff = μkFN Assign positive or negative to friction as appropriate (It is about direction). 5. If the question is requiring the calculation of net force, calculate the net force using friction. If friction is causing the object to slow down and eventually stop and there is no separate applied force, then: Fnet = Ff If there is a force applied and friction is opposing if, then the net force would be: Fnet = Fapplied - Ff

Sample Problem A person pushes a box at a constant velocity across a floor: The box has a mass of 40 kg, and the coefficient of kinetic friction between the box and the floor is 0.35. What is the magnitude of the force that the person exerts on the box?

Solution Velocity is constant, so acceleration = 0 Therefore, no net force on the box. Fapp = Ff Ff = μkFN Normal force = weight of the box (Fg) FN= Fg= mg = (40kg)(10m/s2) = 400N Force of friction is: Ff = μkFN Ff = (0.35)(400N) Ff = 140N

Classwork/Homework Classwork: Complete the Friction Worksheet Homework: Please have a design for your egg drop project and provide a list of supplies.

1/10/18 Do Now 1. Define: gravity and gravitation. 2. Is there a difference between the two terms?

A Typical AP Dynamics Question AP dynamics (force) free - response problems will probably have (most of the time) an accelerating object with multiple forces acting on it. They may have ramps and pulley.

Gravity What is gravity? When will the gravity between two object change? How will a change in gravity impact an object?

Gravity The force of attraction between 2 objects Cause is unknown More mass = stronger attraction Force is weaker when there is a greater distance between objects. Fg∝ m/r (∝ means proportional to) Although we use (9.81 or 10) gravity on the Earth’s surface varies depending on where it is because the Earth is not a perfect sphere.

Gravitational Force Equation Fg ∝ m1 • m2 = m1 m2 = m1 m2 r1 r2 r1 r2 r2 Fg - gravitational force m1 and m2 - mass of the objects r1 = r2 = r - the distance between the two objects, some textbooks used instead of r.

Activity Knowing that: Determine the units for Universal Gravitational Constant. The magnitude is 6.67 x 10-11.

Newton’s Law of Universal Gravitation Fg = 6.67 x 10-11 m1m2 r2 The number 6.67 x 10-11 is called the universal gravitational constant and is represented by G. Thus, Newton’s Law of Gravitation formula is

Deriving Gravity a = g = F m Therefore g = Gm1 r2 Divide both side by m1 Fg = Gm1m2 m2 r2m2 Remember F = ma → a = F m a = g = F m Therefore g = Gm1 r2 If G = 6.67 x 10-11, m1 = mass of the Earth(5.97 x 1024 kg) and r = radius of the Earth Plug in the values, what value did you get for g?

Classwork/ Homework Universal Law of Gravitation worksheet