Review of Dynamics Forces and FBDs A force

Review of Dynamics

Forces and FBDs • A force (F) is a push or a pull, it is a vector quantity – Units are N = 1 kg • m/s 2 – Ex. Tension, Gravity, Normal Force … • A Free Body Diagram (FBD) is a diagram of a single object that shows all the forces acting on the object • The vector sum of the force is called the net force (Fnet) Net force equals sum of all forces

Name of forces • Fg = force of gravity • Fa = applied force • Fk = force of kinetic friction • Fs = force of static friction • T = force of tension • FN = normal force

Drawing FBDs n Ex 1. Draw a FBD of a car speeding up n Ex 2. Draw a FBD of a skateboarder coasting to a stop n. Ex 3. Draw a FBD of a plane taking off from a runway n. Ex 4. Draw a FBD of a person falling at their terminal velocity

Practice Problems • Ex. Determine the net force: 15 N 21 N 4 N 8 N 2 N 5 N 2 N 1 N 40º 5 N 1 N 2 N 5 N

2 D Forces & Applications of Newton’s Laws Textbook: 2. 2 & 2. 3 Homework: WS – 2 D Forces Pg. 87 # 3, 4, 6, 8 Pg. 92 - 93 # 5, 9 Pg. 95 # 3 – 5

Simple Machines (Pulleys) n n A pulley is a simple machine that changes the direction of the force A pulley system is a group of pulleys working together to provide a mechanical advantage • EX. Two identical bags of gumballs, each of mass 0. 200 kg, are suspended as shown below. Determine the reading on the spring scale.

• Ex 1. A 6. 0 kg mass is attached to a 8. 0 kg mass over a frictionless pulley. Determine the acceleration of the masses, and the tension in the string.

The Normal Force • The normal force (FN) is the reaction force provided by a surface to resist an object moving through it • A scale does not measure Fg! It measures FN, also called your apparent weight

• Ex. A 0. 22 kg mice stands on a scale in an elevator. What does the scale read when: a. b. c. The elevator is at rest/constant velocity? Accelerating up at 2. 0 m/s 2? The elevator cable breaks?

Review Friction: • Friction is a force that opposes motion • Friction is caused by microscopic imperfections in surfaces moving across each other • Friction depends on: – The Surfaces (Ff ) – How much surfaces are pressed together (Ff FN) – Ff = Fn

Kinds of Friction • Static friction is the frictional force that must be overcome to start something moving – Fsf = s. Fn • Kinetic friction is the frictional force that must be overcome to keep an object moving – Fkf = k. Fn • In general s > k

• Ex 1. A traveler pulls a suitcase of mass 8. 00 kg across a level surface by pulling on the handle 20. 0 N at an angle of 50. 0° relative to horizontal. Friction against the suitcase can be modeled by μk = 0. 100. (a) Determine the acceleration of the suitcase. (b) What amount of force applied at the same angle would be needed to keep the suitcase moving at constant velocity?

Hooke’s Law Textbook: 4. 5 Homework: WS pg. 206 #2 - 5

Hooke’s Law

Hooke’s Law • Robert Hooke (1635 – 1703) published his law in 1678. • An ideal spring exerts a force (restoring force) proportional to distance the spring is moved from equilibrium – FS = kx – k is the spring constant (N/m) – x is the stretched/compressed distance from equilibrium (m)

• Pg 219 # 6. What magnitude of force will stretch a spring of force constant 78 N/m by 2. 3 cm from equilibrium? • # 5. A student of mass 62 kg stands on an upholstered chair containing springs, each of force constant 2. 4 x 103 N/m. If the student is supported equally by six springs, what is the compression of each spring?

Inclined Planes - Ramps Textbook: 2. 2 & 2. 3

Ramps • A ramp is a simple machine. It reduces the apparent weight of an object, providing a mechanical advantage.

• Ex 1. Determine the acceleration of the block as it’s sliding down a frictionless ramp. g k 3 30º

• Ex 2. Determine the acceleration of the blocks g 2 k 25º Uk = 0. 1 4 kg

• Ex 3. A rollercoaster ride is shown in the diagram below. The mass of the car and rider is 700. 0 kg and the coefficient of friction is 0. 0500. (a) Determine the force that must be applied to the car as it is pulled up the hill at a constant speed of 1. 00 m/s. (b) The car is released at point A with speed 1. 00 m/s. Find the speed at point B.

Inertial/Non-inertial Frame of Reference & Uniform Circular Motion Textbook: 2. 5 & 3. 1

• Frame of reference: – The point of view from which we observe motion – It is the stationary “platform” from which we measure all other motion • Inertial frame of reference: – Where Newton’s first law applies – • Non-inertial frame of reference: – Where Newton’s first law doesn’t apply –

Uniform Circular Motion • An object moving at a constant speed v (m/s), in a circle of radius r (m), experiences a centripetal acceleration

Circular Motion • If an object moves in a circle with a period, T (s); at a frequency, f (Hz):

• Graph the relationship between the magnitude of centripetal acceleration and the radius of rotation (at a constant frequency) • Two balls at the ends of two strings are moving at the same speed in horizontal circular paths. One string is three times as long as the other. Compare the magnitudes of the two centripetal accelerations.

Calculate the magnitude of the centripetal acceleration: • A coin is placed flat on a vinyl record, turning at rpm. The coin is 8 cm from the centre of the record.

Forces in Circular Motion (Part 1) Textbook: 3. 2

Forces in circular motion

Forces in circular motion

• Ex. A 2. 00 -kg stone attached to a rope 4. 00 m long is whirled in a circle horizontally on a frictionless surface, completing 5. 00 revolutions in 2. 00 s. Calculate the magnitude of tension in the rope. [1. 97 x 103 N]

• A 0. 2 kg mass is spinning at a rate of 66 rpm. The length of the rope is 0. 3 m. Determine the angle that the rope makes with the vertical.

• An 82 -kg pilot flying a stunt airplane pulls was doing a loop de loop at a constant speed of 540 km/h. – (a) What is the minimum radius of the plane’s circular path if the pilot’s acceleration at the lowest point is not to exceed 7. 0 g ? – (b) What force is applied on the pilot by the plane seat at the lowest point in the pullout? – (c) What is the apparent weight of the pilot at the top of the loop

Forces in Circular Motion (Part 2) Textbook: 3. 2

Leveled Curve • As objects travel around leveled curves, it is static friction that keeps the objects from skidding.

Banked Curve • Banked curves are used to reduce the reliance on friction and reduce the radius of curvature. • No friction

Banked Curve • With Friction

• Ex. Determine the minimum radius needed to round a leveled curve at 100 km/h with a coefficient of static friction, [r = 606 m]

• Ex. Determine the minimum radius needed to round a frictionless banked curve at 100 km/h. The curve is banked at 20 o. r = 216 m