180 likes | 186 Views
Chapter 5. Forces in Two Dimensions. 5.1 Vectors. Vector problem from Chapter 4: If you pushed on a table with 40 N of force and your friend pushed with 40 N of force in the same direction, the resultant force would be: 80 N.
E N D
Chapter 5 Forces in Two Dimensions
5.1 Vectors • Vector problem from Chapter 4: • If you pushed on a table with 40 N of force and your friend pushed with 40 N of force in the same direction, the resultant force would be: • 80 N
If you pushed on a table with 40 N of force and your friend pushed with 60 N of force in the opposite direction, the resultant force would be: • 20 N towards you
Vectors in Multiple Directions: • To add vectors that are not at right angles to each other: • Create a vector diagram • If they are at right angles: • Create a vector diagram OR • Resolve algebraically using Pythagorean’s Theorem and SOH, CAH, TOA • Pythagorean’s Theorem: R2 = A2 + B2
Practice Problem #1 • A person walks 50 km east and then turns down a street that is 75o south of east and travels another 50 km. • What is the person’s total distance walked? • What is the person’s resulting displacement from the starting point?
Practice Problem #2 • An airplane travels east at 200 m/s. A wind blows towards the north at 50 m/s. What is the resulting velocity of the plane?
Components of Vectors • A single vector may be thought of as a resultant of 2 vectors which are called perpendicular components • There is one horizontal and one vertical component for every vector • Vector resolution – breaking a vector down into its components
Adding Vectors at Any Angle • Resolve each vector into its horizontal and vertical components • Vx=V cos q • Vy=V sin q • Sum the results for each • Find the magnitude using the Pythagorean Theorem • Find angle by the following formula: tan q = Vy (sum) Vx (sum)
Boat Problem! • A boat heads east across a river that is 2.8 km wide with a velocity of 25 km/h. The river flows south with a velocity of 7.2 km/h. • What is the resultant velocity of the boat? • How long does it take the boat to cross the river? • How far upstream is the boat when it reaches the opposite side?
5.2 Friction • Static – starting friction; works against the start of motion • Kinetic – sliding friction; works against keeping an object in motion • Ff = m FN • If the object is moving with a constant velocity, then the applied force (often called horizontal force) is equal to the frictional force so… FH = Ff
m – the coefficient of friction • Greater for rougher surfaces • Lesser for smoother surfaces • Has no units! Is a number between 0 and 1
Try This! • A 64-N box is pulled across a rough horizontal surface. What is the force necessary to keep the box moving at a constant speed if the coefficient of friction between the box and the floor is 0.81?
…and this… • A 9.0 kg crate is resting on a floor. A 61-N force is required to just start motion of the crate across the floor. What is the coefficient of friction between the floor and the crate?
5.3 Force in Two Dimensions • Equilibrium • When the sum of all forces acting on an object is zero • Equilibrant Force • The force that will put all other forces in equilibrium • To calculate: • Find the resultant • The equilibrant is equal in magnitude and opposite in direction • Use the same force and add or subtract 180o to the direction
Try This: • Two forces act on an object. One is 125 N pulling toward 57o. The other is 182 N pulling toward 124o. Find the one force that would put the other two in equilibrium. You may use any method that you want.
Motion Along An Inclined Plane • A skier has several forces working on him as he moves down a hill: • Gravitational force toward center of the earth • Normal force perpendicular to the hill • Frictional force parallel to the hill
Calculating the Components of Weight on an Inclined Plane: • Fgx = Fg sin q (Parallel to the inclined plane) • Fgy = Fg cos q (Perpendicular to the inclined plane)