EQUILIBRIUM EQUILIBRIUM PHYSICS Image From: www.clipartbest.com

BALANCED FORCES If the net force equals ZERO, then we say that a system is balanced. (This doesn’t mean there are no forces acting on the object, the forces are just tied.) Static Equilibrium: The Object is not moving. ∑F = 0 Dynamic Equilibrium: The object IS moving at a CONSANT speed. ∑F = 0

Newton’s First Law Revisited If an object is NOT accelerating then there must NOT be a net force. In other words: ∑F = 0

Practice 1D An elevator is moving up a shaft at a constant speed. The tension in the TWO pulling cables is 1500 N each. How much does the elevator weigh? T T ∑Fx = ∑Fy = T + T - W = I put stations around the 2T = W 2(1500) = W W 3000 N = W

1D. You place a 350 N cantaloupe in the weight basket at the grocery story. The spring above the basket stretches and the basket lowers. How much tension is in the spring now?

Practice 2D Bob is pushing a large crate at a constant speed with 100 N of force. The crate weighs 75 N. Calculate the normal force under the crate and the strength of friction. ∑Fx = ∑Fy = F - f = n F = f 100 N = f f F n - W = n = W W n = 75 N

2D. In a class lab you pull a brick forward on a string at a constant speed. The normal force under the brick is 140 N and the strength of friction is 80 N. Calculate the weight of the brick and the tension in the string.

ANGLES Practice n F 42° f W ∑Fx = ∑Fy = Fcos - f = Fcos = f Suzy pulls a wagon that weighs 525 N at a constant speed with 400 N of force. The handle of the wagon makes an upward angle of 42 o with the ground. Calculate the normal force under the wagon and the strength of friction. ∑Fx = ∑Fy = Fcos - f = n F Fcos = f 400cos(42°) = f f = 297 N 42° f n + Fsin - W = n = - Fsin + W n = - 400sin42° + 525 n = 75 N W

Angles. You are mowing the lawn for your mom Angles. You are mowing the lawn for your mom. The handle on the mower makes a downward angle of 60 o with the ground. You push with 800 N of force and the mower weighs 1000 N. Calculate the normal force under the mower and the strength of grass friction.

HILLS Practice n f W ∑Fx = ∑Fy = Wcos - f = Wcos = f 650cos(70°) = f Ben is ice blocking down a hill with an angle of elevation of 20 o. He slides at a constant speed. If he weighs 650 N, then calculate the normal force under the ice block and the strength of friction. ∑Fx = ∑Fy = Wcos - f = n Wcos = f f 650cos(70°) = f f = 222 N n - Wsin = 70° 20° n = Wsin n = 650sin70° n = 611 N W

Hills. You are driving your car up a 15o hill at a constant speed Hills. You are driving your car up a 15o hill at a constant speed. The car weighs 25,000 N. Calculate the normal force under the car and the force of friction.

Normal force The normal force does NOT always equal the weight of an object. On Flat Ground: The Normal Force = the weight of the object. Angled Force Pushing Down: As you push down the contact pressure increases. Angled Force Pulling Up: As you pull up you relieve the pressure a little bit. On a Hill: Some of gravity pulls you ALONG the hill. This might tip you over, but it does not contribute to the normal force. n = W n > W n < W n < W

solving for angled forces Don’t be afraid to ________________________. divide by a sine or cosine

examples  Bob pushes down on a couch at an angle of 40o . Friction resists the couch with 225 N of force. How hard does he need to push to keep the couch moving at a constant speed? f F = ? n ∑Fx = Fcos - f = Fcos = f f cos cos 40° F = 225 cos40° F W F = 294 N

Samantha works at a copy shop Samantha works at a copy shop. The manager asked her to place a 50 N sign out front, so she designs the following. Calculate the tension in the rope and the force in the boom. (A boom is a horizontal rod.)

Jack and Jill go up a hill to fetch a pail of water Jack and Jill go up a hill to fetch a pail of water. Jack falls down and slides down the hill at a constant speed. If the force of friction is 500 N and the angle of elevation is 63o , then how much does Jack weigh?

Triangles are often used in construction as a strong shape to support large amounts of weight. Let’s look at the math involved. A triangular bracer is used to support a bridge. If the bracers make a 60 o angle with the surface of the bridge, and the truck on the bridge weighs 250,000 N then how much force does each brace need to be able to handle?