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Equilibrium Notes
1 – Translational Equilibrium
Ex. A 20.0 kg object is suspended by a rope as shown. What is the net force acting on it?
Ex. Ok that was easy, now that same 20.0 kg object is lifted at a velocity of 4.9 m/s. What is the net force acting on it?
Because in both case the net force on the objects is zero they are said to be in ___________________. If the object is stationary it is said to be in ______________________________, while an object moving at a constant velocity is in _______________________________.
These are both case where the object is in ______________________ ____________________________.
Translational motion refers to motion along a line, therefore: The condition of equilibrium:
________________ = ___________________ And so,
________________ = ___________________
________________ = ___________________
Ex. A 64 N object is suspended using ropes as shown in the diagram. Calculate tensions T 1 and T 2 in the ropes.
35 o^50 o
T 1 T 2
Strategy 1: Components
- Choose a point in the system that is in equilibrium, with all forces acting on it. In this case use _____________.
- Draw an _____ _____ _____!
- Break these forces...
- Use…
Strategy 2: Create a closed vector diagram
- Since we know that Fnet = 0 at any point in equilibrium, what would happen if we added if we add up all of the force vectors?
- Use Sine Law, Cosine Law, or whatever means necessary to solve the triangle…
- NEVER assume that it is a ________________________ unless you can prove it geometrically.
Ex. An object is suspended as shown. If the tension in one of the ropes is 50 N as shown, what is the weight of the object?
You can use Strategy 1 or Strategy 2 , just be sure you know both ways. You’re bound to hit a brick wall eventually and it’s nice to be able to try it from a different angle, no pun intended...
37 o
T 1
T 2 = 50 N
Ex: Two students sit on opposite sides of an 800 N teeter-totter. Student 1 has a mass of 65 kg and sits at the very end of the teeter-totter. Student 2 has a mass of 90 kg. How far from the pivot should he sit in order to achieve equilibrium?
Extension: What are the vertical and horizontal components of the supporting force provided by the hinge in the last question?
Ex: A 3500 kg truck is parked on a bridge as shown. If the bridge deck itself has a mass of 6500 kg find the supporting force provided by each of the two support posts.
15 m
5 m
2.6 m
Equilibrium Notes
3 – Torque Not at 90
o
Although we’ve already learned about torque, we don’t quite have the whole story. So far we have only seen torque provided by forces acting perpendicular to the body in equilibrium. What happens if a force acts in a direction other than perpendicular to the body?
Ex A 2.2 m long 50.0 N uniform beam is attached to a wall by means of a hinge. Attached to the other end of the beam is a 100 N weight. A rope also helps support the beam as shown.
a) What is the tension in the rope? b) What are the vertical and horizontal components of the supporting force provided by the hinge?
100 N
30 o
First we draw the beam with the forces acting on it and their distances from the pivot:
So, whenever we are calculating the torque on a body we must ALWAYS use the _________________________ _______________________ of the force.
Ok now go solving! a)
b)
Notice that if we break the tension in the rope into component forces, the ______________ component does not contribute to the torque in either the clockwise or counterclockwise direction
