Physics 2514 Lecture 13 P. Gutierrez Department of Physics & Astronomy University of Oklahoma Physics 2514 p. 1/18
Goals We will discuss some examples that involve equilibrium. We then move on to a discussion of friction. Physics 2514 p. 2/18
Newton s Laws of Motion 1) An object that is at rest will remain at rest, or an object that is moving will continue to move (in a straight line) with constant velocity, if and only if the net force acting on the object is zero. 2) An object of mass m subjected to forces F 1, F 2, F 3,... will undergo an acceleration a given by F net = m a where F net = n i=1 F i 3) To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal and directed to contrary parts. Physics 2514 p. 3/18
Equilibrium Let s first consider problems of static equilibrium Equilibrium corresponds to the case that the object has zero net force acting on it F net = 0 Two types of equilibrium conditions Static equilibrium corresponds to the case when the object is at rest Dynamic equilibrium corresponds to the case when the object moves at a constant velocity Both correspond to F net = 0. Physics 2514 p. 4/18
Solving Problems To solve problems using Newton s laws of motion, we will follow the same problem solving procedure as for the case of kinematics. Rewrite the problem in a couple of sentences; 1. State the situation; 2. What variables are we solving for; Draw a force diagram Free Body Diagram State the known and unknown variables; Solve the problem algebraically; Substitute numbers into the problem. Physics 2514 p. 5/18
Example 1 Consider a lead block of mass 5 Kg held against a frictionless wall with a force applied at an angle of 30 as shown in the figure. What is the magnitude of the force required to keep the block from sliding? PSfrag replacements θ F Physics 2514 p. 6/18
Solution Brief description A 5 Kg block is held against a frictionless wall with a force acting at 30 relative to the horizontal. What is the magnitude of P required to keep the block in static equilibrium? replacements θ PSfrag replacements P Free body diagram y P n θ x m g Physics 2514 p. 7/18
Solution Known θ = 30 w = mg ĵ = 49 PSfrag ĵ N replacements Unknown P, n P θ y m g n x Equations: Fx = n P x = n P cos θ = 0 Fy = P y mg = P sin θ mg = 0 { n = P cos θ P = mg/ sin θ } P = mg/ sin(30) = 98 N Physics 2514 p. 8/18
Example 2 A 1000 Kg beam is supported by two ropes. Calculate the tension in each rope. y PSfrag replacements T 1 α β T2 x m g Physics 2514 p. 9/18
Example 3 A 1000 Kg beam is supported by two ropes. Calculate the tension in each rope. y Known α = 20 T β = 30 PSfrag replacements 1 w = mg ĵ = 9800 ĵ N α β T2 Unknown T 1, T 2 m g x Physics 2514 p. 10/18
Example Known α = 20 β = 30 PSfrag replacements T1 w = mg ĵ = 9800 ĵ N α y β T2 Unknown T 1, T 2 m g x T 2x T 1x = T 1 sin α T 2 sin β = 0 T 1y + T 2y mg = 0 = T 1 cos α + T 2 cos β mg = 0 } { T1 = 6396 N T 2 = 4375 N Physics 2514 p. 11/18
Clicker Joe and Bill are playing tug-o-war. Joe is pulling with a force of 200 N. Bill is simply hanging on, but skidding towards Joe at a constant velocity. What is the magnitude of the force of friction between Bill s feet and the ground. 1. 200 N 2. 400 N 3. 0 N 4. 300 N 5. None of the above Physics 2514 p. 12/18
Friction Next to gravity, friction is the most common force that we interact with. It allows us to walk, slows us down, and prevents us from moving. There are 3 types of friction (all act to oppose motion) Static fraction f s µ s N when no motion occurs; Kinetic friction f k = µ k N, when object is moving; Rolling friction f r = µ r N, when objects rolls. Physics 2514 p. 13/18
Clicker For which situation is the frictional force the largest. Physics 2514 p. 14/18
Solution Physics 2514 p. 15/18
Example 3 A 50 kg steel box is in the back of a dump truck. The truck s bed, also made of steel, is slowly tilted. At what angle will the file cabinet begin to slide? Brief description: A 50 kg steel box is on a steel incline plane. What is the maximum angle the incline can have for the box to remain in static equilibrium? Physics 2514 p. 16/18
Solution Known µ s = 0.80, m = 50 kg Unknown angle θ of incline Normal force n Equations of motion: mg sin θ µ s n = 0 mg cos θ + n = 0 } µ s = tan θ θ = tan 1 µ s = 38.7 Physics 2514 p. 17/18
Assignment Read the sections on Newton s second law and its applications: Sections 5.2, 5.3, 5.6 Physics 2514 p. 18/18