Forces in equilibriumSo this means…• There is no acceleration• The sum of the forces = 0• Further… – The sum of force in the x-direction = 0 – The sum of forces in the y-direction = 0 ΣFx = 0 ΣFy = 0
ExampleA cafe sign with a mass of 65.5 kg is being held up by 2 cables as shown in the picture to the left. Calculate the tension in each of the ropes. X Direction T2 cos35 T1 cos19 T2 T1 T1 0.866T2 T2sin35 T1sin19 T2cos35 T1cos19 T2 sin 35 T1 sin 19 mg Catsup & Mustard 0.574T2 0.326T1 642 0.574T2 0.282T2 642 0.856T2 642 mg T2 750 N T1 = 650 N
What if the object is not in equilibrium?If it is not in equilibrium, then what’s going on with its motion???It is changing in some way!!It can be….stopping, slowing down, speedingup, changing direction, beginning to move… USE NEWTON’SACCELERATING! SECOND LAW!!
What if the object is not in equilibrium?1. Draw a free body diagram2. Break vectors into components if needed3. Find the NET force by adding and subtracting forces that are on the same axis as the acceleration.4. Set net force equal to “ma” this is called writing an EQUATION OF MOTION. ΣFx = max ΣFy = mayNOTE: To avoid negative numbers, always subtract the smaller forces from the larger one.
example A bucket attached to a rope is lifted from a well. The mass of the bucket and the water in the bucket are 10.0 kg, and the tension in the rope is 100 Newtons. What is the acceleration1. of the bucket? diagram Draw a free body2. Break vectors into components if needed3. Find the NET force by adding and subtracting forces that are on the same axis as the acceleration.4. Set net force equal to “ma” this is called writing an EQUATION OF MOTION. a = 0.2 m/s2
ExampleAn elevator with a mass of 2000 kg rises with an acceleration of 1.0 m/s/s. What is the tension in the supporting cable? Equation of Motion T FNET = ma T - mg = ma T = ma + mg T = (2000)(1) + (2000)(9.8) T= 21,600 N mg
elevators • Maximum tension in • Minimum tension elevator occurs T occurs when there is T when Tthere is an - mg = ma a downward mg - T = ma upward ma + mg T = acceleration acceleration T = ma - mga a mg mg
elevators• There are typically 3 phases to an elevators motion: – At a constant speed – When it comes to a stop – When it starts moving• As a result, the tension on the elevators rope WILL change, AND the weight you read on a scale will change