PHY 101 1nd Edition Lecture 11 Outline of Last Lecture I. 4.4 Newton’s Second LawII. Gravitational ForceIII. Gravitational Force, Mass, WeightOutline of Current Lecture IV. Newton’s Third LawV. Application of Newton’s LawsVI. Objects in EquilibriumCurrent Lecture4.4 Newton’s Third Law- Forces always exist in pairs – action and reaction forceso Equal in magnitudeo Opposite in directiono Act on different objectso ** if object 1 and object 2 interact the force exerted by object 1 on object 2 (F12) is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1 (F21) – F12 = - F214.5 Application of Newton’s Laws- Draw free-body diagram- Ex. Pulling a crate- How many forces acting on the crate? (neglect friction)- Equation of the motion of crate:o X-component: max = To Y-component: may = Fn – mg = 0 No acceleration along the yObjects in EquilibriumThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.- Objects either at rest or moving with constant velocity are said to be in equilibrium- In other words, the vector sum of the external forces on an object in equilibrium is zero.Example: Traffic light- weight: 100N- find the tension (force) in each of the 3 cables- in the y-direction: T3 – mg = 0; T3 = mg = 100N- equilibrium condition of the knot- in the x-direction T1x + T2x = 0o eq 1: T1cos(143) + T2cos(53) = 0- in the y-direction T1y + T2y – mg = 0o eq. 2: T1sin(143) + T2cos(53) - mg = 0 mg = 100N- solve eq 1 for T2o eq. 3: T2 = -T1cos(143)/cos(53) = 1.33T1 = T2cos(143) = -0.799o T1sin(143) + (1.33T1)sin(53) – mg = 0- Solve for T1o T1 = 60.1N- Solve for T2o T2 = 1.33T1 = 79.9 NExample: Runaway Car- A car with mass m on an icy driveway inclined at 20°- A) calculate the acceleration of the car (neglect friction)o Step 1: choose coordinateso X-axis : down the slopeo Y-axis: normal to the slopeo **normal = perpendicular to the slopeo Step 2: free-body diagramo Step 3: geometry (directions, angles)Incline Coordinates and Angles- Normal Force:o Fn = mgcosΘ- Because net force along the y-direction is zero:o Sum Fy = Fn = mgcosΘ = 0- X-component of the gravitational forceo Fx = mgsinΘ **Normal force has no x-component**- Acceleration of the car along the y-direction: 0- Net force along the x-direction:o Fx = Fgsin20 = mgsin20- Acceleration along the x-directiono Ax = Fx/m = mgsin20/m = gsin20 = 3.35m/s2- B) if the length of the driveway is 25 m and the car starts from rest, how long does it taketo travel to the bottom of the slope?o Use kinematicso Δx = 1/2at2 = 25mo 25 = (1/2)(3.35)t2 = 3.86s- C) what is the speed at the bottom?o Vx = at = (3.35)(3.86) =
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