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Classical Mechanics Review 1: Units 1-6 Mechanics Review 1, Slide 1 Slide 2 Example: Atwood Machine Two objects of unequal mass are hung vertically over a frictionless pulley of negligible mass. Determine the magnitude of the acceleration of the two objects and the tension in the string. Mechanics Review 1, Slide 2 m2gm2g m1gm1g a T a T m1m1m1m1 m2m2m2m2 Slide 3 Example: Two Blocks and a Pulley A block of mass m 1 on a horizontal surface with coefficient of kinetic friction k, is connected to a ball of mass m 2 by a cord over a frictionless pulley. A force of magnitude F at an angle with the horizontal is applied to the block and the block slides to the right. Determine the magnitude of the acceleration of the two objects. Mechanics Review 1, Slide 3 Slide 4 Example: Loop the Loop A pilot of mass m in a jet aircraft executes a loop-the- loop. In this maneuver the aircraft moves in a vertical circle of radius 2.70 km at a constant speed of 225 m/s. A. Determine the force exerted by the seat on the pilot at the bottom of the loop. A: 2.91 mg B. Determine the force exerted by the seat on the pilot at the top of the loop. A: 0.913 mg Mechanics Review 1, Slide 4 Slide 5 Example: Three Boxes Three boxes each of mass 14 kg are on a frictionless table, connected by massless strings. A force T 1 pulls on the rightmost box (A) such that the three boxes accelerate at a rate of a = 0.7 m/s 2. 1.What is the magnitude of T 1 ? 2. What is the net horizontal force on A? 3. What is the force that box B exerts on A? 4. What is the net force on box B? 5. What is the force box C exerts on B? Mechanics Review 1, Slide 5 Slide 6 Example: Stone in Free Fall A stone is thrown from the top of a building upward at an angle of 30.0 o to the horizontal with an initial speed of 20.0 m/s. The height of the building is 45.0 m. How long does it take the stone to reach the ground? What is the direction of motion of the stone just before it strikes the ground? Mechanics Review 1, Slide 6 t = 4.22 s = tan -1 (-31.4/17.3) Slide 7 Example: Ski Jump A ski jumper leaves the ski track moving in a horizontal direction with a speed of 25.0 m/s. The landing incline below her falls off with a slope of 35.0 o. Where does she land on the incline? What is her speed when she lands? Mechanics Review 1, Slide 7 Slide 8 Example: Book and Coffee Cup The 2.0 kg book is connected by a light string to a 300 g coffee cup. The book is launched up the frictionless 20 o slope with an initial speed of 5.0 m/s. A. Calculate the acceleration of the book. B. How far does the book go up the slope before it stops? C. Calculate the Tension in the string Mechanics Review 1, Slide 8 Slide 9 Example: Banked Curve A car moving at the designated speed of 13.4 m/s can negotiate a curve even when the road is covered with ice, if the ramp is banked (meaning that the roadway is tilted toward the inside of the curve). The radius of the curve is 50.0 m. A. What is the angular speed of the car? B. What is the acceleration of the car? C. At what angle should the curve be banked? A: 20.1 o Mechanics Review 1, Slide 9 Slide 10 Mechanics Review 1, Slide 10 Example: Field Goal A field goal kicker can kick the ball 30 m/s at an angle of 30 degrees w.r.t. the ground. If the crossbar of the goal post is 3m off the ground, from how far away can he kick a field goal? y-direction v oy = v o sin(30 o ) = 15 m/s y = y o + v oy t + at 2 3 m = 0 m + (15 m/s) t (9.8 m/s 2 ) t 2 t = 2.8 s or t = 0.22 s. x-direction v ox = v o cos(30 o ) = 26 m/s D = x o + v ox t + at 2 = 0 m + (26 m/s)(2.8 s) + 0 m/s 2 (2.8 s ) 2 = 72.8 m D 3 m y x Slide 11 Example: Block on Incline Plane Suppose a block is placed on a rough surface inclined relative to the horizontal. The incline angle is increased until the block starts to move. Show that you can obtain s by measuring the critical angle c at which this slipping just occurs. Mechanics Review 1, Slide 11 Slide 12 Example: Satellite in Orbit Mechanics Review 1, Slide 12 Slide 13 Example: Forces and Inclines Three forces are exerted on an object placed on an inclined plane. The three forces are directed as shown in the figure. The forces have magnitudes F 1 = 3.00 N, F 2 = 8.00 N and F 3 = 6.00 N. A. What is the component of the net force parallel to the incline? B. What is the component of the net force perpendicular to the incline? C. What is the magnitude of the net force? Mechanics Review 1, Slide 13