Mock Exam II PH 201-2F Garrett Higginbotham March 3, 2015 You will have 50 minutes to complete this exam. Each problem is worth 20 points, for a total grade of 100. Formulas 1. Kinematics (a) v = v 0 + at (b) x = x 0 + v 0 t + 1 2 at2 (c) v 2 = v0 2 + 2a(x x 0 ) (d) F = m a 2. Energy, Power, and Work (a) W = F d = F d cos θ (b) KE = 1 2 mv2 (c) W tot = KE 2 KE 1 = KE (d) P av = W T (e) P = F v = F v cos θ (f) U = mg h, gravitational potential energy (g) U = 1 2 k( x)2 (h) KE 1 + U 1 = KE 2 + U 2, conservation of energy (i) W = U 1
3. Momentum and Impulse (a) p = m v (b) J = F ave t (c) Center of Mass i. x cm = m1x1+m2x2+... m 1+m 2+... ii. y cm = m1y1+m2y2+... m 1+m 2+... (d) P = M tot v cm (e) F ext = M tot a cm 4. Torque and Equilibrium (a) τ = F d = F d sin θ (b) Equilibrium Requirements i. F x = 0, ii. τ = 0 Fy = 0, Fz = 0 5. Simple Harmonic Motion (a) f = 1 T (b) ω = 2πf (c) F = kx (d) ω = k m (e) f = ω 2π (f) x = A cos (ωt + φ) (g) v = Aω sin (ωt + φ) (h) a = Aω 2 cos (ωt + φ) = ω 2 x (i) E = 1 2 mv2 + 1 2 kx2 2
Problem One A steel ball of mass 40.0 g is dropped from a height of 2.00 m onto a horizontal steel slab. The ball rebounds to a height of 1.60 m. 1. Calculate the impulse delivered to the ball during impact. 2. If the ball is in contact with the slab for 2.00 ms, find the average force on the ball during impact. 3
Problem Two Three coupled railroad cars roll along and couple with a fourth car, initially at rest. These four roll along and couple to a fifth car initially at rest. This process continues until the speed of the final collection of railroad cars is one-fifth the speed of the initial three cars. All the cars are identical. Ignoring friction, how many cars are in the final collection? 4
Problem Three A child with poor table manners is sliding his 250 g dinner plate back and forth in SHM with an amplitude of 0.100 m on a horizontal surface. At a point 0.060 m away from equilibrium, the speed of the plate is 0.300 m/s. 1. What is the period of the motion? 2. What is the displacement when the speed is 0.160 m/s? 3. In the center of the dinner plate is a 10.0 g carrot slice. If the carrot is just on the verge of slipping at the end point of the path, what is the coefficient of static friction between the carrot slice and the plate? 5
Problem Four Sir Lancelot is trying to rescue the Lady Elayne from Castle Von Doom by climbing a uniform ladder that is 5.0 m long and weights 180 N. Lancelot, who weighs 800 N, stops a third if the way up the ladder. The bottom of the ladder rests on a horizontal stone ledge and leans across the moat in equilibrium against a vertical wall that is frictionless because of a thick layer of moss. The ladder makes and angle of 53.1 with the horizontal. 1. Find the normal and friction forces on the ladder at its base. 2. Find the minimum coefficient of static friction needed to prevent slipping at the base. 3. Find the magnitude and direction of the contact force on the ladder at the base. 6
Problem Five A 40.0 g bullet traveling horizontally with a velocity of magnitude 400 m/s is fired into a wooden block with a mass of 0.800 kg, initially at rest on a level surface. The bullet passes through the block and emerges with its speed reduced to 120 m/s. The block slides a distance of 45.0 cm along the surface from its initial position. 1. What is the coefficient of kinetic friction between block and surface? 2. What is the decrease in kinetic energy of the bullet? 3. What is the kinetic energy of the block at the instant after the bullet passes through it? 7
Problem Six A 100 g potato is tied to a string with length 2.50 m, and the other end of the string is tied to a rigid support. The potato is held straight out horizontally from the point of support, with the string pulled taut, and is then released. 1. What is the speed of the potato at the lowest point of its motion? 2. What is the tension in the string at this point? 8
Problem Seven A physics professor is pushed up a ramp inclined upward at 30.0 above the horizontal as he sits in his desk chair that slides on frictionless rollers. The combined mass of the professor and chair is 85.0 kg. He is pushed 2.50 m along the incline by a group of students who together exert a constant horizontal force of 600 N. The professor s speed at the bottom of the ramp is 2.00 m/s. Use the work-energy theorem to find his speed at the top of the ramp. 9