Physics 211 Spring 2014 Final Practice Exam This exam is closed book and notes. A formula sheet will be provided for you at the end of the final exam you can download a copy for the practice exam from the course website. Calculators are permitted, but no formulas or text related to this exam can be stored on the calculator. No cell phone use is permitted. The exam is two hours long. You must show all of your work to receive credit.
1. (20 pts total) PHY211 Final A h B L A box labeled A of mass m=0.5kg is released from rest at a height h=1.0m above the ground. It slides down a frictionless slope and then moves along a horizontal rough floor. After traveling a distance of L=0.75 m it hits another box of mass 1.0kg and the two boxes stick together. The coefficient of kinetic friction between the box and the horizontal floor is µ=0.6 and g=9.8 m/s 2 a) (3 pts) What is the initial speed of the box after leaving the frictionless slope? b) (3 pts) Draw a free body diagram showing the forces acting on box A before it hits box B c) (4 pts) Calculate how much work is done by friction as the block moves the distance L d) (5 pts) What is the velocity of box A just before it strikes box B? e) (2 pts) Calculate the instantaneous power being expended by the friction force just before box A strikes box B. f) (3 pts) Calculate the initial speed of the combined system after the collision consisting of boxes A and B 1
2.(20 pts total) radius r R A sphere of mass 10kg and radius R=10cm is attached to a rigid rod of radius r=0.25cm that passes through the center of the sphere. A string wrapped around the rod is pulled with a constant tension T=50 N. The moment of inertia of the sphere is given by I=2/5 MR 2 and you can neglect the moment of inertia of the rod. a) (3 pts) What torque acts on the sphere? b) (2 pts) Calculate the angular acceleration of the sphere c) (4 pts) Assuming the sphere starts from rest calculate the angular velocity of the sphere after 10 seconds. d) (2 pts) What is its angular momentum after 10 seconds? d) (4 pts) How many revolutions has the sphere made at this point? e) (5 pts) At t=10 secs the string breaks and the sphere starts to suffer a constant angular deceleration due to frictional effects. The sphere comes to rest after 60 additional revolutions. Calculate the magnitude of the frictional torque acting on the sphere. 2
3.(20 pts total) y θ=30 0 H A cannon situated on the top of a tower of height H=50 m fires a cannon ball at a angle of 30 0 to the horizontal. The cannon ball leaves the cannon at a speed of 200 m/s. x a) (5 pts) Write down equations for x and y coordinates of the cannon ball as functions of time (take g=9.8 m/s) b) (4 pts) How long is the cannon ball in the air before hitting the ground? c) (3 pts) How far horizontally has it traveled by the time it hits the ground? d) (4 pts) What is the maximum height attained by the cannon ball? e). (4 pts) The cannon is now aimed vertically. What is the smallest initial speed for the cannon ball that would allow it to escape from the gravitational field of the Earth (take G=6.67x10-11 Nm 2 /kg 2 the radius of the Earth as 6.4x10 6 m and the mass of Earth to be 5.98x10 24 kg)? 3
4. (20 pts total): A triangular ramp has two sides: the le: side is rough and fric=onal and steeper, with an angle of θ 1 =30 o, while the right side is fric=onless, with an angle of θ 2 =20 o. The height of the ramp is h=20 cm. A block with mass m1=40 g sits on the le: side and it is connected by a massless string over a fric=onless pulley to a smaller mass m2=20 g that sits on the right side. m1 θ 1 h m2 θ 2 1) (5 pts) Draw a free body diagram for mass m1 and a separate free body diagram for m2. 2) (4 pts) In your free body diagram for m1, let the x- axis point along the le: ramp (down and to the le:) and the y- axis point perpendicular to the ramp. Using Newton s second law, write an expression for the accelera=on of m1 along the x- axis and the y- axis. 3) (4 pts) For mass m2 let the x- axis point along the right ramp (down and to the right). Write an equa=on for the accelera=on of m2 downward along this x- axis and the y- axis. 4) (2 pts) Write an equa=on for the rela=onship between the accelera=on of m1 and the accelera=on of m2. 5) (5 pts) What is the minimum value for the coefficient of sta=c fric=on on m1 so that the blocks do not move? 4
5. (20 pts total) A block with mass m = 200 g atached to a massless horizontal spring is oscilla=ng with an amplitude of 2.0 cm and a frequency of 2.0 Hz. The spring is maximally stretched to 2 cm past its rest length at t=0. Let the posi=ve x- axis point to the right, and the origin of the x- axis be at the rest length of the spring. wall 200 g 2 cm 1) (3 pts) What is the angular frequency of the block? Using this angular frequency, write an equa=on for the posi=on of the block x(t) as a func=on of =me. x 2) (3pts) What is the total mechanical energy of the block- spring system? 3) (4 pts) Draw a diagram of the kine=c energy of the block as a func=on of posi=on. Be sure to label the x and y axes and indicate the maximum value of the kine=c energy as well as where it goes to zero. 4) (3 pts) What is the maximum velocity of the block? 5) (4 pts) Just as it passes through an equilibrium point moving to the right, a sharp blow directed to the le: exerts a 20 N force for 1.0 ms. What is the new velocity of the block? 6) (3 pts) What is the new amplitude of oscilla=on? 5