Fall 2008 Quiz #5 PHYS-218Sec Date: Oct. 13, 2008Print NamesThis is your GROUP quiz. Be sure to write all of your assumptions out in words.Draw sketch(es) and derive your equations before coming to an answer. Do NOTwrite the answer alone. Write the answer in a separate paper.1. A small block of mass m is sliding off a frictionless large globe of radius R. It slides from restat the very top of the globe and slides along the surface of the globe. The block leaves the surfaceof the globe when it reaches a height hcritabove the ground. The figure shows the situation for anarbitrary height h. In this figure, the initial value of θ is 90◦and, as it slides down, θ decreases.At θ = θcritthe block leaves the globe.To solve this problem, you have to combine Newton’s second law and energy. Answer thefollowing questions to obtain hcrit.(a) Before the block starts to slide, i.e., when it is at the top of the globe, what is the magnitudeof the normal force?(b) Consider when the block is still sliding the surface but with θ > θcrit. Draw a free-bodydiagram for the block. You need to consider two forces, gravity and the normal force. Choose yourpositive x and y directions as the tangent and (inward) radial directions, respectively. Obtain thex and y components of the net force acting on the block.(c) Using the results of (b), verify that the normal force decreases as θ becomes smaller.(d) Therefore, when the block leaves the surface of the globe, the magnitude of the normal forcebecomes zero. Then the centripetal acceleration is given by the radial component of the weight.What is the radial component Frof the net force at θ? (Note that the object is doing circularmotion before it leaves the globe.)(e) From the figure above, write sin θ in terms of h and R using geometry.(f) The centripetal force is Fr= mv2/R. Write the speed vcritat the critical point in terms ofg, R, and hcrit. This gives one condition for vcrit.(g) To solve the problem, you need to have another condition for vcrit. This can be obtainedfrom energy conservation. Using energy conservation, derive vcrit=p2g(2R − hcrit).(h) You now have two conditions for vcrit. From these two expressions, show that hcrit=5R3.2. (Bonus problem) An object of mass m is traveling on a horizontal surface. There is acoefficient of friction µ between the object and the surface. When the object encounters a springat x = 0, its speed is v [see Fig. (a)]. The object compresses the spring until x = d, stops, andthen recoils and travels in the opposite direction. When it reaches x = 0 again on its return trip,it stops. Find the spring constant k in terms of m, µ, v and g.(a) Write the energy conservation law for the motion of the object from Fig.(a) to Fig.(c).(b) Write the energy conservation law for the motion of the object from Fig.(b) to Fig.(c).(c) Combining the two relations, obtain the spring constant k in terms of m, µ, v and
View Full Document
Unlocking...