8.012 Exam I Solutions Problem 1 of 5 Short answer questions. (10 points) Note: DO NOT spend too much time on this problem! It is worth fewer points than the other 4 problems. For each question, circle the correct answer: (a) (2 points) A bee and a train collide. Compared to the magnitude of the force experienced by the bee, the magnitude of the force experienced by the train is smaller larger equal dependent on other details (from Newton's third law) (b) (2 points) A point mass m is placed inside a thin spherical shell of mass M and radius R, at a distance R/2 from the center. Let be a radial unit vector pointing from the point mass away from the center of the shell. The gravitational force exerted on the point mass by the spherical shell is GMm R zero + (c) (2 points) A mass M suspended from the ceiling by a spring (with spring constant k) undergoes simple harmonic motion with an oscillation period P. If the mass is doubled, then the new oscillation period is P/2 P/√2 P PV2 2P 2 W w, P= (d) (2 points) A block of mass M slides down a inclined plane with friction coefficient The surface area of the block in contact with the inclined plane is A, and the frictional force on the block is f. If we use a different block (made of the same material) with contact area 24 but the same mass M, then the frictional force on the second block will be approximately 1/4 1/2 2/ 4/ f=µN depends on weight but not on surface area (e) (2 points) When a mass moves through air or fluid at low velocity, it experiences a viscous drag force. (This is different than the turbulent drag felt at high velocity.) For a low velocity, the viscous drag force is approximately proportional to Problem 2 of 5 Masses on an accelerating pulley. (20 points) Masses M1 and M2 are connected by a massless, inextensible string over a frictionless pulley of negligible mass. The pulley accelerates upwards with constant acceleration A due to an external force. Gravity is directed downward. (a) (5 points) Draw the force diagrams for M1 and M2. (b) (15 points) Find the accelerations of M1 and M2 in the inertial x-y reference frame shown. (a) \[M,g\] \[M_{2}g\] Tension acting on both masses is identical since the rope is massless.

8.012 Exam I Solutions

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