2211_Sp21_MT1

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Georgia Institute Of Technology *

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2211

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Physics

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Apr 3, 2024

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PHYS 2211 - Mini-Test 1 - Spring 2021 “In accordance with the Georgia Tech Honor Code, I have completed this test while adhering to these instructions.” Sign your name on the line above
Vectors [50pts] A particle moves in a trajectory (blue line) that consists of three consecutive semicircles, all of which have the same radius and with their centers on the dotted line. The particle starts at location A, then moves along the trajectory to location B, then C, then D, then E, then F, and then G. At each location, an orange arrow indicates the instantaneous velocity of the particle. All the velocities have the same magnitude. Using the numbered directions shown by the rosette, indicate (by number) which arrow best represents the direction of the quantities listed below. If a quantity has zero magnitude or cannot be determined, indicate that using the corresponding number. 1. [4 pts] The position vector at location A. 2. [4 pts] The (instantaneous) momentum at location B. 3. [4 pts] The change in position (displacement) between location A and location B. 4. [4 pts] The change in position (displacement) between location B and location D. 5. [4 pts] The change in velocity between location B and location F. 6. [4 pts] The change in velocity between location C and location F. 7. [4 pts] The change in momentum between location B and location C. 8. [4 pts] The change in momentum between location C and location E. 9. [4 pts] The acceleration between location C and location D. 10. [4 pts] The net force between location E and location F.
Two vectors ~u and ~w live in the xy plane. The magnitudes of the vectors are u and w respectively, and they make angles θ and φ with the coordinate axes as shown in the figure. 11. [5 pts] Select the correct expression for ~u in component form. < - u cos θ, u sin θ, 0 > < u cos θ, - u sin θ, 0 > < - u sin θ, u cos θ, 0 > < u sin θ, - u cos θ, 0 > 12. [5 pts] Select the correct expression for ~w in component form. < - w cos φ, w sin φ, 0 > < w cos φ, - w sin φ, 0 > < - w sin φ, w cos φ, 0 > < w sin φ, - w cos φ, 0 >
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Saving Gwen Stacy [50pts] In The Amazing Spider-Man #122, the Goblin abducts Peter’s girlfriend, Gwen Stacy, and lures Spider-Man to the Brooklyn Bridge where he lets Gwen fall. Spider-Man tries to save Gwen by swinging upwards and he catches her. However, after the catch Spider-Man realizes that Gwen has died / Figure 1 shows Gwen as she falls down and the tra- jectory of Spider-Man as he will catch her at point O . At that point, Gwen’s momentum is given by the vec- tor ~ p i and Spider-Man’s force when catching Gwen is given by vector ~ F . Notice that Spider-Man’s vector force has two components, F x and F y . 1. [15 pts] Gwen’s momentum at point O is ~ p i = < 0 , - 500 , 0 > kg m/s, and the force Spider-Man applies when he catches her is ~ F = < 100 , 1000 , 0 > N. What would be Gwen’s final momentum ~ p f one second after Spider-Man catches her? You may ignore gravity in this very short time interval. 2. [5 pts] Determine the change in Gwen’s momentum in the y direction only. Can you explain why Gwen died? 3. [5 pts] Did Gwen’s momentum change in the x direction? Did it change in the z direction? Explain why or why not.
Figure 2 shows an alternative universe where Spider- Man took our physics course and decided to swing in a way that the force he applied when catching Gwen at point O was ~ F = < 100 , 400 , 0 > N instead. 4. [15 pts] Gwen’s initial momentum is still ~ p i = < 0 , - 500 , 0 > kg m/s. What would be her final momentum ~ p f one second after Spider-Man catches her in this case? You may continue ignoring gravity. 5. [5 pts] Determine the change in Gwen’s momentum in the y direction only in this alternate scenario. Do you think Gwen would survive in this case? Briefly explain. 6. [5 pts] If we knew Gwen’s mass and wanted to calculate her velocity at point O , what formula would we use to relate velocity and momentum: Newton’s ( ~ p = m~v ) or Einstein’s ( ~ p = γm~v )? Would it matter?