Physics 131-2 Test 1


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Questions (10 pts. apiece) Answer in complete, well-written sentences WITHIN the spaces provided.

  1. Consider a ball tossed up into the air. What is the acceleration of the ball at the highest point of its trajectory? Why?

  2. Consider two measurements of some distance, $\rm 9.7~cm$ and $\rm 10.1~cm$. How many significant figures should be kept in the average? Explain.

  3. You're driving along the highway at a constant velocity in car A and speed up to pass another car (car B) moving at a constant speed. Starting from some time before you speeded up, draw the position versus time graph for both vehicles until you have passed the other car and returned to a constant speed. Use the graph below. Clearly label your drawing and only consider one-dimensional motion along the road.

    =10cm \epsfbox{t1bf1.eps}

  4. How does the vertical acceleration of a projectile influence the horizontal acceleration? What is your evidence?

  5. In our analysis of circular motion we showed that for two points close together on the trajectory of the particle

    \begin{displaymath} {\Delta v \over v } = {\Delta r \over r} \qquad {\rm and} \qquad \Delta r \approx \Delta s \end{displaymath}

    where $v$ is the velocity, $r$ is the position, and $s$ is the arc length. Using these facts and the definition of acceleration, show that

    \begin{displaymath} a = {v^2 \over r} \qquad . \end{displaymath}

Problems. Clearly show all reasoning for full credit. Use a separate sheet to show your work.

1. 15 pts. When a large star explodes and becomes a supernova the remaining core can become a neutron star. If a neutron star has a radius $r = 10^4~m$ and rotates every $\rm 1.2~s$, then what is the centripetal acceleration of a particle on the star's equator?

2. 15 pts. A rocket is fired vertically from rest and ascends with a constant vertical acceleration of $\rm 3.0~m/s^2$ for $\rm 5.0~s$ and then the engine cuts off. How long does it take for the rocket to reach its maximum altitude?

3. 20 pts. You've graduated from college and fulfilled a childhood dream to become a homicide detective in a large city. On your first day at work, you're investigating the death of a man who was found $\rm 4.5~m$ from the base of his apartment building and $\rm 20~m$ below his balcony. Do you think the death is accidental? Explain.

Some constants.


Acceleration of gravity ($g$) $9.8~m/s^2$