Physics 131-1 Test 2


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

  1. What is the definition of an integral in terms of a limit?

  2. How is acceleration related to mass? What is your evidence? Sketch your answer on the graph below. Label the axes properly.

    \epsfbox{f1a.eps}

  3. Two masses are hung by strings draped over pulleys and connected by a spring scale as shown in the figure. The spring scale is not moving and reads twice the mass $m$. Is this correct? Explain?

    =4.5cm \epsfbox{f2a.eps}

  4. What is Roche's limit?

  5. A particle is made to move in two different circular orbits during two different time periods. The radii of curvature and the speeds are shown in the table below. Which arc requires the greatest centripetal force? Why?

    Arc Speed Radius
    1 $2v_0$ $r_0$
    2 $3v_0$ $3r_0$

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

1. 15 pts. A 4.0-kg block moves in a straight line on a horizontal frictionless surface under the influence of a force that varies with position as shown in the figure. How much work is done by the force as the block moves from the origin to $x=10.0~m$?

\epsfbox{f4a.eps}

2. 15 pts. A typical neutron star can have a mass of $m= 2.0\times 10^{30}~kg$ but a radius of only $r=10^4~m$.
  1. What is the gravitational acceleration at the surface of such a star?
  2. How fast would a pebble be moving if it fell from rest through a distance $d=1.0~m$? Ignore friction or the rotation of the star.

3. 20 pts. You are riding in a car that is going around a flat curve that has a radius of $\rm 50.0~m$ from the middle of the car to the center of curvature. A good-luck charm that is hanging from a 0.3-m long string from the rear-view mirror has a mass $m=0.1~kg$. The string makes an angle $\theta = 35.0^\circ$ to the vertical. What is the speed $v$ of the car?

Some constants.


Acceleration of gravity ($g$) $9.8~m/s^2$ Neutron mass $1.67\times 10^{-27}~kg$
Gravitation constant $6.67 \times 10^{-11}~N-m^2/kg^2$