Physics 131-3 Test 2


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

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    An object can move along a horizontal line in the + direction. Assume friction is so small it can be ignored. The object's velocity-time graph is shown in the first plot below. Sketch the shapes of the acceleration-time and force-time graphs on the axes below. Explain your reasoning.


    \includegraphics{f1.eps}

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    What is the relationship between acceleration and mass when the applied force is kept constant? Answer in words and with a sketch. Explain your reasoning.

    \includegraphics{f2.eps}

  3. What is the definition of an integral in terms of some limit?

  4. Suppose you hang two equal masses as shown below and the system is not moving. What is the tension in the spring? Explain your reasoning.

    \includegraphics{f3.eps}

  5. The block on the incline shown below is sliding down the incline at a constant velocity so kinetic friction is operating. Draw the free-body diagram of the forces acting on the block. Are any components of the net force on the block in equilibrium (i.e., equal to zero)? Explain.

    \includegraphics{f4.eps}

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

1. 15 pts. Suppose the coefficient of static friction between the road and the tires on a NASCAR stock car is $\mu = 0.5$ during a Winston Cup race. What speed will put the car on the verge of sliding as it rounds a level curve of $R=25~m$ radius?

2. 15 pts. A 2.0-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 $x=5.0~m$?



\includegraphics{f5.eps}

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

3. 20 pts. Imagine a landing craft approaching the surface of Callisto, one of Jupiter's moons. If the engine provides an upward force $F_1 = 3000~N$, the craft descends at a constant speed. If the engine only provides an upward force $F_2 = 2500~N$, the craft accelerates downward at $a_2 = -0.4~m/s^2$.

(a)
What is the magnitude of the free-fall acceleration at the surface of Callisto?

(b)
What is the mass of the landing craft?

Some constants.


Acceleration of gravity ($g$) $9.8~m/s^2$ Neutron mass $1.67\times 10^{-27}~kg$
Gravitation constant $6.67 \times 10^{-11}~N-m^2/kg^2$ Proton mass $1.67\times 10^{-27}~kg$
Earth's radius $6.37\times 10^6~m$