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Physics 1003 ? STRL

 

Final Examination

 

Spring 2016

 

1. 4 particles are connected and suspended, as shown in Figure 1, by 5 massless, non-stretching

 

strings, and one massless bar.

 

a. Draw a free body diagram for each particle, including the angles.

 

b. What is the tension in the top string holding up the whole system?

 

c. Set up, but do not solve, the equations necessary to find the other tensions and the

 

normal forces if the system is in equilibrium.

 

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2. A 5 meter wide, 200 kg block is travelling along a frictionless surface with a velocity of 20 m/s.

 

Sitting atop it, at the leftmost edge, is a much smaller, 3kg block. Refer to Figure 2.

 

a. If the 5 meter wide block is suddenly and instantaneously brought to a complete stop,

 

what must the coefficient of kinetic friction between the two blocks be for the much

 

smaller block to come to a stop at the rightmost edge of the 5 meter block?

 

b.

 


 

How much work had to be done to stop the 200 kg block?

 


 

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3. An ice-cube with a volume of 0.00003 m3 floats in a cup of liquid water.

 

a. Determine the amount of the ice-cube?s mass above and below the water.

 

b. Now the ice-cube has a volume 30,000 m3 and floats in a suitably larger cup of liquid

 

water. Determine the amount of the ice-cube?s mass above and below the water.

 

c. Compute the ratio of ?mass above? to ?mass below,? i.e. (mass above)/(mass below),

 

for your values from parts a) and b). Are the ratios equal?

 

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4. There is a type of subatomic particle known as a muon. It has an average lifetime of about 2.2 x

 

10-6 seconds and when it?s produced by the atomic processes within the cores of stars it can

 

have a velocity of 98% of the speed of light.

 

a. At that speed, how long will it last in a laboratory that is stationary relative to the

 

traveling muon?

 

b. Using the extended lifetime calculated in part a), determine how far the muon can

 

travel in that time?

 


 

[Diagram 1]

 


 

[Diagram 2]

 


 

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Friendly Formulae

 

Weight Force: ???? = < 0 , ? >, where = 9.81 m/s2

 


 

Friction Force Magnitude: = , where is the Normal Force Magnitude

 

? ? = ?

 


 

? = ()

 


 

? = ()

 


 

. . =

 


 

1

 

2

 

2

 


 

. . = ?

 

. . =

 


 

1

 

(?)2

 

2

 


 

= . + . .

 

, = ,

 

.. = ?

 

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Density: =

 


 


 


 


 

Buoyant Force Magnitude : =

 

is the density of the displaced fluid

 

is the volume of the displaced fluid

 

g is the magnitude of acceleration due to gravity, 9.81 m/s2

 

Density of liquid water: 1000 kg/m3

 

Density of solid water: 917.43 kg/m3

 

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Time Dilation: ?

 


 

?

 


 

=

 


 

?

 

2

 


 

?1? 2

 


 


 

? 3 ? 108 /

 


 

 

Paper#9257442 | Written in 27-Jul-2016

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