The Great Sandini is a 60.0-kg circus performer who is shot from a cannon (actua

Question

The Great Sandini is a 60.0-kg circus performer who is shot from a cannon (actually a spring gun). You don’t find many men of his caliber, so you help him design a new gun. This new gun has a very large spring with a very small mass and a force constant of 1100 N/m that he will compress with a force of 4400 N. The inside of the gun barrel is coated with Teflon, so the average friction force will be only 40.0 N during the 4.00 m he moves in the barrel. At what speed will he emerge from the end of the barrel, 2.50 m above his initial rest position?

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Below is a sketch of the initial state of the situation described in this problem. Draw the most suitable set of coordinate axes for this problem. Note that even though you can choose the y=0 level to be wherever you like, in most situations it is best to set the zero height to coincide with either the initial or final position, so that the calculations for the gravitational potential energy become easier. For this reason, in this particular problem place the origin of your coordinate axes on the black dot marking the performer's initial position. Draw only the positive portion of the coordinate axes.

Draw the vectors starting at the black dot. The location and orientation of the vectors will be graded. The length of the vectors will not be graded.

Explanation / Answer

WHen spring is in compressed position, total energy of the spring,

= (1/2)* k*x^2

where x is compression length, x = F/k = 4400/1100 = 4 m

=(1/2)*(1100)*(4^2)

=8800 J....(1)

Now energy at the top of the barrell,

= K.E + P.E. + Frictional loss,

Here frictiona force is 40 N, so energy desiipitation due to friction =Fr*x 40*x = 40*4 =160 J

=(1/2)*m*v^2 + m*g*h+160...(2)

Using conservation of energy,

(1) = (2)

8800=(1/2)*m*v^2 + m*g*h-160.

(1/2)*60*v^2 + 60*9.81*2.5+160=8800.

v^2 = 238.95

Speed when coming out of barrell,

v=15.45 m/s.

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