The Great Sandini is a 60-kg circus performer who is shot from a cannon (actuall

Question

The Great Sandini is a 60-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 N during the 4.0 m he moves in the barrel. At what speed will he emerge from the end of the barrel, 2.5 m above his initial rest position?

Explanation / Answer

Given

Mass of the performer m = 60 kg

Spring constant k =1100 N/m

Force of compression Fc = 4400 N

Force of friction Fr = 40 N

Length of the barrel L = 4.0 m

Emerging height h = 2.5 m

Solution

Compression length of spring

Fc = kx

x = Fc/k

x = 4400/1100

x = 4 m

Energy provided by spring

ES = ½ kx2

ES = ½ x 1100 x 42

ES = 8800 J

Work done against friction

Wf = Fr x L

Wf = 40 x 4

Wf = 160 J

Work done against gravity

Wg = mgh

Wg = 60 x 9.8 x 2.5

Wg = 1470 j

Net kinetic energy

E = Es – Wf – Wg

E = 8800 – 160 – 1470

E = 7170 J

½ mv2 = 7170

mv2 = 14340

v2 = 14340/60

v = 15.46 m/s

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