a.) calculate the speed with which the nugget leaves the barrel if you can ignor

Question

a.) calculate the speed with which the nugget leaves the barrel if you can ignore friction.
b.) calculate the speed with which the nugget leaves the barrel if a constant resisting force of 6.00 NA is acting on the nugget as it moves along the barrel.
c.) For the situation in part (b), at what position along the barrel does the nugget have the greatest speed and what is that speed?

5. (20 pts) You have designed a new pratotype for a loaded gun that shoots chicken nuggets. The spring that you are using can be considered massless and has a force constant of k 400 N/m. As a test, you load a chicken nugget with a mass of 0.0300kg into the barrel and compress the spring 6.00 cin. Holding the barrel so that it is harizontal, yau release the spring, propelling the nugget out of the barrel which is also 6.00 cm long As a result, the nugget loses contact with the spring when it leaves the barrel. (a) Calculate the speed with which the nugget leaves the barrel if you can ignore friction. (b Calculate the speed with which the nugget leaves the barrel if a constant resisting force of 6.00 N is acting on the mugget as it moves along the barrel (c) For the situation in part (b), at what position along the barrel does the nugget have the greatest speed and what is that speed?

Explanation / Answer

k = 400 N/m
m = 0.03 kg
x = 6.0 cm = 0.06 m
L = 6.0 cm = 0.06 m

(a)
Let the speed be v.
Using Energy conservation,
Initial Spring Potential Energy = Final Kinetic Energy
1/2*k*x^2 = 1/2*m*v^2
400 * 0.06^2 = 0.03*v^2
v = 6.93 m/s

(b)
Fr = 6.0 N
Work done against friction, = Fr * L
Using Energy conservation,
Initial Spring Potential Energy = Final Kinetic Energy + Work done against friction
1/2*k*x^2 = 1/2*m*v^2 + Fr*L
1/2 * 400 * 0.06^2 = 1/2 * 0.03 * v^2 + 6.0 * 0.06
v = 4.9 m/s

(c)
Speed will be greatest , when the Net Force = 0 , (ie spring force = Friction force)
k*x = 6.0 N
400 * x = 6.0
x = 0.015 m
x = 1.5 cm
So position from the starting point of nugget = 4.5 cm

(d)
Using Energy conservation,
Initial Spring Potential Energy = Final Kinetic Energy + Final Spring Potential Energy  + Work done against friction
1/2 * 400 * 0.06^2 = 1/2 * 0.03 * v^2 + 1/2 * 400 * 0.015^2 + 6.0 * 0.045
v = 5.2 m/s

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