Learning Goal: To practice Problem-Solving Strategy 7.2 Problems Using Mechanical Energy II. 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?

Let's analyze the situation a little, we have a compressed spring so it has an elastic energy that will become part kinetic energy and a potential part for the man to get out of the barrel, in addition there is a friction force that they perform work against the movement. So the variation of mechanical energy is equal to the work of the fictional force

[tex]W_{fr}[/tex] = ΔEm = [tex]Em_{f}[/tex] -Em₀

Let's write the mechanical energy at each point

Initial

Em₀ = Ke = ½ k x²

Final

[tex]Em_{f}[/tex] = K + U = ½ m v² + mg y

Let's use Hooke's law to find compression

F = - k x

x = -F / k

x = 4400/1100

x = - 4 m

Let's write the energy equation

fr d = ½ m v² + mgy - ½ k x²

Let's clear the speed

v² = (fr d + ½ kx² - mg y) 2 / m

v² = (40 4.00 + ½ 1100 4² - 60.0 9.8 2.50) 2/60.0

v² = (160 + 8800 - 1470) / 30

v = √ (229.66)

v = 15.8 m/s

lcoley8 lcoley8 · Answer 2 · 2020-04-27T03:45:48+02:00

lcoley8 lcoley8

27-04-2020

Answer:

The speed is 15.4601 m/s

Explanation:

the solution is in the attached Word file

Answer Link