Question

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?

Answer 1

Answer:

v = 15.8 m/s

Explanation:

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

    $W_{fr}$ = ΔEm = $Em_{f}$ -Em₀

Let's write the mechanical energy at each point

Initial

    Em₀ = Ke = ½ k x²

Final

   $Em_{f}$ = 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

Answer 2

Answer:

The speed is 15.4601 m/s

Explanation:

the solution is in the attached Word file

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