SP3. A slingshot consist of a rubber strap attacked to a Y- shaped frame, with a

Question

SP3. A slingshot consist of a rubber strap attacked to a Y- shaped frame, with a small pouch at the center of the strap to hold a small rock or other projectile. The rubber strap behaves much like a spring. Suppose that for a particular slingshot a spring constant of 600N/m is measured for the rubber strap. The strap is pulled back approximately 40cm (0.4m) prior to being released.
a. What is the potential energy of the system prior to release?
b. What is the maximum possible kinetic energy that can be gained by the rock after release?
c. If the rock has a mass of 50g (0.05kg), what is its maximum possible velocity after release?
d. Will the rock actually reach these maximum values of kinetic energy and velocity? Does the rubber strap gain kinetic energy? Explain.

Explanation / Answer

   The constant of rubber strap, k = 600 N/m    The expansion of rubber strap, x = 0.4 m    (a) The potential energy of the system, U = (1/2) kx^2 = 48 J    (b) This potential energy of the rubber strap is converted into the          kinetic energy of the rock                                  ? (1/2)mv^2 = (1/2)kx^2                                             v = x ( k / m )^(1/2)          This is the expression for the maximum velocity gained by the rock    (c) The mass of the rock, m = 0.05 kg, then the maximum possible velocity          after release, v = 0.4 ( 600 / 0.05 )^(1/2) = 43.82 m/s    (d) Yes, thr rock must gains the maximum values of velocity and kinetic          energy and the rubber strap is also gain kinetic energy.                   This is why because energy is conserved, The potential energy          of the rubber strap is just converted into the kinetic energy of the rock.          So the rock gains the maximum values of velocity and kinetic energy.        

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