More inelastic problems Homework Question - How Far Do They Slide?

[Spraypaint]

Homework Statement

A movie stuntman (mass 81.8 kg) stands on a window ledge 7.33 m above the floor. Grabbing a rope attached to a chandelier, he swings down to grapple with the movie’s villain (mass 66.4 kg), who is standing directly under the chandelier. (Assume that the stuntman’s center of mass moves downward 7.33 m. He releases the rope just as he reaches the villain) If the coefficient of kinetic friction of their bodies with the floor is uk = 0.71, how far do they slide?

Homework Equations

The Attempt at a Solution

So what I did is first solve for the potential of the stuntman ( 81.8 * 9.8 * 7.33). Then subtract out the friction caused by the two people ( total mass * 9.8 * .71). This is the energy left to the system. So set this equal to F * d where force is equal to total mass * 9.8. And that's how I get my d, which is wrong.

 

[tiny-tim]

So what I did is first solve for the potential of the stuntman ( 81.8 * 9.8 * 7.33). Then subtract out the friction caused by the two people ( total mass * 9.8 * .71). This is the energy left to the system. So set this equal to F * d where force is equal to total mass * 9.8. And that's how I get my d, which is wrong.

Hi Spraypaint!

The collision is inelastic … energy is not conserved in the collision …

you have to find the initial joint speed before you can start to apply conservation of energy.

 

[nlightner]

I would like to point out that the approach taken in this solution is incorrect. The problem involves a collision between two bodies, so it cannot be solved using energy conservation alone. Instead, the conservation of linear momentum should be used to determine the distance the two bodies will slide after the collision. The initial momentum of the stuntman and the villain before the collision is equal to the final momentum after the collision. This can be expressed as m1v1 + m2v2 = (m1 + m2)v, where m1 and m2 are the masses of the stuntman and the villain, respectively, v1 and v2 are their initial velocities, and v is their final velocity after the collision. From this equation, the final velocity can be calculated, and then the distance they will slide can be determined using the equation v^2 = u^2 + 2as, where u is the initial velocity (which is zero in this case), a is the coefficient of kinetic friction, and s is the distance. It is important to note that the mass of the rope and the chandelier should also be taken into account in the calculation of the total mass.