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A movie stuntman (mass 80.0 kg) stands on a window ledge 5.0 m above the floor. Grabbing a rope attached to a chandelier, he swings down to grapple with the movie's villain (mass 70.0 kg), who is standing directly under the chandelier. (Assume that the stuntman's center of mass moves downward 5.0 m. He releases the rope just as he reaches the villain.)

a) With what speed do the entwined foes start to slide across the floor?
b) If the coefficient of kinetic friction of their bodies with the floor is mu_k= 0.205 , how far do they slide?

2007-02-21 14:50:43 · 2 answers · asked by Paul Wall 2 in Science & Mathematics Physics

2 answers

(a)
S=A sin(wt) (for a simple harmonic motion)
A- the amplitude
w – angular frequency
t – time

w=2 pi f (Relationship between angular frequency (w) and frequency f.)

f=1/T (T – period of occilation)
Period T=2 pi sqrt(l/g) (for a simple pendulum)
l - length of the rope (string)
g – gravitational acceleration

w= 2 pi/T=2 pi/(2 pi sqrt(l/g))
w=sqrt(g/l)
So S= A sin(sqrt(g/l) t)
The velocity then is
S’=V=A C cos(sqrt(g/l) t)-
At thetime of impact
V=A sqrt(g/l)

m1V=(m1+m2)V2 before and just after ‘grappling’.
V2=m1V/(m1+m2)
V2= m1 A sqrt(g/l)/(m1+m2)

A – Is the horizontal distance from the stuntman and the villain before the stuntman jumps
L – Distance from the chandelier hook to the stuntman’s center of mass.
m1- mass of the stuntman.
m2 – mass of the villain.


(b)
F(before) = m1 a

Work done against friction = u(m1+m2)g D
Kinetic energy of stuntman was used to do that work against friction.
Ke= .5m1V^2

Then
D=(.5m1V^2)/[u(m1+m2)g]
Where V=A sqrt(g/l)

I hope it helps.

2007-02-22 02:41:03 · answer #1 · answered by Edward 7 · 0 0

♠ thus his pot E=m1*g*h, here m1=80kg, h=5m;
♣ at grapple kin E of both = 0.5m1*v^2 +0.5m2*v^2, here m2=70kg;
thence balance:
♦ m1*g*h = 0.5m1*v^2 +0.5m2*v^2, hence speed of both
v =sqrt(2m1*gh /(m1+m2)) =7.23m/s;
♥ friction f=(m1+m2)*g*u =(m1+m2)*a, hence deceleration a=u*g;
and how-far is s=0.5a*t^2, where t=v/a;
thus s=0.5a*(v/a)^2 = 0.5*7.23^2 /0.205/9.8 = 13.01m;

2007-02-25 12:44:28 · answer #2 · answered by Anonymous · 0 0

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