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1.Question:
A penguin is going down a slide. The coefficient of kinetic friction between the penguin and the slide has a value of 0.77. It takes three times as long to slide down this slide as it would if the slide were frictionless. Find the angle of the slide.
2. My answer: I chose solving it using mechanical energies
Suppose it reaches ground state after covering distance d,
Equations of mechanical energy;
with friction:
Ek+Epg=Wf+Ek1+Epg1 Wf=-0.77.d.mg.cos(alfa)
mv^2/2+mg.d.sin(alfa)=-0.77dmgcos(alfa)+mV^2/2+mgh(final) divide by m (h final=0 taking ground state when it covers d)
v^2/2+gdsin(alfa)=-0.77gdcos(alfa)+V^2/2--------------------{1}
without friction: Ek+Epg=Ek1+Epg1 (Epg1=0)
mv^2/2+mg.3dsin(alfa)=mV^2/2 divide by m (V after cutting 3d without friction equal V after cutting 1d with friction)
v^2/2+3d.g.sin(alfa)=V^2/2----------------------------{2}
{2} - {1}:... tan(alfa)=0.77.g/2
that gives ALFA=75.155 degree Is it correct?
A penguin is going down a slide. The coefficient of kinetic friction between the penguin and the slide has a value of 0.77. It takes three times as long to slide down this slide as it would if the slide were frictionless. Find the angle of the slide.
2. My answer: I chose solving it using mechanical energies
Suppose it reaches ground state after covering distance d,
Equations of mechanical energy;
with friction:
Ek+Epg=Wf+Ek1+Epg1 Wf=-0.77.d.mg.cos(alfa)
mv^2/2+mg.d.sin(alfa)=-0.77dmgcos(alfa)+mV^2/2+mgh(final) divide by m (h final=0 taking ground state when it covers d)
v^2/2+gdsin(alfa)=-0.77gdcos(alfa)+V^2/2--------------------{1}
without friction: Ek+Epg=Ek1+Epg1 (Epg1=0)
mv^2/2+mg.3dsin(alfa)=mV^2/2 divide by m (V after cutting 3d without friction equal V after cutting 1d with friction)
v^2/2+3d.g.sin(alfa)=V^2/2----------------------------{2}
{2} - {1}:... tan(alfa)=0.77.g/2
that gives ALFA=75.155 degree Is it correct?