A box with mass m sits at the bottom of a long ramp thatis sloped upward at an angle a above the horizontal. You give the boxa quick shove, and after it leaves your hands it is moving up the rampwith an initial speed v0. The box travels a distance d up the ramp andthen slides back down. When it returns to its starting point, the speedof the box is half the speed it started with; it has speed v0 /2. What isthe coefficient of kinetic friction between the box and the ramp? (Youranswer should depend on only a.)

A box with mass m sits at the bottom of a long ramp thatis sloped upward at an angle a above the horizontal. You give the boxa quick shove, and after it leaves your hands it is moving up the rampwith an initial speed v0. The box travels a distance d up the ramp andthen slides back down. When it returns to its starting point, the speedof the box is half the speed it started with; it has speed v0 /2. What isthe coefficient of kinetic friction between the box and the ramp? (Youranswer should depend on only a.)

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