Q1- Use the work-energy theorem to calculate the minimum speed that you must giv

Question

Q1- Use the work-energy theorem to calculate the minimum speed that you must give the box at the bottom of the incline so that it will reach the skier... Problem: You are a member of an alpine rescue team and must get a box of supplies, with mass 2.10 , up an incline of constant slope angle 30.0 so that it reaches a stranded skier who is a vertical distance 3.50 above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.0010?2. Since you can't walk up the incline, you give the box a push that gives it an initial velocity; then the box slides up the incline, slowing down under the forces of friction and gravity. Take acceleration due to gravity to be 9.81 .

Explanation / Answer

0.5 m v^2 = m g h + u m g cos30 (h/sin30)

0.5 v^2 = g h + u g cos30 (h/sin30)

0.5 v^2 = g h + u g h cot30 h

v^2 = 2 g h + 2 u g h cot30 h

v = sqrt(2 g h (1 + u cot30))

v = sqrt(2*9.81*2.6*(1+0.06*cot30))

==> v = 7.50 m/s

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