A 36 kg block slides with an initialspeed of 5 m/s up a ramp inclined at anangle

Question

A 36 kg block slides with an initialspeed of 5 m/s up a ramp inclined at anangle of 25o with thehorizontal. The coefficient of kinetic friction between the blockand the ramp is 0.3. Use energyconservation to find the distance along the incline that the blockslides before coming to rest.
m
(Hint: You will need to relate the distance slid to the heightattained.)
A 36 kg block slides with an initialspeed of 5 m/s up a ramp inclined at anangle of 25o with thehorizontal. The coefficient of kinetic friction between the blockand the ramp is 0.3. Use energyconservation to find the distance along the incline that the blockslides before coming to rest.
m
(Hint: You will need to relate the distance slid to the heightattained.)

Explanation / Answer

final speed vf = 0, let the distance be s, the high for that distance will be h =s*sin(25) work done by friction W1 = -mgcos(25)**s for energy conservation, (1/2)m(5m/s)2 + W1 = mgh = mg*s*sin(25) => (1/2)m(5m/s)2 -mgcos(25)**s= mgh =mg*s*sin(25) distance s = (1/2)m(5m/s)2 /[mgcos(25)* + mg*sin(25)]      =  (1/2)*36kg*(5m/s)2 /[36kg*9.8m/s2cos(25)*0.3+ 36kg*9.8m/s2*sin(25)]      = 1.84m (1/2)m(5m/s)2 -mgcos(25)**s= mgh =mg*s*sin(25) distance s = (1/2)m(5m/s)2 /[mgcos(25)* + mg*sin(25)]      =  (1/2)*36kg*(5m/s)2 /[36kg*9.8m/s2cos(25)*0.3+ 36kg*9.8m/s2*sin(25)]      = 1.84m

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