a 5.245 kg block is released from rest at a height of 4.25 m on africtionless ra

Question

a 5.245 kg block is released from rest at a height of 4.25 m on africtionless ramp (left ramp). The left ramp is at an angleof 27.6 degrees to the horizontal. The block then slides downthe left ramp and smoothly onto a frictionless horizontal surface. After the block has traveled 5.098 m on the frictionlesshorizontal surface it encounters a 4.9 m long rough patch. The coefficient of kinetic friction between the block and therough patch is 0.100. When the block leaves the rough patchit continues 13.988 m over the horizontal frictionless surface,then slides smoothly up a second frictionless ramp (right ramp)until it stops. The right ramp is at an angle of 33.3 degreesto the horizontal. a) what is the initial total energy of the block? b) what is the total energy of the block at the bottom of thefirst ramp? c) what is the total energy of the block just before it hitsthe rough patch? d) what is the total energy of the block right after it leavesthe rough patch? e) what is the max height the block goes up to on the secondramp?
After reaching the max height on the right ramp, the blockslides back down and begins to travel toward the left ramp. The block continues to slide back and forth between the rampsuntil it finally stops. f) where does the block finally stop? g) how many trips does the block make? ( the first trip to theright ramp is trip #1 and the following trip to the left ramp istrip #2) a) what is the initial total energy of the block? b) what is the total energy of the block at the bottom of thefirst ramp? c) what is the total energy of the block just before it hitsthe rough patch? d) what is the total energy of the block right after it leavesthe rough patch? e) what is the max height the block goes up to on the secondramp?
After reaching the max height on the right ramp, the blockslides back down and begins to travel toward the left ramp. The block continues to slide back and forth between the rampsuntil it finally stops. f) where does the block finally stop? g) how many trips does the block make? ( the first trip to theright ramp is trip #1 and the following trip to the left ramp istrip #2)

Explanation / Answer

mass m = 5.245 kg
Initial velocity u = 0 height h = 4.25 m angle = 27.6 degrees Distance S = 5.098 m Length of rough pathch S ' = 4.9 m The coefficient of kinetic friction between the blockand the rough patch is = 0.100 Distance of frictionless surface S " = 13.988m Angle of the right ramp ' = 33.3degrees a) the initial total energy of the block = mgh = 218.45J b) the total energy of the block at the bottom of thefirst ramp = 218.45 J Since it is friction less c) the total energy of the block just before it hits therough patch = 218.45 J Since it is friction less and fromlaw of conservation ofenergy d) the total energy of the block right after it leaves therough patch E = 218.45 - ( f S ' ) where f = frictional force = mg              =5.14 So, E = 218 .45 - ( 5.14 * 4.9 ) = 193.65 J e) Speed after rough patch V = ? speed of the block at bottom of the 1 st ramp v =[ 2gh ]                                    v = 9.126 m / s speed after rough pathch V = ? where   a = accleration = - g = - 0.98 m / s ^2 So, V ^ 2 - v^ 2 = 2aS '                   V = [ v ^ 2 + 2aS ' ]                      = 8.58 m / s the max height the block goes up to on the second ramp H = V ^2 / 2g                                                                                         = 3.75 m

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