Help on energy conservation?

Energy conservation... help please!!?

• Answer:

  An 8.70kg block slides with an initial speed of 1.66m/s up a ramp inclined at an angle of 27.4 degrees to the horizontal. The coefficient of kinetic friction between the block and the ramp is 0.3. Use energy conservation to find the distance the block slides before coming to rest. Initial KE = ½ * 8.70 * 1.66^2 = 12 Initial PE = 0 Friction force = μ * mass * 9.8 * cos 27.4º Work of friction = 0.3 * 8.7 * 9.8 * cos 27.4º * d = 22.7 d The work of friction reduces KE Final PE = mass * 9.8 * final height If the block slides d meters up a ramp inclined at an angle of 27.4 degrees to the horizontal, the final height = d * sin 27.4º Final PE = 8.7* 9.8 * d * sin 27.4º = 39.2 d J Final KE = 0 Initial KE + Initial PE - Work of friction = final KE + final PE 12 + 0 – 22.7 d = 0 + 39.2 d 12 = 61.9 d 0.194 m d = 0.194 m CHECK BY F = M * A Force parallel = mass * 9.8 * sin 27.4º Friction force = μ * mass * 9.8 * cos 27.4º ∑ Forces = mass * 9.8 * sin 27.4º + μ * mass * 9.8 * cos 27.4º = mass * a a = 9.8 * sin 27.4º + μ * 9.8 * cos 27.4º = a = 9.8 * sin 27.4º + 0.3 * 9.8 * cos 27.4º = 4.5 + 2.61 = 7.11 m/s^2 vf^2 – vi^2 = 2 * a * d 0 – 1.66^2 = 2 * 7.11 * d d = 0.194 m the answer is OK