Okay here goes: 6) A 76 kg box slides down a 24 degree ramp with anacceleration

Question

Okay here goes: 6) A 76 kg box slides down a 24 degree ramp with anacceleration of 3.2 m/s^2. Find the coefficent of kinetic frictionbetween the box and the ramp. 7) What acceleration would a 161 kg mass have down thisramp? 8) A box of books weighing 346 N moves with a constantvelocity across the floor when it is pushed witha force of417 N exerted downward at an angle of 31.9 degrees below thehorizontal. Find the coefficent of kinetic friction between the boxand the floor. 9) A freight train has a mass of 2.3 x 10^7 kg. If thelocomotive can exert a constant pull of 7.5 x 10^5 N, how longwould it take to increase the speed of the train from rest to 84.9km/h? (Disregard friction.) 10) A 3.1 kg block is pushed along the ceiling witha constant applied force of 87 N that acts as an angle of 59degrees with the horizontal. The block accelerates to the right at6.4 m/s^2. What is the coefficent of kinetic friction between theblock and the ceiling? 11) A 4.7 kg bag of groceries is in equilibrium on an inclineof 30 degrees. What is the magnitude of the normal force on thebag? All problems use 9.81 for gravity. Someone please help me I CANT DO IT AAAHHHH!!! Okay here goes: 6) A 76 kg box slides down a 24 degree ramp with anacceleration of 3.2 m/s^2. Find the coefficent of kinetic frictionbetween the box and the ramp. 7) What acceleration would a 161 kg mass have down thisramp? 8) A box of books weighing 346 N moves with a constantvelocity across the floor when it is pushed witha force of417 N exerted downward at an angle of 31.9 degrees below thehorizontal. Find the coefficent of kinetic friction between the boxand the floor. 9) A freight train has a mass of 2.3 x 10^7 kg. If thelocomotive can exert a constant pull of 7.5 x 10^5 N, how longwould it take to increase the speed of the train from rest to 84.9km/h? (Disregard friction.) 10) A 3.1 kg block is pushed along the ceiling witha constant applied force of 87 N that acts as an angle of 59degrees with the horizontal. The block accelerates to the right at6.4 m/s^2. What is the coefficent of kinetic friction between theblock and the ceiling? 11) A 4.7 kg bag of groceries is in equilibrium on an inclineof 30 degrees. What is the magnitude of the normal force on thebag? All problems use 9.81 for gravity. Someone please help me I CANT DO IT AAAHHHH!!!

Explanation / Answer

6) Fg - Ff = F mgsin - mgcos = ma = (gsin - a)/gcos = ((9.8)(sin24) -3.2)/(9.8)(cos24) = .088 7) mgsin - mgcos = ma mass cancels out of the equation so it would still have3.2 m/s/s down theramp 8) Fnormal = 346 N + 417cos31.9 N = 700.02N Fx = 417sin31.9 N = 220.36 N Fnormal = Fx = Fx/Fnormal = (220.36)/700.02 =.315 9) ma = F a = F/m a = (v)/t v/t = F/m t = vm/F 84.9 km/h = 23.58 m/s t = 23.58(2.3x107)/(7.5x105) =723.12 seconds = 12.05minutes 10) Do the same thing as in 8) with the new numbers 11) Fnormal = mgcos = 4.7(9.8)cos30 =39.9 N (I used 9.8 instead of 9.81. I didnt see that until the endbut you get the idea) = Fx/Fnormal = (220.36)/700.02 =.315 9) ma = F a = F/m a = (v)/t v/t = F/m t = vm/F 84.9 km/h = 23.58 m/s t = 23.58(2.3x107)/(7.5x105) =723.12 seconds = 12.05minutes 10) Do the same thing as in 8) with the new numbers 11) Fnormal = mgcos = 4.7(9.8)cos30 =39.9 N (I used 9.8 instead of 9.81. I didnt see that until the endbut you get the idea)

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