to move the box 7.18 m, starting from rest? tween cr Answer in units of s. 002 (
ID: 1596678 • Letter: T
Question
to move the box 7.18 m, starting from rest? tween cr Answer in units of s. 002 (part 1 of 2) 10.0 points Find the A student decides to move a box of books into her dormitory room by pulling on a rope at- tached to the box. She pulls with a force of The coeff 160 N at an angle of 32° above the horizon 3.3 kg cra tal. The box has a mass of 25.6 kg, and the The acc coefficient of friction between box and floor is 0.262. The acceleration of gravity is 9.8 m/s2 1600 320 25.6 kg H 0.262 Find the acceleration of the box. Answer in units of m/s2 What min 003 (part 2 of 2) 10.0 points the crate pe The student now starts moving the box up a vent the crat 14.9 incline, keeping her 160 N force directed Answer in at 32 above the line of the incline. 32 25.6 kg If the coefficient of friction is unchanged,Explanation / Answer
(a)
Weight of box = mg = 25.6*9.8 = 250.88N The boxes weight pushes it onto the floor.
A component of the tension on the rope subtracts from the box's weight.
The force pushing the box on the floor is 250.88-160sin32 = 166.09N
If the angle the rope made were 90 degrees, all of the 130N would subtract (sin90=1).
If the rope pulled at 0 degrees, none of the rope tension would subtract from the weight (sin0=0).
The friction force is 166.09*0.262 = 43.516 N.
The component of rope tension pulling the box is
160cos32=135.68 The net force pulling the box is 135.68-43.516 =92.171N
F = ma
a = 92.171/25.6
a = 3.6m/s2
(b)
The force pushing the box on the ramp = 250.88cos14.9 = 242.4444 N
If the ramp were level, all the box's weight would push the box onto the ramp (cos0 = 1)
Subtract component of rope tension lifting box = 160sin(32-14.9) = 47.046N
Friction force = (242.444 - 47.046)*0.3 = 51.194N
The component of rope tension pulling the box up the ramp is 160cos(32-14.9) = 152.926 N
The component of the box's weight resisting being pulled up the ramp is 250.88sin14.9 = 64.509 N
The net force pulling the box up the ramp is then 152.926 - 64.509 = 88.416 N
a = F/m
a = 88.416/25.6
a = 3.45 m/s2
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