A 1200kg mass rests on a track inclined at 30 degrees to the horizontal.
A force P inclined at 18 degrees TO THE TRACK (48 degrees to the horizontal) causes the carriage to move up the track at constant velocity (i.e. no acceleration). Coefficient of friction is 0.2; determine P. Use gravity as 9.8 ms^-1.
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Constant velocity means no net forces act on the mass.
Parallel forces: Gravity = (m)(g)(sin30) = 5880N
Frictional force = (0.2)(Normal force)
That's all I've got so far :/
A force P inclined at 18 degrees TO THE TRACK (48 degrees to the horizontal) causes the carriage to move up the track at constant velocity (i.e. no acceleration). Coefficient of friction is 0.2; determine P. Use gravity as 9.8 ms^-1.
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Constant velocity means no net forces act on the mass.
Parallel forces: Gravity = (m)(g)(sin30) = 5880N
Frictional force = (0.2)(Normal force)
That's all I've got so far :/
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You're on the right track; just need to identify a few additional forces. Along the axis of the ramp, you already identified the component of the weight pulling it down the ramp (m*g*sin(30)). Now look at the force P pulling it up the ramp. For the component of the force along the ramp, we want to use the cosine of the angle between the ramp and the force (18 degrees). So the force along the ramp, which acts opposite of gravity is P*cos(18). Finally, along the plane of the ramp, you have friction. Since the object is moving up the ramp, friction must be pulling it toward the bottom of the ramp. Friction, as you have stated, is 0.2*NormalForce. So those are your three forces acting along the axis of the ramp. Unfortunately, you have two unknowns: P and NormalForce. Move to the other axis.
Acting perpendicular to the ramp is the other component of gravity: m*g*cos(30). Also, your force P pulls up away from the ramp with a force of: P*sin(18). Your normal force also pushes up away from the ramp. So you have three forces here as well, but this time, the normal force is your only unknown.
Use the set of perpendicular forces to solve for NormalForce. Then plug NormalForce back into the set of your first three equations to solve for P. Remember since there is no acceleration, all forces in each case must add up to 0. So it should look like this.
P*sin(18) + NormalForce - m*g*cos(30) = 0
...solve for NormalForce...
Now plug that into the equation below to solve for P.
P*cos(18) - 0.2*NormalForce - m*g*sin(30) = 0
Hope this helps you understand the setup a little better. Good luck.
Acting perpendicular to the ramp is the other component of gravity: m*g*cos(30). Also, your force P pulls up away from the ramp with a force of: P*sin(18). Your normal force also pushes up away from the ramp. So you have three forces here as well, but this time, the normal force is your only unknown.
Use the set of perpendicular forces to solve for NormalForce. Then plug NormalForce back into the set of your first three equations to solve for P. Remember since there is no acceleration, all forces in each case must add up to 0. So it should look like this.
P*sin(18) + NormalForce - m*g*cos(30) = 0
...solve for NormalForce...
Now plug that into the equation below to solve for P.
P*cos(18) - 0.2*NormalForce - m*g*sin(30) = 0
Hope this helps you understand the setup a little better. Good luck.
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coefficient of friction= Force Friction / Force Normal
0.2=Force friction/5880
Force Friction=1176 N
0.2=Force friction/5880
Force Friction=1176 N
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f=mg,