SOLUTION: A 6000 lb suv is being winched up a ramp onto a flat bed trailer. If the ramp is at a 25 degree angle, how much force will be required by the winch to pull the suv up the ramp? rou

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Question 117069This question is from textbook
: A 6000 lb suv is being winched up a ramp onto a flat bed trailer. If the ramp is at a 25 degree angle, how much force will be required by the winch to pull the suv up the ramp? round to the nearest pound. This question is from textbook

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
In this forum it's pretty hard to do drawings that support geometric problems such as this one.
.
So, let's just say that for a weight on a ramp that goes up at an angle alpha the
portion of the weight W that acts perpendicular to the ramp is given by the equation:
.
W%5Bn%5D+=+W%2Acos%28alpha%29
.
and the portion of the weight W that acts parallel to and down the ramp is given by the
equation:
.
W%5Bt%5D+=+W%2Asin%28alpha%29
.
In this problem, the weight W is the weight of the SUV which is given as 6000 lbs and the
angle alpha of the ramp is 25 degrees.
.
The winch will have to generate enough force to overcome the portion of the weight of the
SUV that acts parallel to and down the ramp. [This assumes the rolling friction of the vehicle
is negligible.] So the winch will have to produce an amount of force equal to:
.
W%5Bt%5D+=+W%2Asin%28alpha%29+=+6000%2Asin%2825%29+=+6000%2A+0.422618261+=+2535.71
.
Once the vehicle is in motion the winch will have to pull with a force of 2535.71 lbs
parallel to the ramp to keep the SUV rolling up the ramp at a steady rate of movement.
.
Hope this helps you to understand the problem a little better. If you expect to do many of
these problems, you might want to memorize these two "ramp" equations.
.