Snow Toboggan
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A parent pulls a toboggan with 3 kids at a constant velocity for 38 m along a horizontal snow covered trail.?
The total mass of the children and the toboggan is 66 kg. The force the parent exerts is 58 N ( 18 degrees above the horizontal). a) Determine the magnitutde of the normal force and the coefficient of kinetic friction. b) Determine the work done on the toboggan by kinetic friction.
First, draw a Free body diagram for the situation.
Since the Normal force and the Gravitational force are the same, (because the tobaggon isnt floating in air) you know that graviational force is 66 Newtons. You can therefore find out that the Normal force is also 66 Newtons. Your answer to the first part in question a) of the magnitude of Normal force is 66 N.
The formula for Kinetic friction is “Ff=μFn.” By plugging in 58Cos 18 degrees in your calculator, you can find out that that Fa or Ff (in the X direction) is equal to 55N. Also you can do 58 Sin 18 degrees to find the force exerted in the Y direction (this would be much easier to explain if an FBD was present.) You must now add the Normal Force of the tobaggon (which was 66N with this force to give a total force in the Y direction of 84N) Ff (force of friction) is equal to Fa because it is constant velocity. Now you can plug this into your formula: 55N = μ 84N and rearrange and get 55N/84N = μ. Therefore, the coefficient of kinetic friction is 0.6547or simply 0.65(no units.)
Onto b)! The formula is W=Fd so simply take the force and divide it by the distance given in the question. The Force of kinetic friction is 55 N because it is a constant speed it is same as Fa (applied force) Distance comes from question, So: W = (55N)(38m)
W= 2090 Joules.
Hope that helped!
2008 US National Toboggan Championships Camden Snow Bowl
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