does the weight of a toboggan affect its speed?

Question

if you had two people on a toboggan and then pushed them down a hill and then later on you add one more person to the two so now you have three. would the speed of the toboggan increase or decrease.

Answer 1

One of the often overlooked real world factors in problems like this is the role of air friction. At the speeds encountered in toboggan runs, the role of air friction cannot be neglected..

By adding people to the toboggan, you are adding mass while not appreciably adding to the surface area affected by air friction; the sledders sit behind each other, so the total surface area on which the friction acts does not change very much with each person you add.

So how does adding mass without adding surface area affect things. Think about dropping one 8.5x11 in sheet of paper; the effects of air friction on its motion are clear. Now, drop a whole stack of pages; by adding mass without adding surface area, the acceleration of gravity down becomes greater than the air friction up, and the stack of (let;s say, 200 sheets) falls much faster.

In the same way, adding mass to a sled without increasing surface area will cause the heavier sled to travel more rapidly down the slope.

Ain't air friction fun?

Answer 2

A simple analysis indicates that it would stay the same. The rate of acceleration down the slope is given by:

a = g(sinθ − μcosθ)

where:
g = acceleration due to gravity (a constant 9.8 m/sec²);
θ = the angle of the slope;
μ = the "coefficient of friction," a measure of the effect of friction between the toboggan and the snow.

Note that the total weight of the occupants does not enter into the equation. That's why I say it would not make any difference.

On the other hand, there could be complicating factors. If the snow is not very tightly packed, then adding an additional occupant could sink the runners deeper into the snow, effectively increasing the value of μ (and therefore decreasing the acceleration). Also, if you take into account air resistance, adding an occupant will increase the downward force while not making much difference to the upward air resistance, and this would effectively speed you up.

Answer 3

The net force acting on the toboggan and passenger is f = (m + M)a = W sin(theta) - k W cos(theta); where W is the total weight = (m + M)g of the passengers (m) and sled (M), k is the coefficient of sliding friction, and theta is the slope of the toboggan run.

Thus a = g(sin(theta) - k cos(theta)) is the acceleration of the sled. This clearly shows that the masses of the sled and of the passengers cancel out. Therefore, pile 'em on, there will be no change it the sled's acceleration behavior over the same run. [What can you do to get more a? Hint: look at the k term from friction.]

Answer 4

The simple answer is yes, generally the more weight you put in it, the faster a tobaggan or sled will travel - up to a certain limit.