Santa's Sleigh (Newton's 2nd Law-1D) Acceleration, Horizontal Motion

• Angelx26
In summary: This would allow for more complicated calculations, but would also require more information, such as the time-varying strength of the force.The problem statement should be more specific about what is meant by "average force."

Angelx26

Homework Statement
Santa's sleigh, which has a mass of 62.5 kg (without Santa as an occupant), is pulled by eight tiny reindeer with an
average force of 8350 N over a 60.0-m stretch of snow before becoming airborne. Assuming the sleigh started
from rest, what was the sleigh's takeoff speed? (Ignore friction).

I am using a study guide that doesn't show much work, only shows the answers. I know it involves Newton's 2nd Law.
Relevant Equations
F=ma.
All I know is that it involves Newton's 2nd law F=ma.
Im wondering if I use average acceleration (vf-vi)/time
I'm not sure where else to go from here.

Angelx26 said:
Homework Statement: Santa's sleigh, which has a mass of 62.5 kg (without Santa as an occupant), is pulled by eight tiny reindeer with an
average force of 8350 N over a 60.0-m stretch of snow before becoming airborne. Assuming the sleigh started
from rest, what was the sleigh's takeoff speed? (Ignore friction).

I am using a study guide that doesn't show much work, only shows the answers. I know it involves Newton's 2nd Law.
Homework Equations: F=ma.

All I know is that it involves Newton's 2nd law F=ma.
Im wondering if I use average acceleration (vf-vi)/time
I'm not sure where else to go from here.

Do you think each reindeer pulls with a force of 8350N, or is that the total? It's not clear to me what is meant.

Where is Santa? Why isn't he in his sleigh? That's another puzzle.

And, yes, you can take ##F_{avg} = ma_{avg}##

Highway_Dylan and scottdave
Since the reindeer pull with an average force, then that implies an average acceleration, to me.

One moment while we wait for @haruspex to call attention to the blunder in the problem statement...

The problem setter is begging for you to apply the concepts of work and energy here.

scottdave said:
Since the reindeer pull with an average force, then that implies an average acceleration, to me.
Yes, but without knowing the duration that does not help.
jbriggs444 said:
One moment while we wait for @haruspex to call attention to the blunder in the problem statement...

The problem setter is begging for you to apply the concepts of work and energy here.
Thanks for the invitation... you know I can't resist.
@Angelx26 , sadly there is not enough information to answer the question. Had you been told it was a constant force then there would have been several ways to solve it, e.g. using work=force x distance, or F=ma together with v2-u2=2as. The two are essentially the same.

As it is, it depends how the force varies with time. E.g. if no force at all for 9 seconds then 83500N for one second then work = 83500N x 60m = ½mv2, but if a constant force then work is only 8350N x 60m.

scottdave, Highway_Dylan and jbriggs444
I agree that the question should have been stated clearer. My best guess is that by the "average force" of ##8350\text{ N}## it is meant that the total force exerted by the eight tiny reindeer at every moment is ##8350\text{ N}##, i.e. the sleigh is pulled by a constant force of ##8350\text{ N}##. As was discussed, if the force varies with time the given information is incomplete and ##8350\text{ N}## per reindeer is probably too much, even for Santa's reindeer.

So I'd just solve it for the simplest case of a constant force, but yeah, the wording is somewhat murky.

I guess the word "average" is often used in these problems because a constant force sounds unrealistic, so the intended assumption is that the force stays close to a certain value, with some relatively small variation. This would support a further simplifying assumption that the force is constant for the purpose of calculation.

A better statement would be to assume that the force is approximately constant.

Delta2

1. How does Santa's sleigh accelerate?

According to Newton's second law of motion, an object's acceleration is directly proportional to the net force acting on it and inversely proportional to its mass. Therefore, the acceleration of Santa's sleigh is dependent on the amount of force applied by the reindeer and the mass of the sleigh.

2. What is the net force acting on Santa's sleigh?

The net force acting on Santa's sleigh is the combined force of the reindeer pulling the sleigh forward and any opposing forces such as air resistance. This net force determines the acceleration of the sleigh.

3. How does the mass of the sleigh affect its acceleration?

The mass of the sleigh directly affects its acceleration. According to Newton's second law, the greater the mass of an object, the greater the force needed to accelerate it. Therefore, a heavier sleigh would require more force from the reindeer to achieve the same acceleration as a lighter sleigh.

4. Does the horizontal motion of the sleigh affect its acceleration?

Yes, the horizontal motion of the sleigh also affects its acceleration. If the sleigh is on a flat surface, the horizontal velocity of the sleigh will remain constant, resulting in a constant acceleration. However, if the sleigh is moving up or down a slope, the horizontal motion will change, resulting in a change in acceleration.

5. How does air resistance affect the acceleration of Santa's sleigh?

Air resistance is an opposing force that acts on the sleigh as it moves through the air. This force can slow down the sleigh and affect its acceleration. The greater the surface area of the sleigh, the greater the air resistance, and therefore, the slower the acceleration. This is why Santa's sleigh is designed to be aerodynamic, with a streamlined shape to reduce air resistance.