Go Rudolph Go!

Classical Mechanics Level 2

Eight reindeer, each with mass of $400~\mbox{kg}$ , are attached to Santa's sleigh in four rows of two reindeer each. The last two reindeer, Donner and Blitzen, are attached to the reindeer in front of them and Santa's sleigh, with total mass $1200~\mbox{kg}$ , behind them by their harnesses. On liftoff on Christmas Eve, the reindeer accelerate straight up from the North Pole at $5~\mbox{m/s}^2$ . What is the force in Newtons the harness exerts on Santa's sleigh during sleigh liftoff?

Details and assumptions

The acceleration of gravity is $-9.8~\mbox{m/s}^2$ .

The answer is 17800.

5 solutions

Christopher Boo
Nov 13, 2013

The force reacted on the sleigh are

1) Gravity force, $W=mg$ direction: down

2) The pulling force by the reindeers, $T$ direction: up

Now, we analyse the problem and by Newton's second law of motion we can get

$\sum F=ma$

$T-W=ma$

$T=ma+mg$

$T=(1200)(5)+(1200)(9.8)$

$T=17760N$

**Note: The mass of the eight reindeer is not used because they are not involved in the object which force is reacted on it. The only object which force is reacted on is the sleigh.

Vincent Tandya
Nov 11, 2013

We know that $F=ma$ .

Since we know that $m=1200 \text{ kg}$ and $a=5+9.8=14.8\text{ m/s}^2$ , we can subtitue the values.

$F=1200\cdot 14.8 = 17800 \text{ Newtons}$

Noel Lo
Nov 11, 2013

Consider the 1200 kg mass. Resultant force = Tension in harness - Weight ma= T- mg T = m(a+g) = 1200(5+9.8) = 1200(14.8) = 17760 N

Rui-Xian Siew
Nov 17, 2013

F=ma. When the harness is pulled upwards, the net acceleration exerted on it is 5+9.8=14.8 and the force is F=ma=14.8x1200= $\boxed{17800N}$

Tanisk Annapurna
Nov 12, 2013

F=ma total mass=1200 kg as accl. is in opposite direction so (g+a) = 14.8 F = 1200*14.8

Go Rudolph Go!

The answer is 17800.

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