Newton's second law: rudolph the red nosed reindeer is pulling a 25 kg sled across the snow in a field. the coefficient of kinetic friction is .12 the rope that is pulling the sled is coming off at a 29 degree angle above the horizontal. find the force in the rope when the acceleration is .12 m/s^2.

Explanation:

Data:

Mass

Coefficient of kinetic friction

Angle =

Acceleration =

Solution:

By Newton's first law we know that for the x-axis:

Where is the resulting force, and is the friction force.

And for the y-axis:

, where N is the normal force, and W is the weight of the sled.  

We know that the resulting force's acceleration is , and by using Newton's second law, we obtain:

.

Now, the horizontal component of the force in the rope will be given by

, since the resulting force is completely on the x-axis, and the friction opposes to the speed of the sled.

To obtain the friction force, we must know the normal force:

Clearing N in the y-axis equation:

So we can express the x-axis equation as follows:

Finally, solving for F we get