Acceleration (with and without friction)

[tascja]

Homework Statement

Consider the skier on the slope. She and her equipment have a mass of 60kg. She is on an incline that makes a 25deg incline [she is sliding down the hill].
a. what is her acceleration if friction is negligible?
b. what is her acceleration if friction is known to be 45N?

Homework Equations

Fnet = ma

The Attempt at a Solution

a.
Fnet = ma
588sin25 = 60a
a = 1.30 m/s^2

b.
Fnet = ma
588sin25 - 45 = 60a
a = 2.05 m/s^2

im not sure what I am doing wrong. but the answer book says i should be getting a) 4.41m/s^2 and for b)3.4 m/s^2. If someone could please explain where I am going wrong that would be greatly appreciated :)

 

[jqnsmart]

You seem to be setting up the problem correctly, but the calculation is off. Try instead to find the answer with acceleration isolated (a=F/m). That might make calculating things simpler.

 

[nlightner]

Your equations and calculations are correct, but you have made a mistake in the values you are using for the forces. The force due to gravity (weight) is not 588N, it is 588cos25N. So your equations should be:

a.
Fnet = ma
588cos25 = 60a
a = 4.41 m/s^2

b.
Fnet = ma
588cos25 - 45 = 60a
a = 3.4 m/s^2

Remember, when solving problems involving forces on an incline, you need to use the component of the force that is parallel to the incline, which is given by the cosine of the angle. Hope this helps!