# Homework Help: More 2D Vector Problems GAK!

1. May 11, 2005

### jen333

Hey,
i have two 2D vector problems here that i'm stuck on! help is appreciated!

1) A boy sits at the top of a slide. When the slide makes an angle of 35.0 degrees with the horizontal, the boy is just on the verge of slipping. If the boy starts to move down the slide, the slide angle can be reduced to 33.0 degrees and the boy is then able to descend the slope at 2.00m/s. Find µk and µs. (the answers, respectively, are 0.649 and 0.700)

I've drawn diagrams of the problem already, but what i'm stuck on is just how to calculate µs and µk. all of the formulas that i am aware of calculating these use mass. ie) µk= Ff/Fn. what sort of ways can i execute this problem without using mass????

2) A 45.4kg box is placed at the top of an incline (µs = 0.500, µk= 0.400) will the box move? If it does, what is its speed at the bottom of the incline? (the answer is 4.25m/s)

i'm not sure, but i'm thinking that there will have to be an acceleration greater than 9.81m/s^2 inorder to move. i have a diagram here in which a 45.4kg box is placed on an incline at 30.0 degrees to the horizontal and is 3.00m high. :yuck:

Last edited: May 11, 2005
2. May 11, 2005

### OlderDan

1) Gravity pulls the boy straight downward, You can break the weight vector into two components; one is parallel to the slde and the other is perpendiculat to the slide. The component of weight that is perpendicular to the slide must be equal and opposite the normal force. The component of weith that is parallel to the slide must be equal and opposite the friction. Every force in this problem will be proporional to the boy's mass. It divides out of the equations.

After you get #1, #2 will make more sense. In this case friction will not be able to offset the component of weight parallel to the incline. There will be a resulting acceleration of the mass, but it will be far less than g.