Going down a slide CONSERVATION OF ENERGY

[mizzy]

Homework Statement

Suppose a slide is 35.0 meters high, but is a straight slope, inclined at 45 degrees with respect to the horizontal.

a) find the speed of a 60.0kg thrill seeker at the bottom of the slide, assuming no friction.
b) if the thrill seeker has a speed of 20.0m/s at the bottom, find the change in mechanical energy due to friction
c) find the magnitude of the force of friction

Homework Equations

KEi + PEi = KEf + PEf

The Attempt at a Solution

a) since there is no friction, mechanical energy is conserved. So therefore using the above equation: KEi + PEi = KEf + PEf. However, i have difficulty when the question adds an angle. When do I know when to break into x and y components??

In this case, KEi = 0, PEi = mgy1, KEf = 1/2mv^2, PEf = 0

Therefore, PEi = KEf
mgy1 = 1/2mv2^2
square root of 2gy1 = v2^2 (where y1 = 35m)

is that right?

 

[naele]

Your notation is a little confusing, but from your set up you want to solve for v in the following equation

$mgy_1=\frac{1}{2}mv_2^2$

 

[minger]

However, i have difficulty when the question adds an angle. When do I know when to break into x and y components?

That's a great thing about the energy method of solving problems like this. Energy is energy. It doesn't matter how you get from State 1 to State 2. You can largely ignore what happens in between.

Now, in "real-life", there will always be friction. The friction is defined as the normal component of the weight, multiplied by the friction coefficient. That means that the shallower the angle, the greater the friction force, and the slower resulting speed. However, neglecting friction, you can ignore that fact.

 

[mizzy]

So when do you consider the angles? Only when there is friction?

 

[rwisz]

b) Since the speed at the bottom is given, we can use the equation KE = 1/2mv^2 to find the kinetic energy. Then, we can subtract this value from the initial potential energy (mgy1) to find the change in mechanical energy due to friction.

c) To find the magnitude of the force of friction, we can use the equation Ff = μmg, where μ is the coefficient of friction and g is the acceleration due to gravity. The coefficient of friction can be determined experimentally or given in the problem.