Max height at the top of the ramp of object launched by spring

[andrewwg94]

Homework Statement

Ok so I had this problem on my quiz today and I am really anxious to see if i got it right.
It went something like this:

You have a frictionless horizontal platform and a ramp with kinetic friction of 0.3. The ramp is 20 degree of the ground. A 2 kg block/object is launched by a spring with k=1000 N/m at the beginning of the horizontal ramp. The spring is stretched back 20 cm. So the idea is that it is launched on the horizontal platform before eventually going up the ramp. use 9.8 for g.

Homework Equations

I used KE_i + PE_i - W_friction = KE_f+PE_f

The Attempt at a Solution

I basically found the KE due to the spring to be 20N. Then using that i calculated work lost due to friction. P. Energy at top of ramp = mgh. so i solved for h.

I got h=.7385

Everything made sense when i did it. I don't know if that's right though.

 

[cepheid]

Welcome to PF,

I basically found the KE due to the spring to be 20N. Then using that i calculated work lost due to friction. P. Energy at top of ramp = mgh. so i solved for h.

Did you mean 20 J (joules)? Energy is measured in joules, not Newtons. If so, this is correct. Your equation, which expresses the basic physical concept behind this problem (namely the conservation of energy) is also correct. Energy is conserved, hence:

KE_i + PE_i = KE_f + PE_f + W_fric

Initially, the object is not moving, hence KE_i = 0. All of the energy is in the form of elastic potential energy (energy stored in the spring). So PE_i = (1/2)kx² = 20 J.

At the very end, when the object has traveled as high as it is going to go, it is also not moving. Hence, KE_f = 0. All of these 20 joules have been converted into some combination of gravitational potential energy and heat (the latter being equal to the work done by friction).

20 J = mgh + W_fric

W_fric = F_fric * d

where F_fric is the frictional force, and d is the distance traveled along the ramp by the object. The distance d is related to h by simple trigonometry, which means that you can express everything in terms of one variable: h.

For the frictional force, F_fric = μF_N, where F_N is the normal force acting on the object. The normal force always acts perpendicular (i.e. normal) to the two surfaces that are in contact. So, in this case, the normal force is perpendicular to the ramp surface, which means that you need to use the geometry (specifically the inclination angle of the ramp) to figure out what it is. You can figure out what it is by noting that all forces perpendicular to the ramp have to balance each other out, so the normal force is just equal (in magnitude) to the component of the weight that acts perpendicular to the ramp.

So, it looks like you may have been doing well in the beginning, but then did not compute W_fric properly, at least based on what you posted above.