What does KE equal in this impossible physics problem?

[riseofphoenix]

c, d, and e I don't know how to solve

For d I tried doing

v_f² = v_i² +2ad
V_f = √(2*9.8*2.3) = 6.71 m/s

Assuming the inclined plane is frictionless
Since m2 is roped to m1, it's velocity up the ramp will be 6.71m/s too

The total increase in KE is then 0.5[8+6]*6.71^2 = 315.16 J

^

"INCORRECT"

Right now I need a genius to tell me how to get the answer ASAP -.-

Since (d) is wrong, so is e. -.-

-----------------------------------

EDIT:

(c)

m1 falls 2.3m and therefore has -6*9.8*2.3 = -135.24 J difference.

m2's PE increases 8*9.8*sin 30°*2.3 = +90.16 J difference.

The total change then is 90.16 - 135.24 = -45.08 J

Ok so how does this relate to part d and e though? How would I solve for those two last ones?

(d)

KE = -PE
KE = -mv?

(e)

 

[gneill]

You pinned down the change in potential energy in your EDIT, so that's good.

Since energy is conserved, the change in PE must be balanced by an equivalent change in KE (equal in magnitude, opposite in sign).

What's the formula for KE of a moving mass? How much mass is moving in the problem?

 

[riseofphoenix]

You pinned down the change in potential energy in your EDIT, so that's good.

Since energy is conserved, the change in PE must be balanced by an equivalent change in KE (equal in magnitude, opposite in sign).

What's the formula for KE of a moving mass? How much mass is moving in the problem?

KE = 1/2mv²

And m₁ = 6 kg is moving..

What next?

 

[gneill]

KE = 1/2mv²

And m₁ = 6 kg is moving..

What next?

So you're saying that m₂ is not moving? Isn't it connected to m₁ via a rope? Don't they move at the same time? Didn't the gravitational potential of both change?

 

[riseofphoenix]

So you're saying that m2 is not moving? Isn't it connected to m1 via a rope? Don't they move at the same time? Didn't the gravitational potential of both change?

Oh yeah m1 and m2 are both moving.
And yes (?) the gravitational potential changed (?)

I need to put the conceptual stuff into a formula tho and find the total KE of the system though... :(

 

[gneill]

How can I solve for KE?

You already did that when you found the change in PE. Conservation of energy: the sum PE + KE is a constant. If PE goes down, KE goes up by the same amount.

 

[riseofphoenix]

You already did that when you found the change in PE. Conservation of energy: the sum PE + KE is a constant. If PE goes down, KE goes up by the same amount.

So KE = mv?

 

[gneill]

So KE = mv?

Nooooo! mv is momentum.

You've already found the system's change in PE. The change in KE must be equal in magnitude (but opposite in sign).

 

[riseofphoenix]

Nooooo! mv is momentum.

You've already found the system's change in PE. The change in KE must be equal in magnitude (but opposite in sign).

So the answer is:

ΔKE = -ΔPE
ΔKE = -(-45.08)
ΔKE = 45.08

??

 

[gneill]

Oh yeah m1 and m2 are both moving.

So what is the total mass that's moving?

And yes (?) the gravitational potential changed (?)

Right, the gravitational potential of BOTH masses changed (yielding a net change in total gravitational potential energy). But the important thing is that BOTH masses are moving.

I need to put the conceptual stuff into a formula tho and find the total KE of the system though... :(

PE + KE = constant.

So ΔKE = -ΔPE

 

[gneill]

So the answer is:

ΔKE = -ΔPE
ΔKE = -(-45.08)
ΔKE = 45.08

??

Yes. Surely the underlying theme of the chapter you're currently studying must be energy conservation for gravitational PE and KE?

 

[riseofphoenix]

Yes. Surely the underlying theme of the chapter you're currently studying must be energy conservation for gravitational PE and KE?

Ohh ok...
And yeah it is!

So what about the last one, part (e) for final velocity of the system?

ΔKE = -ΔPE
ΔKE = -(45.08)
ΔKE = 45.08
0.5mv² = 45.08
0.5(m₁ + m₂)v² = 45.08
0.5(6+8)v² = 45.08
7v² = 45.08
v² = 6.44
v = 2.53 m/s ??

 

[gneill]

Yes, that looks good.

 

[riseofphoenix]

Yes, that looks good.

Thanks!