Finding final velocity for Conservation of Energy Problem

In summary, the formula for finding final velocity in a conservation of energy problem is <em>Vf = √(2gh + Vi^2)</em>, and the initial velocity can be determined using <em>Vi = √(Vf^2 - 2gh)</em>. The conservation of energy principle can be applied to any situation, but some common mistakes to avoid include not considering all forms of energy, using incorrect units, and not accounting for external forces. The final velocity can be negative if the object changes direction, but the magnitude is still calculated using the same formula.
  • #1
senpim
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0

Homework Statement


Problem statement and diagram in the photo

Homework Equations


K = 1/2 mv^2
U = mgh

The Attempt at a Solution


E_0 = E1
K_0 + U_0 = K_1 + U_1

using relevant equations and solving for v1 I get:
v_1 = sqrt((v_0)^2 + 2gh_1)

Then E_1 = E_2

solving for the final velocity and the top of the 2nd hill v_2:

v_2 = 1.4 m/s

There is no answer in the back of the book for this problem, just checking to see if my answer is correct, Thanks!
 

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  • #2
Yes.
 

What is the formula for finding final velocity in a conservation of energy problem?

The formula for finding final velocity in a conservation of energy problem is Vf = √(2gh + Vi^2), where Vf is the final velocity, g is the acceleration due to gravity, h is the change in height, and Vi is the initial velocity.

How do you determine the initial velocity in a conservation of energy problem?

To determine the initial velocity in a conservation of energy problem, you can use the formula Vi = √(Vf^2 - 2gh), where Vi is the initial velocity, Vf is the final velocity, g is the acceleration due to gravity, and h is the change in height.

Can you use the conservation of energy principle to find the final velocity in any situation?

Yes, the conservation of energy principle can be applied to any situation as long as there are no external forces acting on the system and all forms of energy are taken into account.

What are some common mistakes to avoid when finding the final velocity in a conservation of energy problem?

Some common mistakes to avoid when finding the final velocity in a conservation of energy problem include not considering all forms of energy (such as kinetic and potential energy), using the wrong units for measurements, and not accounting for external forces such as friction.

Can the final velocity be negative in a conservation of energy problem?

Yes, the final velocity can be negative in a conservation of energy problem if the object is moving in the opposite direction of the initial velocity. This indicates a change in direction, but the magnitude of the final velocity is still calculated using the same formula.

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