Stuck on a Conservation of Energy problem

In summary, a 1.9-kg block slides down a curved, frictionless ramp from a height of 1.5m to 0.25m above the ground. The block leaves the ramp with a horizontal velocity and lands distance D away. For both A) and B), the time is 4.0s at distance D. To find the distance D, we can use the equation for energy conservation (mgh + 1/2mv^2 = mgh + 1/2mv^2) and solve for v(2) by setting v(1) to 0. From there, we can use the given time and velocity to find the distance D. If the ramp has friction,
  • #1
ova5676
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Homework Statement


A 1.9-kg block slides down a curved, frictionless ramp. The top of the ramp is 1.5m above the ground; the bottom of the ramp is 0.25m above the ground. The block leaves the ramp moving horizontally, and lands distance D away.

A) What is distance D away?

B) Suppose the ramp is not frictionless. Find the distance D for the case in which friction on the ramp does 9.7 J of work on the block before it enters the horizontal (and still frictionless) section towards D.

For both A) and B) the time is 4.0s at distance D.


Homework Equations


Potential Energy (1) + Kinetic Energy (1) = Potential Energy (2) + Kinetic Energy (2)
mgh(1) + 1/2*m*v^2(1) = mgh(2) + 1/2*m*v^2(2)

(basically the first part is at the top of the ramp and the final is at the bottom of the ramp)

The Attempt at a Solution


Since the ramp is frictionless, the block is going at a constant speed. However, when I tried using the equation it didn't work out so there's probably another way.
 
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  • #2
You have posted the correct formula. However, the block is accelerated: it has no velocity at the top, but a positive velocity at the bottom. Obviously, m and g are given in the problem. Can you give me the appropriate values for h(1), v(1), h(2) and v(2) ?
 
  • #3
h(1) is 1.5m (reference point is the ground).

h(2) is 0.25m (reference point is the ground).

We don't know v(1) or v(2).
 
  • #4
ova5676 said:
We don't know v(1) or v(2).
I would presume that the block starts from rest at the top of the ramp. So v(1) = 0. Use energy conservation to solve for v(2).
 

FAQ: Stuck on a Conservation of Energy problem

1. What is the Conservation of Energy principle?

The Conservation of Energy principle is a fundamental law of physics that states that energy cannot be created or destroyed, but can only be converted from one form to another. This means that the total amount of energy in a closed system remains constant over time.

2. How do I know if a problem involves Conservation of Energy?

A problem involves Conservation of Energy if it involves the transfer or transformation of energy from one form to another. This can include situations such as a moving object, a falling object, or a system with different forms of energy.

3. How do I apply the Conservation of Energy principle to a problem?

To apply the principle of Conservation of Energy, you must first identify all the forms of energy present in the system and track their changes throughout the problem. Then, you can use the equation Einitial = Efinal to ensure that the total energy remains constant.

4. What are some common mistakes when solving Conservation of Energy problems?

One common mistake is forgetting to consider all forms of energy present in the system, such as kinetic, potential, and thermal energy. Another mistake is not properly accounting for energy losses due to factors like friction or air resistance.

5. How can I check my answer for a Conservation of Energy problem?

To check your answer, you can re-evaluate the problem using different equations or methods. You can also compare your final energy values to the initial energy values to ensure that they are equal. Additionally, checking the units of your final answer can help identify any errors in calculation.

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