a person is sled-riding down a hill that is 15.0 ft high. starting at the top with a speed of 10.0 ft/s, the sled reaches the bottom with a speed of 25.0 ft/s. (A) determine whether mechanical energy has been conserved. (B) why might mechanical energy not be conserved?

To determine whether mechanical energy has been conserved, we need to compare the initial mechanical energy of the sled at the top of the hill with its final mechanical energy at the bottom.

(A) To calculate the initial mechanical energy (Ei), we use the formula:

Ei = Kinetic Energy (Ki) + Potential Energy (Pi)

At the top of the hill, the sled has only potential energy since it is not moving horizontally. The potential energy (Pi) is given by the formula:

Pi = m * g * h

Where:
m = mass of the sled (which we'll assume is constant)
g = acceleration due to gravity (approximately 32 ft/s^2)
h = height of the hill (15.0 ft)

Now, let's calculate the potential energy at the top:

Pi = m * g * h

Next, we calculate the final mechanical energy (Ef) at the bottom of the hill. At this point, the sled has both kinetic energy (Kf) and potential energy (Pf). The kinetic energy is given by the formula:

Kf = (1/2) * m * v^2

Where:
v = velocity of the sled (25.0 ft/s)

And the potential energy (Pf) is given by:

Pf = m * g * 0

Since the sled is at the bottom of the hill, the height (h) is zero. Therefore, Pf becomes zero.

Now, let's calculate the final mechanical energy:

Ef = Kf + Pf
Ef = (1/2) * m * v^2 + 0

Compare Ei and Ef to determine if mechanical energy is conserved:

If Ei = Ef, then mechanical energy is conserved.
If Ei ≠ Ef, then mechanical energy is not conserved.

(B) Mechanical energy may not be conserved due to various factors such as:
1. Friction: If there is friction between the sled and the hill, some mechanical energy is transformed into heat due to the work done against friction.
2. Air resistance: As the sled moves through the air, there might be air resistance, causing a loss of mechanical energy in the form of heat and sound.
3. Non-ideal conditions: In real-life scenarios, energy losses can occur due to factors like vibrations, deformations, or losses to the surrounding environment.

Remember, to make an accurate determination, we would need to know more details about the system, including any factors that could affect the conservation of mechanical energy.