A 29.0 kg child slides down a long slide in a playground. She starts from rest at a height h1 of 17.00 m. When she is partway down the slide, at a height h2 of 8.00 m, she is moving at a speed of 6.90 m/s. Calculate the mechanical energy lost due to friction

Between h1 and h2 she has lost this amount of PE=mg(h1-h2), which is the PE change.

lossEnergy=PEchange-KE

To calculate the mechanical energy lost due to friction, first, we need to find the initial mechanical energy of the child at the top of the slide and the final mechanical energy of the child at the midway point.

The initial mechanical energy (E₁) of the child at the top of the slide is given by the formula:

E₁ = m * g * h₁

Where:
m = mass of the child = 29.0 kg
g = acceleration due to gravity = 9.8 m/s²
h₁ = height at the top of the slide = 17.00 m

E₁ = 29.0 kg * 9.8 m/s² * 17.00 m

E₁ = 4,549.4 J (Joules)

The final mechanical energy (E₂) of the child at the midway point is given by the formula:

E₂ = (1/2) * m * v₂² + m * g * h₂

Where:
v₂ = velocity at the midway point = 6.90 m/s
h₂ = height at the midway point = 8.00 m

E₂ = (1/2) * 29.0 kg * (6.90 m/s)² + 29.0 kg * 9.8 m/s² * 8.00 m

E₂ = 1,338.12 J + 2,264.8 J

E₂ = 3,602.92 J (Joules)

The mechanical energy lost due to friction (ΔE) is the difference between the initial and final mechanical energies:

ΔE = E₁ - E₂

ΔE = 4,549.4 J - 3,602.92 J

ΔE = 946.48 J (Joules)

Therefore, the mechanical energy lost due to friction is 946.48 Joules.

To calculate the mechanical energy lost due to friction, we first need to find the initial mechanical energy and the final mechanical energy.

The mechanical energy of an object at any given point is the sum of its kinetic energy and its potential energy. The equation for mechanical energy is given by:

E = KE + PE

Where E is the mechanical energy, KE is the kinetic energy, and PE is the potential energy.

At the top of the slide (height h1), the child has only potential energy since she is at rest. The equation for potential energy is given by:

PE = mgh

Where m is the mass of the child (29.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height above the reference point.

Using the given values, we can calculate the potential energy at the top of the slide:

PE1 = (29.0 kg) * (9.8 m/s^2) * (17.00 m)

Next, at a height h2, the child has both kinetic energy and potential energy. The equation for kinetic energy is given by:

KE = 1/2 * mv^2

Where v is the velocity.

Using the given values, we can calculate the kinetic energy at the height h2:

KE2 = 1/2 * (29.0 kg) * (6.90 m/s)^2

Now, the final mechanical energy (EF) is the sum of the kinetic energy (KE2) and the potential energy (PE2) at the height h2:

EF = KE2 + PE2

Finally, to calculate the mechanical energy lost due to friction (E_lost), we subtract the final mechanical energy (EF) from the initial mechanical energy (E1):

E_lost = E1 - EF

You can plug in the values and perform the calculations to find the mechanical energy lost due to friction.