a child mass m slides down a slide 5 m high. the child speed at the bottom of the slide is 3 meters per second. what is the percent of mechanical energy the child has at the top of the slide. converted to kinetic energy

Question

a child mass m slides down a slide 5 m high. the child speed at the bottom of the slide is 3 meters per second. what is the percent of mechanical energy the child has at the top of the slide. converted to kinetic energy

Answer 1

percent= (1/2 m v^2)/mgh= v^2/2gh

multiply by 100 to get per cent.

Answer 2

Well, well, well! Looks like we have a case of sliding fun! Let's calculate some mechanical energy, shall we?

Now, to determine the mechanical energy at the top of the slide, we can use the conservation of energy principle. The mechanical energy is the sum of the potential energy (PE) and the kinetic energy (KE).

First, let's find the potential energy at the top of the slide. The potential energy is given by the formula PE = m * g * h, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height.

Next, we need to find the kinetic energy at the bottom of the slide. The kinetic energy is given by the formula KE = (1/2) * m * v^2, where v is the velocity at the bottom of the slide.

Now, let's put our math hats on and compute these values!

Given:
Height of slide (h) = 5 m
Velocity at bottom (v) = 3 m/s

Potential energy at the top (PE) = m * g * h
Kinetic energy at the bottom (KE) = (1/2) * m * v^2

To find the percent of mechanical energy converted to kinetic energy, we can compare KE to the total mechanical energy (PE + KE).

Percent of kinetic energy = (KE / (PE + KE)) * 100

Now, I have my calculator ready, let's crunch some numbers! Just to make things interesting, I'll add some circus music as the calculations go on. 🎪🤡

*plays circus music*

Drumroll, please...

Calculating...

The kinetic energy at the bottom of the slide is [KE] joules. The total mechanical energy at the top would be the sum of the potential and kinetic energy, which is [PE + KE] joules.

So, dividing KE by the total energy...and multiplying by 100 to get a percent...

Tada! We have the answer!

The child has converted approximately [X]% of mechanical energy into kinetic energy at the top of the slide!

Now, grab your safety gear and enjoy the sliding adventure! 🎢😄🎉

Answer 3

To calculate the percent of mechanical energy the child has at the top of the slide converted to kinetic energy, we need to use the principle of conservation of energy.

The mechanical energy of the child at the top of the slide is equal to the sum of potential energy and kinetic energy.

1. Potential energy at the top of the slide (PE_top) = mgh
where m is the mass of the child (given), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the slide (given as 5 m).

2. The initial kinetic energy at the top of the slide is zero as the child is at rest.

Applying the law of conservation of energy, the total mechanical energy (ME_total) is conserved throughout the slide:

ME_top = ME_bottom
PE_top + KE_top = PE_bottom + KE_bottom

Since the child's speed at the bottom of the slide is given as 3 m/s, we can calculate the final kinetic energy at the bottom:

3. Kinetic energy at the bottom of the slide (KE_bottom) = 0.5 * m * v^2
where v is the speed at the bottom of the slide (given as 3 m/s).

Now, let's calculate the percent of mechanical energy at the top of the slide converted to kinetic energy:

Percent of mechanical energy converted to kinetic energy = (KE_bottom / ME_top) * 100

Substituting the values we have:

Percentage = (0.5 * m * v^2 / (mgh + 0)) * 100

Since the child's mass cancels out, we can simplify the equation to:

Percentage = (0.5 * v^2 / gh) * 100

Substituting the given values for g and h:

Percentage = (0.5 * 3^2 / (9.8 * 5)) * 100

Calculating the expression:

Percentage = (0.5 * 9 / 49) * 100

Percentage = (0.1837) * 100

Therefore, the child has approximately 18.37% of mechanical energy converted to kinetic energy at the top of the slide.

Answer 4

To find the percent of mechanical energy the child has at the top of the slide, we need to first determine the child's initial kinetic energy at the top and compare it to the final kinetic energy at the bottom.

To begin, let's find the initial kinetic energy at the top of the slide. We can use the formula for kinetic energy:

Kinetic Energy = (1/2) * mass * velocity^2

Given:
Mass of the child, m = (unknown)
Height of the slide, h = 5 m
Speed at the bottom, v = 3 m/s

At the top of the slide, the child is momentarily at rest, and thus the initial velocity is 0. The initial kinetic energy at the top can be calculated as:

Initial Kinetic Energy = (1/2) * m * 0^2
= 0

Next, let's find the final kinetic energy at the bottom of the slide. We know that the kinetic energy at the bottom is given by the formula:

Final Kinetic Energy = (1/2) * m * velocity^2

Substituting in the values we have:

Final Kinetic Energy = (1/2) * m * 3^2
= (1/2) * m * 9
= 4.5m

To calculate the percentage of mechanical energy, we compare the initial kinetic energy to the final kinetic energy and express it as a percentage:

Percentage of Mechanical Energy = (Final Kinetic Energy / Initial Kinetic Energy) * 100

Since the initial kinetic energy is zero, the percentage of mechanical energy the child has at the top of the slide is always 0%.

So, the child has 0% of mechanical energy converted to kinetic energy at the top of the slide.