- #1

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## Homework Equations

Total Energy = Kinetic Energy + Potential Energy

T.E = 1/2mv^2 + m(g)(h)

## The Attempt at a Solution

Distance Child travels

Sin 30 = 4/ x

x = 8m

T.E at top

= 1/2mv^2 + m(9.8)(h)

= 40m

Last edited:

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- Thread starter xRadio
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In summary, the distance a child travels is 8 meters when sin(30 degrees) is 4 divided by x. The conservation of energy states that the total energy of the system must be the sum of kinetic and potential energy. The child's potential energy is the sum of the kinetic energy and the distance they travel, while their kinetic energy is the product of their mass and the speed they are moving.

- #1

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Total Energy = Kinetic Energy + Potential Energy

T.E = 1/2mv^2 + m(g)(h)

Distance Child travels

Sin 30 = 4/ x

x = 8m

T.E at top

= 1/2mv^2 + m(9.8)(h)

= 40m

Last edited:

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- #2

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- #3

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TE at bottom=pe+ke where pe=0

however, there is energy lost in going from top to bottom in form of friction.

so TE at top=TE at bottom plus frictional energy. You are given a magnitude for friction and have computed the distance right, can you finish from here?

edit: this was more or less simultaneous post, I think its actually easier using energy eqn, but solveable from either approach.

- #4

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40m = 1/2mv^2 + 1/4m

v = 12.6 - m

is this correct?

And I don't know how to calculate the mass.

v = 12.6 - m

is this correct?

And I don't know how to calculate the mass.

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- #5

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mgh=1/2mv^2+Ff*distance where Ff=frictional force

we know from problem, that frictional force = 1/4mg

so mgh-1/4*(mg)*8m= 1/2mv^2

(8m from your calculations involving length of slide)

- #6

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40m-1/4*(m)*8m= 1/2mv^2

40m - 2m = 1/2mv^2

76m / m = v^2

v = 8.7 m/s

Question stated that friction is 1/4m not 1/4mg. Or is it suppose to be 1/4mg?

- #7

Homework Helper

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- #8

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This is what I got now:

40m-1/4*(m)*8m= 1/2mv^2

40m - 20m = 1/2mv^2

20m / m = v^2

v = 4.47 m/s

40m-1/4*(m)*8m= 1/2mv^2

40m - 20m = 1/2mv^2

20m / m = v^2

v = 4.47 m/s

- #9

Homework Helper

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Where did the 1/2 from the kinetic energy go? You dropped it in the second last line.

- #10

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This is what I got now:

40m-1/4*(m*g)*8m= 1/2mv^2

40m - 20m = 1/2mv^2

40m / m = v^2

v = 6.3 m/s

- #11

Homework Helper

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I agree with that answer.

- #12

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Do you think you can help me with my last problem?

https://www.physicsforums.com/showthread.php?t=164105

The law of conservation of energy states that energy cannot be created or destroyed, but can only be transformed from one form to another. This means that the total amount of energy in a closed system remains constant over time.

The conservation of energy applies to everyday life in various ways, such as when we turn on a light switch, the electrical energy is converted into light and heat energy. It also applies to activities like driving a car, where the chemical energy in gasoline is converted into kinetic energy to move the car.

Energy transformation occurs in many forms, such as when a battery-powered device converts chemical energy into electrical energy. Other examples include burning wood, which converts chemical energy into heat and light energy, and photosynthesis, which converts solar energy into chemical energy in plants.

The conservation of energy is directly related to the first law of thermodynamics, which states that energy cannot be created or destroyed. This law is a fundamental principle of physics and is the basis for the law of conservation of energy.

The conservation of energy has many real-world applications, including electricity generation, transportation, and environmental conservation. It is also used in industries such as manufacturing and construction to optimize energy usage and reduce waste.

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