Math / Algebra

QuestionQuestion 10 of 10 An object with a mass of 10 kg has a potential energy of 2000 J . Based on this Information, how high above the ground is the object? (10 points) A. 196000 m B. 20000 m

Studdy Solution

STEP 1

What is this asking? How high up is a 10 kg object if it has 2000 Joules of potential energy? Watch out! Don't forget to use the correct units and the correct value for acceleration due to gravity!

STEP 2

1. Define potential energy
2. Solve for height

STEP 3

Alright, so, potential energy, right?
It's all about the potential for an object to do work because of its position.
The higher up something is, the more potential energy it has!
The formula is $PE = m \cdot g \cdot h$ , where $PE$ is the potential energy, $m$ is the mass, $g$ is the acceleration due to gravity, and $h$ is the height.

STEP 4

We know the object's mass ( $m = 10$ kg) and its potential energy ( $PE = 2000$ J).
We also know the acceleration due to gravity on Earth is approximately $g = 9.8$ m/s².
We're trying to find $h$ , the height.

STEP 5

Let's plug the values into our formula: $2000 = 10 \cdot 9.8 \cdot h$ .
See how we just replaced the letters with the numbers we know?

STEP 6

Now, let's simplify! $10 \cdot 9.8 = 98$ , so our equation becomes $2000 = 98 \cdot h$ .

STEP 7

To get $h$ by itself, we need to divide both sides of the equation by 98.
Remember, what we do to one side, we must do to the other!
So, we have $\frac{2000}{98} = \frac{98 \cdot h}{98}$ .
The 98's on the right side divide to one, leaving us with $h = \frac{2000}{98}$ .

STEP 8

Now, we just need to calculate that division! $\frac{2000}{98} \approx 20.4$ .
So, $h \approx 20.4$ meters.

STEP 9

The object is approximately 20.4 meters above the ground.

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QuestionQuestion 10 of 10 An object with a mass of 10 kg has a potential energy of 2000 J . Based on this Information, how high above the ground is the object? (10 points) A. 196000 m B. 20000 m

Studdy Solution

STEP 1

What is this asking? How high up is a 10 kg object if it has 2000 Joules of potential energy? Watch out! Don't forget to use the correct units and the correct value for acceleration due to gravity!

STEP 2

1. Define potential energy
2. Solve for height

STEP 3

STEP 4

We know the object's mass ( $m = 10$ kg) and its potential energy ( $PE = 2000$ J).
We also know the acceleration due to gravity on Earth is approximately $g = 9.8$ m/s².
We're trying to find $h$ , the height.

STEP 5

Let's plug the values into our formula: $2000 = 10 \cdot 9.8 \cdot h$ .
See how we just replaced the letters with the numbers we know?

STEP 6

Now, let's simplify! $10 \cdot 9.8 = 98$ , so our equation becomes $2000 = 98 \cdot h$ .

STEP 7

To get $h$ by itself, we need to divide both sides of the equation by 98.
Remember, what we do to one side, we must do to the other!
So, we have $\frac{2000}{98} = \frac{98 \cdot h}{98}$ .
The 98's on the right side divide to one, leaving us with $h = \frac{2000}{98}$ .

STEP 8

Now, we just need to calculate that division! $\frac{2000}{98} \approx 20.4$ .
So, $h \approx 20.4$ meters.

STEP 9

The object is approximately 20.4 meters above the ground.

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QuestionQuestion 10 of 10 An object with a mass of 10 kg has a potential energy of 2000 J . Based on this Information, how high above the ground is the object? (10 points) A. 196000 m B. 20000 m

Studdy Solution

STEP 1

What is this asking? How high up is a 10 kg object if it has 2000 Joules of potential energy? Watch out! Don't forget to use the correct units and the correct value for acceleration due to gravity!

STEP 2

1. Define potential energy2. Solve for height

STEP 3

STEP 4

We know the object's **mass** (m=10m = 10m=10 kg) and its **potential energy** (PE=2000PE = 2000PE=2000 J).We also know the **acceleration due to gravity** on Earth is approximately g=9.8g = 9.8g=9.8 m/s².We're trying to find hhh, the **height**.

STEP 5

Let's plug the values into our formula: 2000=10⋅9.8⋅h2000 = 10 \cdot 9.8 \cdot h2000=10⋅9.8⋅h.See how we just replaced the letters with the numbers we know?

STEP 6

Now, let's simplify! 10⋅9.8=9810 \cdot 9.8 = 9810⋅9.8=98, so our equation becomes 2000=98⋅h2000 = 98 \cdot h2000=98⋅h.

STEP 7

STEP 8

Now, we just need to calculate that division! 200098≈20.4\frac{2000}{98} \approx 20.4982000​≈20.4.So, h≈20.4h \approx 20.4h≈20.4 meters.

STEP 9

The object is approximately **20.4 meters** above the ground.

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Define potential energy
2. Solve for height

We know the object's mass ( $m = 10$ kg) and its potential energy ( $PE = 2000$ J).
We also know the acceleration due to gravity on Earth is approximately $g = 9.8$ m/s².
We're trying to find $h$ , the height.

Let's plug the values into our formula: $2000 = 10 \cdot 9.8 \cdot h$ .
See how we just replaced the letters with the numbers we know?

Now, let's simplify! $10 \cdot 9.8 = 98$ , so our equation becomes $2000 = 98 \cdot h$ .

Now, we just need to calculate that division! $\frac{2000}{98} \approx 20.4$ .
So, $h \approx 20.4$ meters.

The object is approximately 20.4 meters above the ground.