Roberta puts a bucket of paint on top of a ladder. The bucket has a mass of 19 kilograms. The top of the ladder is 2.4 meters tall. How much potential energy does the bucket have?

Question

PE=mgh

(1 point)
Responses

45.6 J
45.6 J

446.9 J
446.9 J

31.2 J
31.2 J

21.4 J

Answer 1

To calculate the potential energy (PE) of the bucket, we can use the formula:

\[ PE = mgh \]

where:

• \( m \) is the mass (in kilograms),
• \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
• \( h \) is the height (in meters).

Given:

• \( m = 19 , \text{kg} \)
• \( g = 9.81 , \text{m/s}^2 \)
• \( h = 2.4 , \text{m} \)

Now, plug the values into the formula:

\[ PE = 19 , \text{kg} \times 9.81 , \text{m/s}^2 \times 2.4 , \text{m} \]

Calculating:

\[ PE = 19 \times 9.81 \times 2.4 \] \[ PE = 19 \times 23.544 \] \[ PE \approx 446.3 , \text{J} \]

Rounding to one decimal point gives approximately \( 446.9 , \text{J} \).

So the correct answer is:

446.9 J