Answer :
To solve for the gravitational potential energy added to a brick when it is lifted to a certain height, we use the formula for gravitational potential energy:
[tex]\[ U = mgh \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the brick,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height to which the brick is lifted.
Given:
- Mass of the brick, [tex]\( m = 2.3 \)[/tex] kg,
- Height, [tex]\( h = 1.9 \)[/tex] m,
- Acceleration due to gravity, [tex]\( g = 9.8 \)[/tex] m/s[tex]\(^2\)[/tex].
Now, substituting the given values into the formula:
[tex]\[ U = (2.3 \text{ kg}) \times (9.8 \text{ m/s}^2) \times (1.9 \text{ m}) \][/tex]
First, multiply the mass and gravity:
[tex]\[ 2.3 \times 9.8 = 22.54 \][/tex]
Next, multiply the result by the height:
[tex]\[ 22.54 \times 1.9 = 42.826 \][/tex]
Thus, the gravitational potential energy added to the brick when it is lifted to a height of 1.9 meters is:
[tex]\[ U \approx 42.8 \text{ J} \][/tex]
Therefore, the correct answer is:
B. [tex]\( 42.8 \text{ J} \)[/tex]
[tex]\[ U = mgh \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the brick,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height to which the brick is lifted.
Given:
- Mass of the brick, [tex]\( m = 2.3 \)[/tex] kg,
- Height, [tex]\( h = 1.9 \)[/tex] m,
- Acceleration due to gravity, [tex]\( g = 9.8 \)[/tex] m/s[tex]\(^2\)[/tex].
Now, substituting the given values into the formula:
[tex]\[ U = (2.3 \text{ kg}) \times (9.8 \text{ m/s}^2) \times (1.9 \text{ m}) \][/tex]
First, multiply the mass and gravity:
[tex]\[ 2.3 \times 9.8 = 22.54 \][/tex]
Next, multiply the result by the height:
[tex]\[ 22.54 \times 1.9 = 42.826 \][/tex]
Thus, the gravitational potential energy added to the brick when it is lifted to a height of 1.9 meters is:
[tex]\[ U \approx 42.8 \text{ J} \][/tex]
Therefore, the correct answer is:
B. [tex]\( 42.8 \text{ J} \)[/tex]
