Answered

A sled is at rest at the top of a slope [tex][tex]$2 m$[/tex][/tex] high. The sled has a mass of [tex][tex]$45 kg$[/tex][/tex]. What is the sled's potential energy?
(Formula: [tex][tex]$PE = mgh$[/tex][/tex])

A. [tex][tex]$90 J$[/tex][/tex]
B. [tex][tex]$56.8 J$[/tex][/tex]
C. [tex][tex]$441 J$[/tex][/tex]
D. [tex][tex]$882 J$[/tex][/tex]



Answer :

To find the sled's potential energy, we can use the formula for gravitational potential energy:

[tex]\[ PE = mgh \][/tex]

Where:
- [tex]\( PE \)[/tex] is the potential energy
- [tex]\( m \)[/tex] is the mass of the sled
- [tex]\( g \)[/tex] is the acceleration due to gravity
- [tex]\( h \)[/tex] is the height

Given:
- Mass ([tex]\( m \)[/tex]) = 45 kg
- Acceleration due to gravity ([tex]\( g \)[/tex]) = 9.8 m/s²
- Height ([tex]\( h \)[/tex]) = 2 m

Now, we can plug in the given values into the formula:

[tex]\[ PE = 45 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 2 \, \text{m} \][/tex]

First, calculate the product of the mass and the acceleration due to gravity:

[tex]\[ 45 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 441 \, \text{N} \][/tex]

Then, multiply this result by the height:

[tex]\[ 441 \, \text{N} \times 2 \, \text{m} = 882 \, \text{J} \][/tex]

So, the sled's potential energy at the top of the slope is:

[tex]\[ 882 \, \text{J} \][/tex]

Therefore, the correct answer is:

[tex]\[ 882 \, \text{J} \][/tex]