If a 0.500-kilogram pair of running shoes weighs 11.55 newtons on Jupiter, what is the strength of gravity there?
The correct answer and explanation is:
To find the strength of gravity on Jupiter, we can use the formula that relates weight (force) to mass and gravity: F=m⋅gF = m \cdot g
Where:
- FF is the force or weight (11.55 N),
- mm is the mass (0.500 kg),
- gg is the gravitational acceleration on Jupiter (which we need to find).
Rearranging the formula to solve for gg: g=Fmg = \frac{F}{m}
Now, substitute the given values: g=11.55 N0.500 kg=23.1 m/s2g = \frac{11.55 \, \text{N}}{0.500 \, \text{kg}} = 23.1 \, \text{m/s}^2
So, the gravitational acceleration on Jupiter is 23.1 m/s².
Explanation:
Weight is the force exerted on an object due to gravity. On Earth, the acceleration due to gravity is approximately 9.8 m/s², which is why a 1 kg object weighs 9.8 N on Earth. On Jupiter, gravity is much stronger, so the same object would weigh more there. This formula shows that Jupiter’s gravity is approximately 2.36 times stronger than Earth’s gravity.
The calculation above uses the fact that weight is directly proportional to mass and gravitational strength. By using the known weight and mass of the shoes, we calculated the gravitational acceleration, which tells us how much stronger gravity is on Jupiter compared to Earth.