Of all the planets in our solar system, Jupiter has the greatest gravitational strength.
a. If a 0.5-kilogram pair of running shoes would weigh 11.55 newtons on Jupiter, what is the strength of gravity there?
b. If the same pair of shoes weighs 0.3 newtons on Pluto (a dwarf planet), what is the strength of gravity there?
c. What does the pair of shoes weigh on Earth?
The correct answer and explanation is:
a. Strength of Gravity on Jupiter
To calculate the strength of gravity on Jupiter, we can use the formula for weight: Weight=Mass×Gravity\text{Weight} = \text{Mass} \times \text{Gravity}
Where:
- Weight = 11.55 N (newtons)
- Mass = 0.5 kg (kilograms)
- Gravity = ? (unknown)
Rearranging the formula to solve for gravity: Gravity=WeightMass=11.55 N0.5 kg=23.1 m/s2\text{Gravity} = \frac{\text{Weight}}{\text{Mass}} = \frac{11.55 \, \text{N}}{0.5 \, \text{kg}} = 23.1 \, \text{m/s}^2
So, the strength of gravity on Jupiter is 23.1 m/s².
b. Strength of Gravity on Pluto
Next, we calculate the strength of gravity on Pluto using the same formula: Weight=Mass×Gravity\text{Weight} = \text{Mass} \times \text{Gravity}
Where:
- Weight = 0.3 N
- Mass = 0.5 kg
- Gravity = ? (unknown)
Rearranging the formula to solve for gravity: Gravity=WeightMass=0.3 N0.5 kg=0.6 m/s2\text{Gravity} = \frac{\text{Weight}}{\text{Mass}} = \frac{0.3 \, \text{N}}{0.5 \, \text{kg}} = 0.6 \, \text{m/s}^2
So, the strength of gravity on Pluto is 0.6 m/s².
c. Weight of the Pair of Shoes on Earth
On Earth, the strength of gravity is approximately 9.8 m/s². To calculate the weight of the same pair of shoes, we use the formula: Weight=Mass×Gravity\text{Weight} = \text{Mass} \times \text{Gravity}
Where:
- Mass = 0.5 kg
- Gravity = 9.8 m/s²
Weight=0.5 kg×9.8 m/s2=4.9 N\text{Weight} = 0.5 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 4.9 \, \text{N}
So, the pair of shoes would weigh 4.9 newtons on Earth.
Explanation
In this problem, the concept of weight is directly related to the force of gravity acting on an object. Weight is determined by multiplying the mass of an object by the gravitational acceleration of the planet or celestial body in question. For different planets, gravity varies, affecting the weight of the same object. For example, Jupiter’s gravity is much stronger than Earth’s or Pluto’s, which is why the shoes weigh more there. Conversely, on Pluto, where gravity is much weaker, the shoes weigh less.
On Earth, the gravitational pull is about 9.8 m/s², which is why the shoes weigh 4.9 N. Each planet has its own gravitational pull, and it impacts how much objects weigh on their surface.