Acceleration due to gravity on Jupiter is two and a half times that on earth. How much would a 250 kg satellite weigh (in N) on Jupiter? (acceleration due to gravity on earth = 10 m/s 2)
Calculating Satellite Weight on Jupiter
This question asks us to find the weight of a satellite on Jupiter, given its mass, the acceleration due to gravity on Earth, and the relationship between gravity on Jupiter and Earth.
Understanding Mass and Weight
- Mass: This is a measure of the amount of matter in an object. It is a fundamental property and remains constant regardless of where the object is (on Earth, Jupiter, or in space). The satellite's mass is given as 250 kg.
- Weight: This is the force of gravity acting on an object's mass. It depends on the mass of the object and the acceleration due to gravity at its location. Weight is a force and is measured in Newtons (N). The formula for weight is:
\[\text{Weight} (W) = \text{Mass} (m) \times \text{Acceleration due to gravity} (g)\]
Given Information
- Mass of the satellite (\(m\)) = 250 kg
- Acceleration due to gravity on Earth (\(g_{earth}\)) = 10 m/s²
- Acceleration due to gravity on Jupiter (\(g_{jupiter}\)) is two and a half times that on Earth, meaning \(g_{jupiter} = 2.5 \times g_{earth}\).
Step-by-Step Calculation
Step 1: Find the acceleration due to gravity on Jupiter.
We know that \(g_{jupiter} = 2.5 \times g_{earth}\). Substitute the given value for \(g_{earth}\).
\[g_{jupiter} = 2.5 \times 10 \, m/s²\]
\[g_{jupiter} = 25 \, m/s²\]
So, the acceleration due to gravity on Jupiter is 25 m/s².
Step 2: Calculate the weight of the satellite on Jupiter.
Use the formula for weight: \(W_{jupiter} = m \times g_{jupiter}\). Substitute the mass of the satellite and the calculated gravity on Jupiter.
\[W_{jupiter} = 250 \, kg \times 25 \, m/s²\]
\[W_{jupiter} = 6250 \, N\]
The weight of the 250 kg satellite on Jupiter would be 6,250 Newtons.
Comparing with Options
Let's compare our calculated weight with the given options:
| Option | Weight (N) |
|---|---|
| 1 | 10 |
| 2 | 625 |
| 3 | 6,250 |
| 4 | 100 |
Our calculated value, 6,250 N, matches Option 3.
Revision Table: Satellite Weight on Jupiter Calculation
| Concept | Formula/Value | Notes |
|---|---|---|
| Mass (\(m\)) | 250 kg | Constant value |
| Gravity on Earth (\(g_{earth}\)) | 10 m/s² | Given value |
| Gravity on Jupiter (\(g_{jupiter}\)) | \(2.5 \times g_{earth}\) | Given relationship |
| Calculated \(g_{jupiter}\) | \(2.5 \times 10 = 25\) m/s² | Step 1 result |
| Weight on Jupiter (\(W_{jupiter}\)) | \(m \times g_{jupiter}\) | Formula for weight |
| Calculated \(W_{jupiter}\) | \(250 \times 25 = 6250\) N | Step 2 result |
Additional Information on Gravity and Weight
- Acceleration due to gravity varies from planet to planet because it depends on the planet's mass and radius. Larger, denser planets generally have stronger gravity.
- Weight is a force vector, pointing towards the center of the gravitational source. Mass is a scalar quantity.
- On the Moon, where gravity is much weaker than on Earth (about 1/6th), the same 250 kg satellite would weigh significantly less than on Earth or Jupiter.
- While gravity is often approximated as 9.8 m/s² on Earth, using 10 m/s² simplifies calculations in many problems like this one and is explicitly stated in the question.
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