The table shows data for the planet Uranus.
| Quantity | Value |
| :-------------------------------- | :---- |
| Escape velocity (km/s) | 21.3 |
| Gravitational acceleration ($m/s^2$) | 8.7 |
| Orbital velocity (km/s) | 6.8 |
| Length of day (hours) | 17.2 |
To the nearest whole number, how much would a 25.0 kg rock weigh on Uranus?
A. 170 N
B. 218 N
C. 430 N
D. 532 N
Answer (1)
Weight is calculated by multiplying mass and gravitational acceleration.
Given mass = 25.0 kg and gravitational acceleration = 8.7 m/s^2.
Calculate weight: 25.0 × 8.7 = 217.5 N.
Round to the nearest whole number: 218 N .
Explanation
Understanding the Problem We are given the gravitational acceleration on Uranus as 8.7 m/s^2 and the mass of the rock as 25.0 kg. We need to find the weight of the rock on Uranus. Weight is calculated as the product of mass and gravitational acceleration.
Applying the Formula To find the weight, we use the formula: Weight = mass × gravitational acceleration Substituting the given values: Weight = 25.0 kg × 8.7 m/s 2
Calculating the Weight Calculating the weight: Weight = 217.5 N
Rounding the Result Rounding the result to the nearest whole number, we get 218 N.
Final Answer Therefore, a 25.0 kg rock would weigh approximately 218 N on Uranus.
Examples
Understanding weight on different planets helps in space mission planning. For example, knowing the weight of equipment on Mars (with its lower gravitational acceleration) versus Earth is crucial for designing efficient transport and robotic systems. If a rover has a mass of 100 kg, its weight on Earth (approximately 9.8 m/s^2) would be 980 N, but on Mars (approximately 3.7 m/s^2) it would only be 370 N. This difference impacts the rover's mobility and energy consumption.
