Compare the force of gravity holding a 10.0 kg rock on the moon. The gravitational field on the moon is 1.6 N/kg.
Understand the Problem
The question is asking to calculate the gravitational force acting on an object on the Moon, given the gravitational field strength of 1.6 N/kg. This involves using the formula for gravitational force (F = m*g) and comparing it to the gravitational force on Earth.
Answer
The gravitational force on the Moon for a 10.0 kg rock is \( 16.0 \, \text{N} \), compared to \( 98.0 \, \text{N} \) on Earth.
Answer for screen readers
The gravitational force acting on a 10.0 kg rock on the Moon is ( 16.0 , \text{N} ), while on Earth it is ( 98.0 , \text{N} ).
Steps to Solve
- Identify the formula for gravitational force
The gravitational force can be calculated using the formula:
$$ F = m \cdot g $$
where:
- ( F ) = gravitational force (in Newtons)
- ( m ) = mass of the object (in kg)
- ( g ) = gravitational field strength (in N/kg)
- Calculate the gravitational force on the Moon
Given:
- Mass of the rock, ( m = 10.0 , \text{kg} )
- Gravitational field strength on the Moon, ( g = 1.6 , \text{N/kg} )
Substituting these values into the formula gives:
$$ F_{\text{moon}} = 10.0 , \text{kg} \cdot 1.6 , \text{N/kg} $$
Calculate ( F_{\text{moon}} ):
$$ F_{\text{moon}} = 16.0 , \text{N} $$
- Calculate the gravitational force on Earth for comparison
The standard gravitational field strength on Earth is approximately ( g = 9.8 , \text{N/kg} ).
Using the same formula for Earth:
$$ F_{\text{earth}} = 10.0 , \text{kg} \cdot 9.8 , \text{N/kg} $$
Calculate ( F_{\text{earth}} ):
$$ F_{\text{earth}} = 98.0 , \text{N} $$
- Compare the forces
Now, compare the two forces:
- Force on the Moon: ( F_{\text{moon}} = 16.0 , \text{N} )
- Force on Earth: ( F_{\text{earth}} = 98.0 , \text{N} )
This shows that the gravitational force on the Moon is significantly less than on Earth.
The gravitational force acting on a 10.0 kg rock on the Moon is ( 16.0 , \text{N} ), while on Earth it is ( 98.0 , \text{N} ).
More Information
On the Moon, the gravitational pull is about 1/6th of that on Earth, which is why objects weigh much less on the Moon compared to Earth.
Tips
- Confusing the gravitational field strengths of the Earth and the Moon.
- Forgetting to multiply the mass by the appropriate gravitational field strength.
- Not recognizing the units of measurement (N/kg vs. kg).
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