# Determining the greater force?

• B
Q: Fred is on Earth, and Jane is on the Moon.

a) Each lifts a 2.0 kg rock. Who has to apply the larger force?
b) Each throws the rock horizontally with initial speed of 6.0 metres per second. Who applies the larger force?

For both questions, I wrote: Fred, because the gravity on Earth is greater than that of the Moon, and so there is a larger force acting upon the rock. But, seeing as it is my answer to BOTH question, I am feeling doubtful, because how can there be the same answer to two questions?

## Answers and Replies

cnh1995
Homework Helper
Gold Member
a) Each lifts a 2.0 kg rock. Who has to apply the larger force?
I believe you're right, it's Fred.
b) Each throws the rock horizontally with initial speed of 6.0 metres per second. Who applies the larger force?
If atmospheric resistance is to be taken into account, I believe it should be Fred. If not, I think both will apply equal force. The rock will take longer to land on moon.

nasu
Gold Member
The second question does not have a good answer, as it is asked.
Even without leaving our planet you can achieve the 6 m/s speed of the rock with any force. It just depends on how long it takes to accelerate the rock.
Of course, besides the horizontal force, you need to apply a vertical force equal to the weight of the rock, in every case.
So assuming that both use the same horizontal force, for the same amount of time, the total force will be larger on Earth.

Regarding your concern, there is no rule to rule out same answer to two different questions.

Q: Fred is on Earth, and Jane is on the Moon.

a) Each lifts a 2.0 kg rock. Who has to apply the larger force?
b) Each throws the rock horizontally with initial speed of 6.0 metres per second. Who applies the larger force?

For both questions, I wrote: Fred, because the gravity on Earth is greater than that of the Moon, and so there is a larger force acting upon the rock. But, seeing as it is my answer to BOTH question, I am feeling doubtful, because how can there be the same answer to two questions?
To throw a rock requires applying force over a distance, or work, on the rock. Work is the dot product of force and displacement. There is no extra force due to gravity horizontally therefore the dot product does not vary with gravity. Therefore, both use the same force (assuming it takes the same amount of time to throw).

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Lifting a rock in lower gravity requires less force. Accelerating a given mass in a direction perpendicular to any gravitational field requires the same force.

nasu
Gold Member
If you want to have horizontal velocity at the end of acceleration you need to exert a vertical force as well. Otherwise the rock falls during the acceleration period and the final velocity won't be horizontal. The question in the OP does not specify that is about the horizontal component of the force only.