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Q & A: gravity and acceleration

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Most recent answer: 02/21/2008
Q:
Hi. I’ve seen the equation for the acceleration of gravity written as 9.81 meters/sec^2 (near the Earth’s surface) or generally it would be x meters/sec^2. Does this mean (if we remove air resistance, etc) that an object "falling" in a gravitational field will constantly accelerate and thus constantly increase it’s speed? If so, is this only because the gravity becomes stronger as you fall towards the object (getting closer to it’s centre)? Theoretically speaking, if the Earth’s gravity was 9.81 meters/sec^2 equally from the surface all the way up to 10 kilometres into the atmosphere, and I jumped out of a plane at 10 kilometres high, would my speed constantly increase until I hit the surface, or would I reach a maximum speed becasue the gravity is theoretically 9.81 meters/sec^2 for the whole 10KMs?
- Brian
Australia
A:
Hi Brian,

You are right that gravity gets stronger when you are closer to a massive object (like the Earth). But that isn't the reason why a falling object continues to accelerate. If the strength of the gravitational field were constant over the entire 10 kilometers, you would still continue to speed up during the entire trip.

Speed is measured in units of meters/second. Acceleration is measured in meters/second^2. Acceleration quantifies the rate of change of velocity. Multiply acceleration by time (really it's an integral, but if the acceleration's constant you can just multiply) and you get the change in velocity. Each second you remain in airless free-fall you change you velocity by about 9.8 meters/second.

The reason parachutists reach a maximum speed is because of the drag force of the air rushing by. This drag force increases with the speed the parachutist falls at, and so there is a speed at which the force of drag is equal and opposite to the force of gravity. Take away the air and the parachutist will continue to accelerate.

If a parachutist starts at rest and falls 10 km in a uniform gravitational field (not quite, but it's not a bad approximation), he will be moving at 443 meters/second when he hits the ground. The whole trip would take about 45 seconds. Adding in the effect of the air will slow him down quite a lot.

Tom

(published on 10/22/2007)

Follow-Up #1: Falling boy

Q:
the Eiffel tower is 300m high, a boy at the top falls over the edge. how long has he got to live?
- germaine davis
England, Norfolk
A:
Not long.  You can work out the time yourself;  T(seconds) = sqrt(2*H/g) where H is the height  in meters and g is the acceleration due to gravity 9.8 m/s2.  This comes from inverting the relation between distance traveled under a constant acceleration.

LeeH

Air friction will presumably buy a tiny bit more time.  /Mike W.

(published on 02/21/2008)

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