2.2b – Calculating energy in the gravitational store

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The energy in the gravitational store can be calculated using the equation

cap e times n times e times r times g times y sub g times r times a times v times i times t times a times t times i times o times n times a times l s times t times o times r times e equals m times a times s times s prefix multiplication of g times r times a times v times i times t times a times t times i times o times n times a times l f times i times e times l times d s times t times r times e times n times g times t times h prefix multiplication of h times e times i times g times h times t

cap e sub g equals m times g times h

The SI unit of energy is the joule (abbreviated as cap j ). The SI units for the other variables are mass in k times g , gravitational field strength in cap n solidus k times g , and height in m .

Example gravitational store question

50 kg person going up 10 m in a liftA patient in a wheelchair with a mass of 50 k times g goes up in a lift by 10 m . What is the increase in the gravitational store of the patient/wheelchair?

equation sequence part 1 cap e sub g equals part 2 m times g times h equals part 3 50 prefix multiplication of 9.8 multiplication 10 equals four 900 cap j equals 4.9 k times cap j

This is using a gravitational field strength on Earth of 9.8 cap n solidus k times g .

Now, if you were paying careful attention, you will have noticed that this is exactly the same amount of work done by the lift on lifting the person up in the previous question (link). This is not a coincidence – in fact, these two examples are intrinsically linked.

The equation for a gravitational store can be worked out by calculating the amount of work done in lifting an object up.

w times o times r times k d times o times n times e equals f times o times r times c times e prefix multiplication of d times i times s times t times a times n times c times e

The distance moved against gravity is the height gained. The force due to gravity is the weight, which is given by the equation:

w times e times i times g times h times t equals m times a times s times s prefix multiplication of g times r times a times v times i times t times a times t times i times o times n times a times l f times i times e times l times d s times t times r times e times n times g times t times h

So, we have:

w times o times r times k d times o times n times e a times g times a times i times n times s times t g times r times a times v times i times t times y equals w times e times i times g times h times t multiplication h times e times i times g times h times t

w times o times r times k d times o times n times e a times g times a times i times n times s times t g times r times a times v times i times t times y equals m times a times s times s multiplication g times r times a times v times i times t times a times t times i times o times n times a times l f times i times e times l times d s times t times r times e times n times g times t times h multiplication h times e times i times g times h times t

cap e times n times e times r times g times y sub g times r times a times v times i times t times a times t times i times o times n times a times l s times t times o times r times e equals m times a times s times s prefix multiplication of g times r times a times v times i times t times a times t times i times o times n times a times l f times i times e times l times d s times t times r times e times n times g times t times h prefix multiplication of h times e times i times g times h times t  

If an object is dropping, the work is done by the gravitational field on the object moving. 

If an object is being lifted up, then the work is being done against the gravitational field by whatever is lifting the object.

Extra info – changing gravitational field strengths

An example that is sometimes asked is how the gravitational store of energy changes on different planets. Lifting a large mass on the Moon is significantly easier than on Earth (once you’ve overcome the problems in getting there and the lack of oxygen and pressure).
Actually, even on Earth the gravitational field strength can change slightly as you increase in altitude, but the changes are so small that it is generally ignored. In fact, if you climb to the top of Everest, the gravitational field strength is still 99.6% of that at sea level.

2.2a – Calculating work done

2.2c – Calculating energy in the kinetic store

Last modified: Monday, 20 December 2021, 9:51 PM