A 2.0 kg toolbox sits on a shelf 1.5 m above the floor. Lifting it up there stored energy with it.
Last lesson, the stored amount was weight × height gained. This lesson turns that into the tidy, named form.
First find the toolbox's weight. In the forces topic you saw weight = mass × gravitational field strength, with g = 9.8 N/kg near Earth's surface.
The toolbox's weight: 2.0 × 9.8 = 19.6 N.
The lift stored weight × height gained: 19.6 × 1.5 = 29.4 J.
Now write the same calculation with symbols. The weight is m × g, so weight × height gained is m × g × h, written mgh.
This stored energy has a name: gravitational potential energy, GPE for short.
The height h is measured from a chosen reference level. For the toolbox, that level is the floor of the room.
Which relation gives an object's gravitational potential energy near Earth's surface?
A second case: a 3.0 kg book held 2.0 m above the floor of the room.
Its weight is 3.0 × 9.8 = 29.4 N. Its GPE, measured from that floor, is 29.4 × 2.0 = 58.8 J.
Take g = 9.8 N/kg in every GPE calculation in this topic.
A 5.0 kg box sits on a platform 2.0 m above a warehouse floor. Take g = 9.8 N/kg. Calculate the box's GPE, measured from the floor.
Write down the values:
m = 5.0 kg, g = 9.8 N/kg, h = 2.0 m, GPE = ?
Write down the equation:
GPE = mgh
Substitute in the values, and calculate:
GPE = (5.0 × 9.8) × 2.0 = 98
The box's GPE is 98 J.
A 2.5 kg stage monitor stands on a riser 2.0 m above the stage floor. Take g = 9.8 N/kg. Calculate the monitor's GPE, measured from the stage floor.
Write down the values:
m = 2.5 kg, g = 9.8 N/kg, h = 2.0 m, GPE = ?
Write down the equation:
GPE = mgh
Substitute in the values, and calculate:
GPE = (2.5 × 9.8) × 2.0 = 49
The monitor's GPE is 49 J.
A 3.5 kg lamp stands on a shelf 2.0 m above the floor. Take g = 9.8 N/kg. Enter the lamp's GPE, measured from the floor, in J.
A hiker's 12 kg pack is moved around camp. Which move raises the pack's GPE?
A 6.0 kg cooler is lifted onto a counter 1.5 m above the kitchen floor. Take g = 9.8 N/kg. Enter the cooler's GPE, measured from the floor, in J.
Xenia's 1.4 kg trophy stands on a shelf 1.8 m above the floor and 0.90 m below the ceiling. Her GPE calculation is measured from the floor. Which value is h?
A window washer hauls a 5.0 kg bucket from the sidewalk up to a platform 4.0 m above it, at a steady speed. Take g = 9.8 N/kg. Enter the GPE the bucket gains, measured from the sidewalk, in J.