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How to Pull Something Heavy Presentation

How to Pull
Something Heavy
fork Lift
tow truck
tractor
strong man
On April 4, 1974, John Massis of
Belgium managed to move two train
passenger cars belonging to New
York’s Long Island Railroad.
He did so by clamping his teeth
down on a bit that was attached to
the cars with a rope and then
leaning backward while pressing his
feet against the railway ties.
The cars together weighed ~80
tons.
Did Massis have to pull with superhuman force
to accelerate them?
Do now:
The car is pulling the green block to the right.
Assume that the system is in equilibrium (that is
that the block is so heavy that the car cannot
move it from its stationary position).
Draw a diagram showing and labeling all the forces
acting on the car and a block!
Direction of
car’s pull
Free Body Diagram
normal force
normal force
force
generated by
motor
tension in the string
force of static
friction
weight of the block
force of kinetic
friction
weight of the car
y
Ncar
Nblock
x
T
T
Fmotor
FblockFriction
FwheelFriction
Wblock
Wcar
In y direction:
π‘€π‘π‘™π‘œπ‘π‘˜ β‹… π‘Žπ‘π‘™π‘œπ‘π‘˜ =
𝐸π‘₯π‘‘π‘’π‘Ÿπ‘›π‘Žπ‘™ πΉπ‘œπ‘Ÿπ‘π‘’π‘  = π‘π‘π‘™π‘œπ‘π‘˜ βˆ’ π‘Šπ‘π‘™π‘œπ‘π‘˜
π‘π‘π‘™π‘œπ‘π‘˜ = π‘Šπ‘π‘™π‘œπ‘π‘˜
π‘€π‘π‘Žπ‘Ÿ β‹… π‘Žπ‘π‘Žπ‘Ÿ =
𝐸π‘₯π‘‘π‘’π‘Ÿπ‘›π‘Žπ‘™ πΉπ‘œπ‘Ÿπ‘π‘’π‘  = π‘π‘π‘Žπ‘Ÿ βˆ’ π‘Šπ‘π‘Žπ‘Ÿ
π‘π‘π‘Žπ‘Ÿ = π‘Šπ‘π‘Žπ‘Ÿ
In x direction:
π‘€π‘π‘™π‘œπ‘π‘˜ β‹… π‘Žπ‘π‘™π‘œπ‘π‘˜ =
𝐸π‘₯π‘‘π‘’π‘Ÿπ‘›π‘Žπ‘™ πΉπ‘œπ‘Ÿπ‘π‘’π‘  = 𝑇 βˆ’ πΉπ‘π‘™π‘œπ‘ π‘˜πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘›
0 = 𝑇 βˆ’ πΉπ‘π‘™π‘œπ‘ π‘˜πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘›
π‘€π‘π‘Žπ‘Ÿ β‹… π‘Žπ‘π‘Žπ‘Ÿ =
𝐸π‘₯π‘‘π‘’π‘Ÿπ‘›π‘Žπ‘™ πΉπ‘œπ‘Ÿπ‘π‘’π‘  = βˆ’π‘‡ βˆ’ πΉπ‘€β„Žπ‘’π‘’π‘™ πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘› + πΉπ‘šπ‘œπ‘‘π‘œπ‘Ÿ
0 = βˆ’π‘‡ βˆ’ πΉπ‘€β„Žπ‘’π‘’π‘™ πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘› + πΉπ‘šπ‘œπ‘‘π‘œπ‘Ÿ
Adding both equations:
𝑇 βˆ’ πΉπ‘π‘™π‘œπ‘ π‘˜πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘› + (βˆ’π‘‡ βˆ’ πΉπ‘€β„Žπ‘’π‘’π‘™ πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘› + πΉπ‘šπ‘œπ‘‘π‘œπ‘Ÿ ) = 0
βˆ’πΉπ‘π‘™π‘œπ‘ π‘˜πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘› βˆ’ πΉπ‘€β„Žπ‘’π‘’π‘™ πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘› + πΉπ‘šπ‘œπ‘‘π‘œπ‘Ÿ = 0
πΉπ‘šπ‘œπ‘‘π‘œπ‘Ÿ = πΉπ‘€β„Žπ‘’π‘’π‘™ πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘› + πΉπ‘π‘™π‘œπ‘ π‘˜πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘›
Now we know that
πΉπ‘šπ‘œπ‘‘π‘œπ‘Ÿ = πΉπ‘€β„Žπ‘’π‘’π‘™ πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘› + πΉπ‘π‘™π‘œπ‘ π‘˜πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘›
πΉπ‘šπ‘œπ‘‘π‘œπ‘Ÿ βˆ’ πΉπ‘€β„Žπ‘’π‘’π‘™πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘› = πΉπ‘π‘™π‘œπ‘π‘˜πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘›
𝐹𝑝𝑒𝑙𝑙 = πΉπ‘šπ‘œπ‘‘π‘œπ‘Ÿ βˆ’ πΉπ‘€β„Žπ‘’π‘’π‘™πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘› = πΉπ‘šπ‘œπ‘‘π‘œπ‘Ÿ βˆ’ πœ‡π‘˜π‘–π‘›π‘’π‘‘π‘–π‘ β‹… π‘Šπ‘π‘Žπ‘Ÿ
FYI: if you want the car to pull over a heavy object, just let
𝐹𝑝𝑒𝑙𝑙 > πΉπ‘π‘™π‘œπ‘π‘˜πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘›
Ncar
Nblock
T
T
Fmotor
FblockFriction
FwheelFriction
Wblock
Wcar
We just found out that:
β€’ The pulling force of the car measured using a spring scale can be expressed as
𝐹𝑝𝑒𝑙𝑙 = πΉπ‘šπ‘œπ‘‘π‘œπ‘Ÿ βˆ’ πœ‡π‘˜π‘–π‘›π‘’π‘‘π‘–π‘ β‹… π‘Šπ‘π‘Žπ‘Ÿ
β€’
To move a block from rest, the pulling force must be greater than the force of
static friction on the block
πΉπ‘šπ‘œπ‘‘π‘œπ‘Ÿ βˆ’ πœ‡π‘˜π‘–π‘›π‘’π‘‘π‘–π‘ β‹… π‘Šπ‘π‘Žπ‘Ÿ > πΉπ‘π‘™π‘œπ‘π‘˜πΉπ‘Ÿπ‘–π‘π‘‘π‘–π‘œπ‘›

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