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Name: ____________________________
Torque and Static Equili
ium: PhET Lab
Introduction:
The term torque (τ, Greek letter tau) is given to the turning effect you observed when applying a
force and is a measurable quantity. To cause rotation, the twisting effect of a force depends on the
magnitude of the force, and on the perpendicular distance between the point or axis of rotation
and the line of force (called the lever arm or moment arm). The torque is defined as the product
of the magnitude of the force, F, and the lever arm, l. We can also think of it as the perpendicular
component of the force times the radial distance r between the axis of rotation and point at which
the force is applied. Therefore, the magnitude of the torque can be found either way.
As we discovered, the torque was greatest for a force exerted 90° to the lever arm (tangential force)
and farthest from the axis of rotation. The quantity of torque decreased as the force was applied
closer to the rotation point and no rotational effect was observed with the force (radial) applied to
the end of the meter stick, when the line of action of the force passed through the axis of rotation.
The meter stick simply exerts a force on you of equal magnitude and opposite direction.
Newton's laws apply to rotational motion just as they do to translational motion. However, it
is torque, not force which must be considered. A rigid body is in equili
ium when there is no
change in the translational motion nor in the rotational motion. That is, the sum of the
externally applied forces is zero, and the sum of the externally applied torques is zero. In this
experiment, you will investigate torques needed to keep a body in rotational equili
ium.
Mathematically, the conditions for equili
ium are thus: ∑ �⃗⃗� = 0 and ∑? = 0.
Note that these are both vector sums, with the force usually have components in the xy-plane,
with torque in the z direction (clockwise, counter clockwise).
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Procedure:
On your
owser, go to https:
phet.colorado.edu/
Click on “simulations” → “Physics” → “Balancing Act” → Download or run
Static Equili
ium on a beam
1. In the menu, select the Balance Lab simulation.
2. Play with the sim and get used to it. Click on all the check boxes on the right to see what each of
them does. Keep mass labels, forces from objects and ruler options checked for your
simulations. Play with moving objects and applying different forces.
3. Besides the middle (permanent) support of the beam, there are two stationary supports on both
sides of the beam. This is seen when the bottom switch is on the left side. You can use this option
to place masses on the beam without moving it.
4. Once you are done placing your masses and want to check if there is balance (static equili
ium),
you can remove the temporary supports by moving the buttom switch to right. In the example
case below, there is no balance or static equili
ium and the system turns clockwise direction.
https:
phet.colorado.edu
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5. When there is balance (or static equili
ium), the beam will not move or turn even after removing
the supports. An example is shown below.
PART A:
1. Make sure there are no masses on the beam and the ruler is active.
2. Place a 10 kg mass (m1) on the right side of the beam, 0.75 m away from the middle support.
Record the mass and its position from the middle support (x1) in Data Table 1 below.
3. Place a 15 kg mass (m2) on the left side and adjust its position until static equili
ium is found.
Record m2 and its position from the middle support (x2) in Data Table 1.
4. Now, calculate the torque (1) created by m1 around the middle support. Don’t forget that torque
is related with force, not the mass. You will need to calculate the weight first.
Calculation for torque 1 (1) including direction:
5. Calculate the torque created by m2 around the middle support.
Calculation for torque 2 (2) including direction:
Data Table 1
Mass m1 (kg) Position x1 Torque 1
Mass m2 (kg) Position x2 Torque 2
6. Draw the free body diagram of the system. Don’t forget to place all the forces on the beam
including normal force from the middle support. Prove the static equili
ium with your
calculations.
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PART B:
1. Make sure there are no masses on the beam and the ruler is active.
2. Place a 10 kg mass (m1) and a 5 kg mass (m2) at two different positions on the right side of the
eam. Record the masses (m1 and m2) and their positions from the middle support (x1 and x2) in
Data Table 2 below.
3. Using a 20 kg mass (m3), find a location on the left side that will balance the beam. Record m3
and x3 in Table 2.
4. Now, calculate the torque (1) created by m1 and torque (2) created by m2 around the middle
support.
Calculation for torque 1 (1) and torque 2 (2)including direction:
5. Calculate the torque created by m3 around the middle support.
Calculation for torque 3 (3) including direction:
Data Table 2
Mass m1 (kg) Position x1 Torque 1
Mass m2 (kg) Position x2 Torque 2
Mass m3 (kg) Position x3 Torque 3
6. Draw the free body diagram of the system. Don’t forget to place all the forces on the beam
including normal force from the middle support. Prove the static equili
ium with your
calculations.
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Questions:
1. Two forces produce the same torque. Does it follow that they have the same magnitude?
2. Give an example of a system in which the net torque is zero, but the net force is nonzero.
3. Give an example of a system in which the net force is zero, but the net torque is nonzero.
4. Explain why the masses are moved back and forth along a scale on a triple-beam balance.