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Physics Lab
It is important that bridges, building, etc. be rigid and at rest. You may say that they always are. But bridges and building do collapse. Engineers and others must understand how to balance forces involved so that the structures are stable.
Review pages 241-249 in your textbook before proceeding.
Equilibrium of a Loaded Beam
When forces act at different points on an object, their vector sum must be zero for the object to be in translational equilibrium (an object in translational equilibrium is not accelerating bodily from place to place). However, such forces could cause the object to rotate. For an object to be in static equilibrium (completely stationary), it must also be in rotational equilibrium.
In this investigation, you will study forces applied at different points on an object that is in static equilibrium; that is, rotational as well as translational equilibrium. When a force causes an object to rotate, it rotates about a pivot. The turning affect of a force on the object is called the torque of that force about the pivot. The torque of a force about a pivot is equal to the product of the magnitude of the force and the perpendicular distance from the pivot to the line along which the force acts. Therefore, the unit for torque is the Newton*metre (N*m).
τ=rF ⊥
The purpose of this investigation is to discover the conditions under which forces acting on an object will maintain the object in (a) translational and (b) rotational equilibrium.
Procedure:
A student weighs a uniform metre stick (that is, its centre of gravity is at the 50 cm mark) and finds that its mass is 150 g. The metre stick is then supported horizontally by two vertical spring balances attached to support stands as shown below. For the example, the pivot point is arbitrarily placed at the 0 cm end of the metre stick. The distances of the points of application of the forces are then measured from this point.
Two different masses (m1 and m2) are attached to the metre stick and their distances from the pivot point are adjusted so that the metre stick remains horizontal. The force, in Newtons, is recorded from each spring balance as well as the forces exerted by the masses (including the metre stick itself) along with their distances from the pivot point. This procedure is performed twice with different masses and the trails are shown under Data.
Data:
g
g
Data Analysis:
Print off the previous page to aid in your analysis. Calculate the force of gravity (F1) acting on the metre stick and record in the table below. Locate and record the force measured by each spring balance. Calculate and record the force exerted by each of the two masses on the metre stick. Determine the distance of the points of application of the forces measured from the pivot point and record in the table below. Note that the pivot point is assigned differently in each of the trials.
Trial #1
F1 F2 F3 F4 F5
Trial #2
F1 F2 F3 F4 F5
Remember that the sum of the forces, ∑ F , involves only the vertical forces, since there are no horizontal forces present and that forces acting upward are positive and forces acting downward are negative. Also, when you are finding the sum of the torques about a
given point, ∑τ , remember to call the counter-clockwise torques positive and the clockwise torques negative.
Calculate the ∑ F for each trial. Show all work. Trial 1:
∑F=
Trial 2:
∑F=
Force
Force (N)
Distance from Pivot (m)
Force
Force (N)
Distance from Pivot (m)
Calculate the ∑τ for each trial. Show all work. Trial 1:
∑τ =
Trial 2:
∑τ =
Calculate the average magnitude of the forces for each trial. Show all work. Trial 1:
Fav = Trial 2:
Fav =
Calculate the average magnitude of the torques for each trial. Show all work.
Trial 1:
τav =
Trial 2:
τav =
Express ∑ F as a percentage of the average magnitude of the forces for each trial. Trial 1:
Trial 2:
Express ∑τ as a percentage of the average magnitude of the forces for each trial. Trial 1:
Trial 2:
Discussion of Results/Conclusions:
What can you conclude about the conditions needed for an object to be in translational equilibrium? Use data to support your conclusion.
What can you conclude about the conditions needed for an object to be in rotational equilibrium? Use data to support your conclusion.
What are some possible sources of error in this experiment?
∑F x100%= Fav
Questions: Show all work
1. The beam shown in figure #024 is in static equilibrium.
a. What is the magnitude of the force, F?
b. If the force was moved to the 10 cm point, what would its magnitude have
to be to keep the beam in equilibrium?
2. The beam shown in figure #025 is in static equilibrium. What is the distance to the 50 N force? (Assume that the beam is uniform)
3. For the situation shown in figure #026,
a. Find the force, F, needed to produce translational equilibrium. b. Find the distance, x, needed to produce static equilibrium.

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