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chemical formula of torque is τ = rF
Typology: Lab Reports
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Figure 8.1: The wood block provides necessary height for the hangers to not touch the table.
Figure 8.2: Clamp - The arrow indicates the correct edge for position measurement.
Fulcrum Meter Stick Vernier Caliper (3) Mass Hangers Masses (3) Hanger Clamps (Clamps) (1) Knife-Edge Clamp Digital Balance Triple-Beam Balance Block of Wood Unknown Mass (Marble or “Silver” Cube)
TA’s Table: (1) Dial-O-Gram Balance
Advance Reading
Text: Torque, center of mass, stable and unstable equi- librium, lever arm
Lab Manual: Appendix B
Objective
To measure torques on a rigid body, to determine the conditions necessary for equilibrium to occur, to per- form error analysis.
Theory
When a force F is applied to a rigid body at any point away from the center of mass, a torque is produced. Torque, τ (Greek letter, tau), can be defined as the tendency to cause rotation. The magnitude of the vec- tor is:
τ = rF sin θ (8.1)
where r is the distance from the point of rotation to the point at which the force is being applied (i.e., lever arm), and F sin θ is the component of the force per- pendicular to r. Note that the unit for torque is mN (meter × newton).
In this experiment, all forces will be acting normal (perpendicular) to the meter stick: θ = 90◦^ ; therefore, sin θ = 1. The equation for torque is simplified:
τ = rF (8.2)
Equilibrium, Latin for equal forces or balance, is reached when the net force and net torque on an object are zero. The first condition is that the vector sum of the forces must equal zero:
ΣF� = ΣF (^) x = ΣFy = ΣFz = 0.0 N (8.3)
The second condition that must be met is that the net torques about any axis of rotation must equal zero. We will use the standard convention for summing torques. Torques that tend to cause counterclockwise rotation, τ (^) cc , will be positive torques, while torques that tend to cause clockwise rotation, τc , will be negative torques.
Σ�τ = Σ�τ (^) cc − Σ�τ (^) c = 0.0 mN (8.4)
The system under consideration for this experiment will need to not only attain equilibrium, but also re- main in equilibrium. This will require that the object be in stable equilibrium, meaning if a slight displace- ment of the system occurs, the system will return to its original position (e.g., a pendulum). If the system were to move farther from its original position when given a slight displacement, it would be in unstable equilibrium (e.g., a ball on a hill).
Once stable equilibrium has been attained for each ex- perimental arrangement, measure the mass at each po- sition using the appropriate balance.
Figure 8.3: Required sketch for each experimental ar- rangement
Once stable equilibrium is attained, sketch each set-up:
x: position F : magnitude of force Arrow : direction of force r: lever arm cc: counterclockwise c: clockwise cm: center of mass f : fulcrum
Name: Section: Date:
Worksheet - Exp 8: Torques and Rotational Motion
Objective: This experiment investigates torque on a rigid body and determines the conditions necessary for static equilibrium.
Theory: When a force �F is applied to a rigid body at any point away from the center of mass, a torque is produced. Torque, τ , can be defined as the tendency to cause rotation. The magnitude of the vector is:
τ = rF sin θ
where r is the distance from the point of rotation to the point at which the force is being applied, and F sin θ is the component of the force perpendicular to r. Note that the unit for torque is the mN (m × Newton). In this experiment, all forces will be acting normal (perpendicular) to the meter stick: θ = 90◦^. Therefore sin θ = 1, and the equation for torque is simplified:
τ = rF.
Rotational equilibrium is obtained when the sum of torques about any axis is equal to zero.
� �τ (^) cc −
�τ (^) c = 0.0 mN
Procedure:
Part 1: Quantitative Analysis of Torque
mhc =
(18 pts)
τ =
Part 3: Unknown Mass
ρ (^) block =
Material: (4 pts)
Density %error: (3 pts)
Density Material (g/cm 3 )
Solids Metal: Aluminum 2. Stainless Steel 7. Brass 8.44 - 8. Bronze 8.74 - 8. Copper 8. Lead 11. Mercury 13. Rock: Granite 2.64 - 2. Slate 2.6 - 3. Diamond 3. Garnet 3.15 - 4. Corundum 3.9 - 4. Wood: Pine (Yellow) 0.37 - 0. Oak 0.60 - 0. Ebony 1.11 - 1. Misc.: Ice 0. Bone 1.7 - 2. Chalk 1.9 - 2. Glass (Lead) 3 - 4
Fluids Atmosphere (STP) 0. Water (20 ◦^ C) 0. Water (0 ◦^ C) 0. Mercury (20 ◦^ C) 13.
