Lab 9: Static Equilibrium

static equilibrium

-A condition where there are no net external forces acting upon a particle or rigid body and the body remains at rest or continues at a constant velocity. -when an object is in translation equilibrium (forces = 0) and rotational equilibrium (torque = 0)

True or False: If we know the sum of the forces acting on an object is zero, then we can say for sure that the object is in equilibrium.

False

While attempting to remove a stubborn lug nut from a wheel on your project car, you apply a force on the end of a long wrench with length 18.5 cm, such that your arm and the wrench form a 90 degree angle. The lug nut isn't budging, so you start to push harder until it finally comes loose when you push with 212 N of force. How much torque was required to loosen the lug nut?

T = force * distance 212 * .185 = 39.2 Nm

Now it's time to put a new set of wheels on your project car. The manual for the new wheels says that the lug nuts should be applied with at least 225 Nm of torque for safety purposes. You can only muster a pushing force of 250 N. If you push against the wrench at an angle of 90 degrees, what is the shortest wrench you would need to tighten the lug nuts to their specifications?

T = force * length 225 Nm = 250N * length = 90 cm

Torque equation

T=Fr

Explain in your own words what is meant by the center of mass

center of mass is where the object meets static equilibrium

You apply a force F on the end of a wrench of length r, while your arm and the wrench form an angle θ. If you start using a new wrench with double the length, what do you expect to happen to the amount of torque you generate?

it should increase by a factor of 2

An object is subjected to a force F applied a distance r away from the axis of rotation at an angle of θ. What is the moment arm of the torque acting on the object?

rsin(θ)

How did your calculated values in trials 1 and 2 compare to your experimental values? What were some possible sources of error?

some possible sources of error could have been not having the stick perfectly balanced. there is also a possibility that the weights were inaccurately placed

If we were to place an imaginary axis of rotation at one end of the meter stick, considering there are still 2 weights placed on the meter stick c. what position on the meter stick is the system equilibrium? Explain

the system is always in static equilibrium b/c there is no point in which torque does not = 0 (rotational equilibrium conditions met), nor is there any point in which the ∑F does not = 0 (translational equilibrium conditions also met)

Describe the relationship between mass and distance in regard to balance.

there has to be relationship b/w mass and distance in order to balance. the object with the greater mass needs to be closer to the center of mass, whereas the lighter masses object could be placed farther away to balance out the heavier mass

Define percentage error. Include the equation used to calculate it

used to compare an experimental measure to a known constant

If we were to place an imaginary axis of rotation at one end of the meter stick, considering there are still 2 weights placed on the meter stick a. how could you use to summation of forces and torques in relation to the axis of rotation being at the end of the meter stick to set up 2 equation?

∑F = 0 = Fa + Fb - m1g - m2g -msg ∑T = 0 =Fara - m1gr1 - m2gr2 - msgrs

Apparatus used

-a meter stick resting on two force sensors will serve as our structure -loads (weights) will be placed at various locations along the meter stick and your job will be to predict how much force will be required at the supports

In this particular experiment, what might cause variation in predicted center of mass and the experimental results from the sensors?

-defect in meter stick: if there are dents along the stick, it may equate in a loss of mass and cause a shift in the center of mass

Name at least two situations you have encountered outside of the lab that involve torque and describe how they illustrate it

-opening a bottle cap -turning open a door knob

Analytical procedure

-predict the location of the center of mass of the meter stick, then find the actual by placing a block of wood underneath -Find Fa and Fb

Torque

-rotational equilibrium -greater the radius = greater the torque (and vice versa)

Define center of mass. Include the equation used to calculate it

-the center of mass is the point at which the mass of an object has a 50:50 ratio; the point where the mass is evenly distributed -Ex: for two masses Xcm = (m1x1 + m2x2)/(m1 + m2)

List 3 "real-life" situations that involve torque and describe how it is illustrated

1. Using a wrench: as your radius increases and moves towards the end of the wrench while applying the same force, torque increases 2. Revolving doors: as you walk into a store, it is easier to go through the door is you push towards the ends of the door b/c the radius and torque increases 3. Turning steering wheel: torque allows car to move in directions other than straight

Counterclockwise torques are considered positive by standard sign convention, while clockwise torques are negative.

True

Is there a point on the meter stick where the sum of the torques would not be zero, that is, is there a location on the meter stick where the system is NOT in static equilibrium? Explain.

no because the meter stick is not moving, therefore there is no acceleration and it stays in static equilibrium

If we were to place an imaginary axis of rotation at one end of the meter stick, considering there are still 2 weights placed on the meter stick b. would there be a point on the meter stick where the summation of the torques would not equate to zero? Explain

no, there is not a point on the meter stick where the sum of torque would be anything other than zero, because the meter stick is not moving to produce torque