Torque and Levers Lesson 5

Feeling Torque: activity When a force or set of forces causes a rigid body to rotate, we say a torque has been applied. Torque – the turning effect caused by a force on a rigid object around a axis or fulcrum, symbol T; it is measured in Newton-meters, or Nm; it can be called a “moment force”

Example: Every time you open a door, you are producing a torque on the door. A small force applied far from the hinges can produce the same amount of torque as a large force applied closer to the hinges. Distance Distance

In order to create the largest amount of torque possible when pushing on the door, the force generated must be at a 90 degree angle to the door. Example 2

The amount of torque produced depends on two factors. The magnitude of the force (F) applied to the rigid object. The distance (d) between the force and the axis or fulcrum.

Using the symbol T for the magnitude of torque, the following statements hold true: T increases as F increases ( T  F) T increases as d increases ( T  d) Torque = force x distance or T = Fd (where F is perpendicular to the ridge object)

F = 84 N D = 0.25 m T = ? Example problem 1: Calculate the magnitude of a wrench experiencing a force of 84 N 0.25 m away from the bolt. F = 84 N D = 0.25 m T = ?

T = Fd = (84 N) ( 0.25 m) = 21 Nm Therefore, the magnitude of the torque on the wrench is 21 Nm.

Torque on Levers Two torques can be calculated for a lever: the effort torque (TE) and the load torque (TL). The associated distances are the effort distance, or effort arm (dE), and the load distance, or load arm (dL). dL dE TL TE

Effort torque = effort force x effort arm TE = FEdE Or Load Torque = load force x load arm TL = FLdL In each case, the force is perpendicular to the lever, which allows us to deal with magnitudes only, thus avoiding vector signs.

Example problem 2: A camper is using a large plank as a first class lever to move a rock. The effort force has a magnitude of 4.5 x 102 N, and the distance from the fulcrum to the effort force is 2.2 m. What is the magnitude of the effort torque produced? (ignore the mass of the plank)

FE = 4.5 x 102 N dE = 2.2 m TE = ? TE = FEdE = (4.5 x 102 N) (2.2 m) = 9.9 x 102 Nm

Therefore, the magnitude of the effort torque produced is 9.9 x 102 Nm.

Static Equilibrium of Levers The word static means at rest. A rigid object that is in static equilibrium is at rest in two ways. It is not moving in any direction It is not rotating

Law of the Lever When a lever is in static equilibrium, the magnitude of the effort torque equals the magnitude of the load torque.

Effort force x effort arm = load force x load arm This law can be written in the equation form Effort torque = load torque Effort force x effort arm = load force x load arm FEdE = FLdL For this equation, only the magnitudes of the quantities are considered. This eliminates the need for positive or negative signs.

Any of the 4 variables can be found by rearranged the equation.

Example problem 3: A camper wants to mount a trailer on blocks for the winter. One corner of the trailer is lifted by applying an effort force using a 3.00 m steel bar. The trailer is applying a load force of 1.8 x 103 N 0.45 m away from the fulcrum. Determine the magnitude of the effort force required (ignore the mass of the bar)

FL = 1.8 x 103 N dL = 0.45 m dE = 3.00 m – 0.45 m = 2.55 m FE = ?

FE = 3.2 x 102 N Therefore the force needed to lift the trailer is 3.2 x 102 N.

For any ridged object, the law of the lever can be stated in more general terms based on which way it is turned. The clockwise torque is balanced by the counter clockwise torque. TCW = TCCW Where TCW = magnitude of the clockwise torque on an object around the fulcrum. Where TCCW = magnitude of the counter clockwise torque on an object around the fulcrum.

Questions: hand in A mechanic applies a force of 540 N perpendicular to a wrench to loosen a nut. Calculate the magnitude of the torque if the distance from the applied force to the nut is (a) 0.30 m and (b) 0.50 m T (2) A person applies a force of 150 N at the hinge side of a door, which means that d is zero. What is the magnitude of the torque produced on the door? C (1) Estimate the magnitude of the maximum effort torque you could produce on a wheel nut using a tire wrench that is 50 cm long. (Hint, Do you think your maximum effort force could be greater than your own weight?) T (1) C (1)

For the following questions, solve for the unknown. Find dE given FE = 15 N, FL = 75 N, and dL = 0.15 m T (1) Find FL given FE = 64 N, dE = 3.5 m, and dL = 0.70 m T (1) Find dL given FE = 32 N, FL = 640 N, and dE = 2.0 m T (1)

Calculate the effort force needed for the situation shown below. T (2) 0.8 m Effort force 1.6 m