Torque

Torque / Moment ~ Turning Force e.g. the force used to open a door d F Torque (or moment) is a vector: By convention, counter clockwise torques are positive and clockwise torques are negative. Units for torque are Nm The Pivot point (or fulcrum) is the point around which the object rotates.

Ex: A meter stick 45 cm Find the Torque exerted on the meter stick due to the 50 g mass that is suspended from it.

Ex: The torque on a door ℓ  = F ℓ

Line of Action of a Force The line of action of a force is an imaginary line of indefinite length drawn along the direction of the force. F2 F1 F3 Line of action

The moment arm of a force is the perpendicular distance from the line of action of a force to the axis of rotation. F1 r F2 F3 r r

Example: An 80-N force acts at the end of a 12-cm wrench as shown Example: An 80-N force acts at the end of a 12-cm wrench as shown. Find the torque. Extend line of action, draw, calculate r. = (80 N)(0.104 m) = 8.31 N m r = 12 cm sin 600 = 10.4 cm

Alternate: An 80-N force acts at the end of a 12-cm wrench as shown Alternate: An 80-N force acts at the end of a 12-cm wrench as shown. Find the torque. positive 12 cm Resolve 80-N force into components as shown. Note from figure: rx = 0 and ry = 12 cm t = (69.3 N)(0.12 m) t = 8.31 N m as before

Static Torque Dynamic Torque Is when the torques acting produce a change in rotational motion. Static Torque Is when the torques acting add together (?) or cancel out, to ensure an object is stationary (rotationally obeys Newton’s 1st Law).

Dynamic Torque - Movement

Static – Stationary

contact force of pivot weight of stand The point on an object where all its weight seems to be concentrated is called the centre of mass (or gravity).

An object in Equilibrium means… contact force of pivot weight of stand weight of mass An object in Equilibrium means…

If these conditions are met, we say that something is in Equilibrium. F=ma If F = 0 then a = 0 =I If  = 0 then  = 0 If these conditions are met, we say that something is in Equilibrium. Fx = 0 Fy = 0  = 0 the total of all the anti- clockwise torques the total of all the clockwise torques =

St = 0 Example: Is the seesaw in this picture balanced? B: Moment = Force x distance = 600 N x 1.5 m = 900 Nm A: Moment = Force x distance = 500 N x 2 m = 1000 Nm No, the seesaw is not balanced. It will turn anticlockwise.

The mass of the boy and the tray is 65 kg. Show the mass of the plank is 11 kg Take g = 9.8 m s-2 5 m 2.5 m F1 = 370 N 740 N F2 = 370 N

The support forces and the weight forces are balanced. 5 m 2.5 m F1 = 370 N 740 N F2 = 370 N The mass of the boy and the tray is 65 kg. Show the mass of the plank is 11 kg Take g = 9.8 m s-2 The support forces and the weight forces are balanced. The upward forces = downward forces 370 N + 370 N = weight of the boy + weight of plank 740 N = 637 N + 103 N Weight = mass x gravity mass = 103/9.8 = 10.5 mass = 11 kg (2sig.fig) Students succeed better in Physics when answers that require calculations: Show all working i.e., equation, substitution and answer. (Criterion 2); Have correct significant figures (Criterion 1); and Show the correct unit (Criterion 1)

Show the mass of the 1 m ruler is about 200 g. Take g = 9.8 m s-2 The weight of the ruler Fw acts at the centre 0.5 m from the end. The support force is labeled Fs 1 m 0.1 m 0.5 m 15 N 0.05 m Fs

Take moments about the support force Fs. Show the mass of the 1 m ruler is about 200 g. Take g = 9.8 m s-2 The weight of the ruler Fw acts at the centre 0.5 m from the end. The support force is labeled Fs 0.1 m 0.5 m 15 N 0.05 m Fs Fw (ruler) Take moments about the support force Fs.

The plank has a weight of 98 N. The boy and tray have a weight of 637 N. How far to the left (d) of the fulcrum (FLS) can the boy stand without the plank tipping? 5.0 m 0.40 m d Fw = 98 N FB = 637 N FLS 2.5m FRS = 0 Take moments about FLS

Torques in the Arm

The angle at which this man’s back is bent places an enormous force on the disks at the base of his spine, as the lever arm for FM is so small.

Given: W=50 N, L=0.35 m, x=0.03 m Find the tension in the muscle W x L

Problems with TWO Pivot points Consider the 400-kg beam shown below. Find TR

An man walks across a shark infested creek An man walks across a shark infested creek. The mass of the bridge is 45 kg and is 5.2 m long. A man of mass 85 kg tentatively walks to a point 1.3 m from end A to get a better view of the sharks below. The man is unaware that termites have weaken support B so that it will support only 500 N. Does the man get wet? B A 1.3 m 5.2 m At what point does he get wet?