Torque

4 m 1 m 2 m F1 F2 100 N 800 N Find F1 and F2

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?

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

Common tools that you exert forces (F) on, thus creating torques around axes (a)

Static – Stationary Dynamic - Movement Torque is defined as the tendency to produce a change in rotational motion. Static – Stationary Where a series of Torques add together or cancel out, to ensure an object is stationary (rotationally obeys Newton’s 1st Law).

Dynamic - Movement

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An object at rest is in equilibrium; the study of such objects is called statics. In order for an object to be in equilibrium, there must be no net force on it along any coordinate, and there must be no net torque around any axis.

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 Y13 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 =

Which mathematical descriptions below match the picture above? You are pushing down on one end of a balance. On the other end is a 1 kg object. The system is in equilibrium. 30 cm 70 cm Which mathematical descriptions below match the picture above? a SFy = 0 = - 10 N + FHAND ON BOARD b SFy = 0 = - 10 N - FHAND ON BOARD + FPIVOT ON BOARD c St = 0 = 10 N (30 cm) – FHAND ON BOARD (70 cm) d St = 0 = 10 N (30 cm) – FHAND ON BOARD (100 cm) a, c 2 a, d 3 b, c 4 b, d

Determine the mass of a 1m ruler Class challenge #1… Determine the mass of a 1m ruler W Fs ? W

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)

St = F block string on beam (1/4 L) – Tright support on beam L = 0 A block hangs on a massless meter stick supported by two scales. The situation is described mathematically: SFy = 0 = Tleft support on beam + Tright support on beam – Fblock string on beam St = F block string on beam (1/4 L) – Tright support on beam L = 0 A student’s picture is shown with one block in the correct position. Which block is that? A B C D 1 A, located at 1 / 4 m to the right 2 B, located at 1 / 3 m to the right 3 C, located at 1 / 2 m to the right 4 D, located at 3 / 4 m to the right

Class challenge #2… Confirm force readings on sensors

Torques in the Arm

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?

Angled Static Torque Problems

The drawbridge at Camelot castle is used to help keep invaders out The drawbridge at Camelot castle is used to help keep invaders out. A group of invaders rapidly and the bridge is raised. One invader jumps on and holds on to the bridge. x y 1 5 4 3 2 A student drew a free body diagram for the drawbridge. Identify the forces represented correctly. 1 2, 4 2 1, 3, 4 3 2, 3, 4 4 1, 3, 5 5 2, 3, 5

What are the missing signs in this statement? A 100 N flower pot is hanging from the end of a 200 N beam 1 meter long. The situation is represented with a force diagram. 30o ½ m x y T Wfp Wb The same situation is described mathematically: St = _100 N(1 m) _200 N (1/2 m) _ (1/2 m) sin 30 T=0 What are the missing signs in this statement? 1 + – – 2 – – – 3 – – + 4 + + + 5 + – +

Class challenge #3… Determine the mass of the wooden board