Static Equilibrium Translational Forces Torque Unit 4 Statics Dynamics vs Statics is the study of and. We study objects. is the study of and. We study objects. Recall Newton s First Law All objects remain at, or continue to move at a unless acted upon by an. Thus, an object will stay at if all of the forces acting on the object each other. We say that the object is in a state of if it is at. An object is in a state of In Static Equilibrium We must consider: Forces that make objects from one. Forces that make an object about a. Page 1
Translation Forces Activity Draw a free body diagram. What is the mass of the object? Find the tensions in the ropes below. Page 2
OR Why do the vectors connect together? We can find the tensions using the Law of Sines Find T 1 Find T 2 Find the mass of the snowflake Page 3
Torques (Rotational Forces) Archimedes said "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world." Centre of Mass (Gravity Spot) The is a single point in a body at which its entire mass is considered to be concentrated. An object can balance on a point only if its center of mass is directly the point. Alternatively, if you hang an object from a string, the object's center of mass will be directly the string. It is usually located near the more part of an object. The centre of mass is also called the, which is the point at which the force of acts. The force of gravity is equal on both sides of the object s centre of. The center of mass is an important point on an aircraft, as it defines the amount of forward or behind the center of gravity that needs to be moved in order to pitch the plane up or down without applying any external forces Page 4
Location of Centre of Mass For shaped objects the centre of mass is at the. For example the centre of mass of a ball (sphere) is located at the of the ball. For shaped objects, the centre of mass is located at its point in a gravitational field. Example: Find the centre of mass of the following: 1. A uniform 10 m log? 2. A uniform 15 m extension ladder? 3. A broom? 4. A Triangle 5. A boomerang? Note: In the case of a boomerang the centre of mass is A male versus A female A person's center of mass is slightly below his/her, which is nearly the center of a person. Males and females have centers of mass Page 5
Females' centers of mass are than those of males. The average ratio of center of mass to height in females is approximately 0.543 and the average ratio of center of mass to height in males is approximately 0.560. Where is the centre of mass of a hammer? When a force is not directed through an object s centre of mass, the force will cause the object to Example: Look in text pages 233 238 Torque Torque: The force caused by a acting at a distance from a Examples: Equation for Torque where is Torque is the distance a Force is applied from a pivot point (aka point of rotation) Page 6
is the component of the force that acts perpendicular to the surface. What are the units for Torque? Is Torque a vector quantity? Examples of Torque 1. Find the torque supplied to a 75 cm wide door by the following forces applied at the edge of the door: A) 20N B) 30 N at 30 o to the perpendicular to the door 2. Suppose a bolt requires 65 Nm to be properly tightened. What force is required if the wrench is 15 cm long? Page 7
Not tested on public, but useful info in real life!! 3. In the old British system (and in the US) torque is measured in ftlbs. How many Nm is one ft-lb? One foot is 0.305 m. One kilogram is 2.2 pounds Static Equilbrium Consists of 2 Parts First Part Translation Forces where is the sum of ALL of the forces acting on an object Second Part Torques (or Moments of Force) where is the sum of ALL of the ( ) acting on an object. NOTE: These forces are NOT acting Page 8
Static Problems Torque (we did translational forces in unit 2) Torque Questions Seesaw problems: 1. Pat and Tyler are playing on a 4 m long seesaw that is supported at the centre. If Pat has a mass of 30 kg and sits at one end of the seesaw, where should Tyler (mass = 35 kg) sit so that the seesaw balances? Page 9
2. A playground seesaw with a total length of 5.0 m and a mass of 30.0 kg is pivoted at its center. A 20.0 kg child sits on one end of the seesaw. a) Where should a person push with a force of 220 N in order to hold the seesaw level? b) Where should a 40.0 kg child sit to balance the seesaw? 3. Consider the diagram below :A load weighing 60 N is to be supported by a force F applied at the end of a 5.0 kg, uniform, lever as shown. What Force is necessary if the fulcrum is placed at position A? 1.2m F A 40cm 60 N Page 10
4. What force is needed to balance the 10.0 kg mass if: A) the seesaw is massless. B) the seesaw has a mass of 42 kg 2.0 m 10.0 kg 1.0 m F 5. In order to hang a mass of M 1 =30.0kg from the horizontal flat roof of a building, a plank of length 2.4 m is placed on the roof. A rock of mass M 2 = 15.0 kg is placed on one end. How far can the end of the plank reach over the building without tipping over? Page 11
Cantilever Problems 1. A 1.5 x 10 3 kg car is crossing a 120 m long flat bridge which is supported at both ends. When the car is 32 m from one end, what force must each end support be able to provide? 2.A 4.0 m diving board is supported by two blocks, one at the end and the second 1.0 m from the end. A 60.0 kg person stands at the end of the board. Find the forces given to the board by the two supports if: A) The board is a Canadian Tire special - no mass. Page 12
B) The mass of the board is 40.0 kg. 3. A uniform rod of mass 13 kg and length 3.0m rests on two points, one at its left end and one at the centre point. What are the contact forces on the rod at these points? Comment on the stability of this situation. Page 13
4. Two people of unequal strength must carry a uniform beam of length L while holding it horizontal. The weaker of the two holds the beam at one end. A) How far from the other end must the stronger person hold the beam in order to support three quarters of the weight? B) Is there a way in which the stronger person can carry the beam at one end and still support more than one half the weight of the beam? 5. In the diagram below, a 10.0 m uniform horizontal beam, weighing 1.00 10 2 N is supported by a rope at each end. If a 4.00 10 2 N box is positioned 2.0 m from the left end of the beam, what is the tension in each of the support ropes (T 1 andt 2 )? (June 2005 - Public) Page 14
Crane Problems (or Suspended load from a strut and cable) 1. Determine the tension in the cable and the compression force in the boom to support the 1.0 x 10 2 kg object. The angle between the boom and the supporting cable is 37. 2. A crane is used to lift a uniform 24 m long pipe with a mass of 730 kg as shown in the diagram below. What minimum tension is required by the cable to lift the end of the pipe off the ground? Page 15
3. A traffic light hangs from a structure as shown. The uniform aluminum pole AD is 4.0 m long and weighs 5.0kg. The weight of the traffic light is 10.0 kg. A) Determine the tension in the horizontal, massless cable CD. B) Determine the vertical and horizontal components of the force exerted by the pivot A on the aluminum pole Page 16
4. A uniform rod of length L and mass of 4.0 kg is hinged at the left end. A 25.0 kg sign is suspended from the right end. A guy wire is connected to the end of the rod and fastened to a wall. A) Draw a free body diagram for the rod. B) Determine the tension in the guy wire. June 2004 Public (i) Sketch the free body diagram for the rod in the diagram. Label all forces. (2 marks) Page 17
(ii) If the mass of the block is 5.0 kg and the rod is uniform with a mass of 0.40 kg, what is the magnitude of the tension in the wire? (3 marks) Ladder Problems For problems involving a ladder (or other object) leaning against a wall, the should be considered. These problems should be limited to forces acting in different directions (i.e., three different sets of components). Page 18
1. A 8.2 kg ladder is resting against a wall such that the angle made with the ground is 75 o. Find the force friction required by the ground to keep the ladder from moving. 2. A 4.0 m ladder is resting against a building such that the foot of the ladder is 0.75 m away from the building. The ladder weighs 99 N. Find the force of friction required at ground level to keep the ladder from sliding if a 75 kg person stands at following locations along the ladder: A) 1.0 m from the bottom of the ladder. Page 19
B) at the middle of the ladder. C) 3.0 m from the bottom. Page 20
D) 3.7 m from the bottom 3. A 5.0 m long ladder leans against a wall at a point 4.0 m above the ground as shown. The ladder is uniform and has a mass of 12.0 kg. A 55 kg painter is standing 3.0 m up the ladder. Assuming the wall is frictionless (but the ground is not) determine the forces exerted on the ladder by the ground and the wall. Page 21