Mechanical Advantage of Levers, Pulleys, Screws, Inclined Planes & Gears PDF

Mechanical Advantage (of Levers) The mechanical advantage of a machine is the amount by which a machine can multiply a force. The force applied to the lever is called the input force. (force you apply) The force the lever applies to the object is called the output force. Mechanical Advantage (of Lev...

Mechanical Advantage (of Levers) The mechanical advantage of a machine is the amount by which a machine can multiply a force. The force applied to the lever is called the input force. (force you apply) The force the lever applies to the object is called the output force. Mechanical Advantage (of Levers) The mechanical advantage of a lever can be calculated in two different ways. The first is by knowing the output and input force. The second is by knowing the input arm distance and output arm distance. OF MA IA IF 1. Output Force & Input Force MA OA 2. Input arm distance / Output Arm distance 1. Calculating Mechanical Advantage of Levers (knowing Force) MA = output force input force (load) (force you apply) A force of 50N is applied to the end of a lever to lift a rock that is 350N. What is the MA of the lever? What is the output force (load)? 350N What is the input force? 50N What the MA? unknown Place all numbers into their correct location in the triangle. Cover the MA with your finger. Divide 350 by 50. Answer: 350N = 7. 7 is the mechanical advantage. 50N OF MA 350 MA IF MA = 7 50 Calculating Mechanical Advantage of Levers (knowing Force) MA = output force input force (load) (force you apply) OF MA Calculate the MA of using the lever to try and lift the back of the vehicle? 350 IF MA 50 Rules of Mechanical Advantage 1. If MA = 0 there is no MA. 2. If MA > 0 you have MA, higher the MA the greater the advantage. This means you are using less force making it easier to move an object. 3. If MA < 0 you have a situation where the output force is more than the input force resulting in no mechanical advantage. OF 2. Calculating Mechanical Advantage of Levers (knowing arm distance) A lever is used to lift a heavy box weighing 500 newtons. The input arm of the lever is 0.5 meters long, while the output arm is 1.5 meters long. What is the mechanical advantage of the lever? What is the output arm length? 1.5M What is the input arm length? 0.5M What the MA? unknown Place all numbers into their correct location in the triangle. Cover the MA with your finger. Divide.5 by 1.5. Answer:.5 = 3. Mechanical advantage of 3. 1.5 MA = input arm distance output arm distance IA MA OA 0.5 MA 1.5 Calculating Mechanical Advantage of Levers Example 1 MA = input arm distance output arm distance IA MA Calculate the MA of using the lever to try and lift the back of the vehicle? OA Calculating Mechanical Advantage of Levers Example 2 MA = input arm distance output arm distance IA MA Calculate the MA of using the lever to try and lift the back of the vehicle? OA Practice MA = output force (load) input force (force you apply) or input arm distance output arm distance OF MA IF IA MA OA Justin uses a wheelbarrow to move a load of bricks. The bricks weight 600 N, which is more than he could carry on his own. Justin uses the wheelbarrow to move the bricks. With the wheelbarrow he can move the bricks with only 120 N. What is the mechanical advantage? Practice MA = output force (load) input force (force you apply) or input arm distance output arm distance OF MA IF 1. IA MA OA Justin uses a wheelbarrow to move a load of bricks. The bricks weight 600 N, which is more than he could carry on his own. Justin uses the wheelbarrow to move the bricks. With the wheelbarrow he can move the bricks with only 120 N. What is the mechanical advantage? MA = Output Force Input Force MA = 600 N 120 N MA = 5, Justin can lift 5 x more with a wheelbarrow than without. Calculating Mechanical Advantage (pulleys) MA = MA = MA = MA = It is easy the calculate the MA of a pulley system by counting the number of pulleys within the system. No matter their diameter, the MA will always be the same as the number of pulleys. Calculating Mechanical Advantage (screws) MA - 2πr p r is the radius of the screw head π is a constant at 3.14 p is the lead of the screw “pitch” (distance of one full rotation, distance between threads) 9mm Calculate the mechanical advantage of a screw whose radius is 9mm and pitch of 3mm. MA - 2πr p MA - 2π(9) 3 MA - 56.52 = 18.84 3 A screw can have a much higher MA when a screwdriver or power tool is used. 3mm Calculating Mechanical Advantage (inclined planes) MA = length of slope height of the slope Calculate the mechanical advantage of a screw whose radius is 9mm and pitch of 3mm. MA = 3m 1m MA = 3 As the height increases and length remains constant, the MA decreases. As the height decreases and length remains constant, the MA increases. To increase the MA you need to increase length amd/or decrease height. Calculating Mechanical Advantage (gears/gear trains) We can find the MA of gears and the GEAR RATIO (GR). MA = 30 = 0.5 60 or GR = 30 = 3 = 3 / 3 = 1 60 6 6 / 3 = 2 GR = 1:2 For every one turn of the driver, the driven turns two times. Speed Ratio While gear ratio is a type of speed ratio, speed ratio can also refer to ratios between the speeds of pulleys, belts, wheels, or any other rotating components. Calculating Mechanical Advantage (gears/gear trains) Calculate the MA and GR of the following. The Effects of Friction on MA Friction can have a significant impact on mechanical advantage. Frictional forces will reduce the efficiency of a machine and result in a decrease in the mechanical advantage of the machine. The machine will require more force to operate, which could make it difficult or impractical to use. One way to reduce the effects of friction on mechanical advantage is to lubricate the machine's moving parts so that they can move more easily. An example of this effect is seen in pulley systems. While ideal pulleys, with no energy loss due to friction, would have a constant mechanical advantage at every pulley, real-world pulleys experience energy loss due to friction. Efficiency EFFICIENCY is a measurement of how well a machine or device uses energy. Efficiency of a system is negatively affected by friction. Most energy is lost and unusable (Ex. Lost as heat) Most complex machines are very inefficient: waste energy. Ex. A car is only 15% efficient, where does the rest of the energy go? The Meaning of Work Work is done when a force acts on an object to make the object move. If there is no force on an object, then no work is being done. Amy uses 20N of force to push a lawn mower 10 meters. How much work does she do? W = F.d W = 20N. 10 meters W = 200 Joules The work input is the work done by the student using the machine—the inclined plane—to lift the person in the wheelchair. In this case, the pushing student exerts a force of 320 N for a distance of 5 m. You can use the formula for work to calculate the work input: 320N x 5 m = 1600 J Without the inclined plane, the force needed to lift the straight up would be 800N over the 2 meters: 800n x 2 m = 1600 J 5m 2m As a result the same work is done no matter regardless of mechanical advantage.