Calculating Mechanical AdvantageSince the mechanical advantage of a machine is determined by the ratio of the output force (Fout) in Newtons, to the input force (Fin) in Newtons, to calculate it we use the following formula:
Mechanical Advantage = output force (N)/input force (N)
MA=Fout/Fin
MA examples:1) 35N of force is exerted onto a crowbar to pry open a box. The crowbar exerts 95N of force onto the box. What is the crowbar's mechanical advantage, rounded to the nearest hundredth? MA=Fout/FinMA=95/35MA=2.71 The crowbar's mechanical advantage is 2.71.
2) Tom turns a screwdriver using 6N of force. The screwdriver applies 20N of force onto the the screw. What is the mechanical advantage of the screwdriver, rounded to the nearest hundredth? MA=Fout/FinMA=20/6MA=3.33 The screwdriver's mechanical advantage is 3.33. 3) Lola is pushing an 81 kg cart up a ramp. She has to exert 95N of force to push the cart up the ramp. What is the mechanical advantage of the ramp, rounded to the nearest hundredth? *First, lets find out how much 81 kg weighs on earth. The force of gravity is 9.8N/kg.F=MgF=81(9.8)F= 793.8N MA=Fout/FinMA=793.8/95MA=8.36 The ramp's mechanical advantage is 8.36. Calculating Ideal Mechanical Advantage for Levers and Inclined PlanesThe ideal mechanical advantage of a lever or an inclined plane is determined by the ratio of the input distance (din), to the output distance (dout). If you do not have the input and output distances of a lever, you can still calculate its IMA by substituting the input distance with the effort arm's length, and the output distance with the load arm's length. Just remember, the arm lengths are not always equal to the input and output distances, but they are always equal in ratio. To calculate the IMA we use the following formula:
Ideal Mechanical Advantage = input distance (unit of measurement)/output distance (the same unit of measurement) IMA=din/dout
Calculating Ideal Mechanical Advantage for Wheels and Axles If you are applying the input force to the axle, the ideal mechanical advantage of a wheel and axle is determined by the ratio of the radius of the axle (ra), to the radius of the wheel (rw). To calculate it, we use the following formula:
Ideal Mechanical Advantage = radius of axle(unit of measurement)/radius of wheel (the same unit of measurement)
IMA=ra/rw
If you are applying the input force to the wheel, the ideal mechanical advantage is determined by the ratio of the radius of the wheel, to the radius of the axle. To calculate it, we use the following formula:
Ideal Mechanical Advantage = radius of wheel (unit of measurement)/radius of axle (the same unit of measurement)
IMA=rw/ra
Calculating Ideal Mechanical Advantage for Pulleys Finding the ideal mechanical advantage of a pulley is easy. If it is a fixed pulley, the IMA is always one. If it is a pulley system or a movable pulley, then the IMA is equal to the number of support ropes.
IMA examples:1) Ralph pushes a box 4.5m up a ramp. The ramp is 2.8m tall. What is the ideal mechanical advantage of the ramp, rounded to the nearest hundredth? IMA=din/doutIMA=4.5/2.8IMA=1.61 The ramp's ideal mechanical advantage is 1.61.
2) Susie uses a lever to lift a box. The load arm of the lever is 2.1m long, and the effort arm is 75cm long. What is the ideal mechanical advantage of this lever, rounded to the nearest hundredth? *Make sure you use the same units, since it is a ratio. 2.1m=210cmIMA=din/doutIMA=75/210IMA=0.36 The lever's ideal mechanical advantage is 0.36. 3) Nathan is using a lever to raise a box to a height of 65cm. He pushes down on the effort arm through a distance of 1.31m. If the effort arm of the lever is 3.42m, then how long is the load arm, rounded to the nearest hundredth? *First, we must find the ideal mechanical advantage.IMA=din/doutIMA=131/65IMA=2.02 *Now we can substitute in the IMA to find the load arm's length.IMA=din/dout2.02=3.42/doutdout=3.43/2.02dout=1.7m The load arm is 1.7m long. 4) Watson holds onto the handle when he uses a screwdriver. The handle's radius is 1.5cm, and the shaft's radius is 2.1mm. What is the ideal mechanical advantage of the screwdriver, rounded to the nearest hundredth? *Make sure you use the same units, since it is a ratio. 1.5cm=15mm IMA=rw/raIMA=15/2.1IMA=7.14 The screwdriver's mechanical advantage is 7.14, if you hold onto the handle.Reversing the Equation If you already have the MA or IMA and you need to find out what another variable is, you can easily do that by isolating the variable you need to find. For example:
If you were given the MA and the input force, and you had to find the output force, you would rearrange the formula to: Fout=MA x Fin
If you were given the MA and the output force, and you had to find the input force, you would rearrange the formula to: Fin = Fout/MA
Calculating Mechanical AdvantageSince the mechanical advantage of a machine is determined by the ratio of the output force (Fout) in Newtons, to the input force (Fin) in Newtons, to calculate it we use the following formula:
Mechanical Advantage = output force (N)/input force (N)
MA=Fout/Fin
MA examples:1) 35N of force is exerted onto a crowbar to pry open a box. The crowbar exerts 95N of force onto the box. What is the crowbar's mechanical advantage, rounded to the nearest hundredth?
MA=Fout/FinMA=95/35MA=2.71
The crowbar's mechanical advantage is 2.71.
2) Tom turns a screwdriver using 6N of force. The screwdriver applies 20N of force onto the the screw. What is the mechanical advantage of the screwdriver, rounded to the nearest hundredth?
MA=Fout/FinMA=20/6MA=3.33
The screwdriver's mechanical advantage is 3.33.
3) Lola is pushing an 81 kg cart up a ramp. She has to exert 95N of force to push the cart up the ramp. What is the mechanical advantage of the ramp, rounded to the nearest hundredth?
*First, lets find out how much 81 kg weighs on earth. The force of gravity is 9.8N/kg.F=MgF=81(9.8)F= 793.8N
MA=Fout/FinMA=793.8/95MA=8.36
The ramp's mechanical advantage is 8.36.
Calculating Ideal Mechanical Advantage for Levers and Inclined PlanesThe ideal mechanical advantage of a lever or an inclined plane is determined by the ratio of the input distance (din), to the output distance (dout). If you do not have the input and output distances of a lever, you can still calculate its IMA by substituting the input distance with the effort arm's length, and the output distance with the load arm's length. Just remember, the arm lengths are not always equal to the input and output distances, but they are always equal in ratio. To calculate the IMA we use the following formula:
Ideal Mechanical Advantage = input distance (unit of measurement)/output distance (the same unit of measurement)
IMA=din/dout
Calculating Ideal Mechanical Advantage for Wheels and Axles
If you are applying the input force to the axle, the ideal mechanical advantage of a wheel and axle is determined by the ratio of the radius of the axle (ra), to the radius of the wheel (rw). To calculate it, we use the following formula:
Ideal Mechanical Advantage = radius of axle(unit of measurement)/radius of wheel (the same unit of measurement)
IMA=ra/rw
If you are applying the input force to the wheel, the ideal mechanical advantage is determined by the ratio of the radius of the wheel, to the radius of the axle. To calculate it, we use the following formula:
Ideal Mechanical Advantage = radius of wheel (unit of measurement)/radius of axle (the same unit of measurement)
IMA=rw/ra
Calculating Ideal Mechanical Advantage for Pulleys
Finding the ideal mechanical advantage of a pulley is easy. If it is a fixed pulley, the IMA is always one. If it is a pulley system or a movable pulley, then the IMA is equal to the number of support ropes.
IMA examples:1) Ralph pushes a box 4.5m up a ramp. The ramp is 2.8m tall. What is the ideal mechanical advantage of the ramp, rounded to the nearest hundredth?
IMA=din/doutIMA=4.5/2.8IMA=1.61
The ramp's ideal mechanical advantage is 1.61.
2) Susie uses a lever to lift a box. The load arm of the lever is 2.1m long, and the effort arm is 75cm long. What is the ideal mechanical advantage of this lever, rounded to the nearest hundredth?
*Make sure you use the same units, since it is a ratio. 2.1m=210cmIMA=din/doutIMA=75/210IMA=0.36
The lever's ideal mechanical advantage is 0.36.
3) Nathan is using a lever to raise a box to a height of 65cm. He pushes down on the effort arm through a distance of 1.31m. If the effort arm of the lever is 3.42m, then how long is the load arm, rounded to the nearest hundredth?
*First, we must find the ideal mechanical advantage.IMA=din/doutIMA=131/65IMA=2.02
*Now we can substitute in the IMA to find the load arm's length.IMA=din/dout2.02=3.42/doutdout=3.43/2.02dout=1.7m
The load arm is 1.7m long.
4) Watson holds onto the handle when he uses a screwdriver. The handle's radius is 1.5cm, and the shaft's radius is 2.1mm. What is the ideal mechanical advantage of the screwdriver, rounded to the nearest hundredth?
*Make sure you use the same units, since it is a ratio. 1.5cm=15mm IMA=rw/raIMA=15/2.1IMA=7.14
The screwdriver's mechanical advantage is 7.14, if you hold onto the handle.Reversing the Equation
If you already have the MA or IMA and you need to find out what another variable is, you can easily do that by isolating the variable you need to find. For example:
If you were given the MA and the input force, and you had to find the output force, you would rearrange the formula to:
Fout=MA x Fin
If you were given the MA and the output force, and you had to find the input force, you would rearrange the formula to:
Fin = Fout/MA
You can use this format to fit all the equations.
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