How to find an unknown mass using a lever
PLEASE FILL THE BLANKS FOR FULL CREDIT.
PLEASE R-E-A-D before declaring you are "confused"
The work is individual but please use collaborative learning.
DISCUSSION: What is a torque ?
A torque (or turning effect) is what causes an object to rotate.
The same way a force is what causes an object to move in a straight line.
Let's say you want to open the door of the Physics lab by pushing it:
An object at rest is in equilibrium. The sum of the forces exerted is zero. The resting object also shows another aspect of equilibrium. Because the object has no rotation, the sum of the torques exerted is zero.
The see-saw is a simple machine that rotates about a pivot or fulcrum. It is a type of lever. Levers make work easier to accomplish a variety of tasks. Suppose you try to balance an elephant on a see saw. The elephant weighs 2000 kg and you weighs 50kg. The elephant is to stand 2m from the fulcrum. How far from the fulcrum you need to stand from the fulcrum, on the other side, to balance the elephant ?_________________________
hint: torque exerted by elephant = torque exerted by player
EQUILIBRIUM : The torque exerted by the elephant = torque exerted by the player.
PART 1:
PURPOSE:
You will balance a meter stick with a known mass and an unknown mass. You will compute the mass of the unknown.
PROCEDURE:
STEP1: Balance the meterstick horizontally with nothing hanging from it. Record the position of the CG of the meter stick.
Position of meter stick CG (center of gravity) = ______________________
Balance the meter stick on a knife-edge at the CG.
Using a string or rubber band, attach an object of unknown mass, such as a rock, at the 90-cm mark of the meter stick, as shown below. Place a known mass on the other side of the meter stick to balance the meter stick.
STEP2:Compute the distances from the fulcrum (knife-edge) to each object.
distance from fulcrum to unknown mass ______________________
distance from fulcrum to known mass _______________________
ANALYSIS
1) These two distances as known as lever arms. The lever arm is the distance from the fulcrum to the place where the force acts. In the following space, write an equation for balanced torques, first in words and then with the known values. Compute the unknown mass.
mass computed = __________________________
2) using a spring scale, measure the unknown mass. mass true = ___________________________
3) Calculate the percentage difference (% error) = (computed - true) / true x 100 = _______________ (positive number)
PART 2
PURPOSE: We will use the same idea to compute the mass of the meter stick.
PROCEDURE:
STEP1: Place the fulcrum exactly on the 85cm mark. Balance the meter stick using a single mass hung between the 85cm and 100cm marks. Record the mass used and its position:
mass= __________________ position: _______________________
pub google
ANALYSIS
1) the weight that you hung balances the weight of meter stick located at the CG (computed above around 50cm mark).
Draw a lever diagram: Draw an horizontal line for the meter stick and draw the 2 forces acting on it. Don't forget to draw the fulcrum as a triangle ∆. label your diagram
2) Compute the mass of the meter stick using:
torque exerted by the weight of the meter stick = torque exerted by the weight of the mass.
mass computed __________________________
3) Find the true mass of the meter stick: true mass ________________
4) Compute the % error ___________________
GOING FURTHER
1) A 45 kg girl is sitting on a seesaw 0.6m from the balance point (fulcrum). How far, on the other side, should a 60kg boy sit so that the seesaw will remain in balance ?/
2) You pen the lab door but that time your force makes a 30 degrees angle with the door:
Let's trace an X,Y coordinate system. F is attached to the origin. The X-axis is along the lever arm and the Y-axis is perpendicular to the lever arm.
A) Trace in green or blue of x-component of F (Fx) and the y-component of F (Fy).
hint: first trace Fx from the origin to right , then Fy connects the head of Fx to the head of F.
Only Fy is producing the torque that opens the door: τ = Fy x L .Fy is perpendicular of the lever arm (the door)
L is the distance between the axis of rotation and the origin (where the force is applied) = lever arm.
If F= 5N, L = 80cm and angle = 30 find the y-component of Fy = _______________ (use sine and F=5N)
. τ = _____________ (hint: use τ = Fy x L don't forget to convert cm to m first)
If now you open the dorr with a 5N force but that time the force is perpendicular to the door. (the angle is 90 degrees).
τ = _____________ (hint : use τ = F x L. In that case, Fy = F)
conclusion __________________________________________________________
hint: if you want to open a door, it is more efficient to apply the force __________________________
A torque (or turning effect) is what causes an object to rotate.
The same way a force is what causes an object to move in a straight line.
Let's say you want to open the door of the Physics lab by pushing it:
The torque τ measures how efficient is your action in moving the door. The torque depends on your push (the force F) and on the distance L
(called lever arm) between the axis and the point where the force is
applied. Here we suppose that the applied force is perpendicular to the
door. torque = force x lever arm Units are N.m
So if the force you applied is 5N, and the distance L is 80 cm then τ = _________ N.m (convert cm to m)
Something to remember: counterclockwise torques are positive and clockwise torques are negative.
So if I close the door of the lab by pulling the door clockwise then τ = _________ N.m (same force and distance).
So if the force you applied is 5N, and the distance L is 80 cm then τ = _________ N.m (convert cm to m)
Something to remember: counterclockwise torques are positive and clockwise torques are negative.
So if I close the door of the lab by pulling the door clockwise then τ = _________ N.m (same force and distance).
An object at rest is in equilibrium. The sum of the forces exerted is zero. The resting object also shows another aspect of equilibrium. Because the object has no rotation, the sum of the torques exerted is zero.
The see-saw is a simple machine that rotates about a pivot or fulcrum. It is a type of lever. Levers make work easier to accomplish a variety of tasks. Suppose you try to balance an elephant on a see saw. The elephant weighs 2000 kg and you weighs 50kg. The elephant is to stand 2m from the fulcrum. How far from the fulcrum you need to stand from the fulcrum, on the other side, to balance the elephant ?_________________________
hint: torque exerted by elephant = torque exerted by player
EQUILIBRIUM : The torque exerted by the elephant = torque exerted by the player.
PART 1:
PURPOSE:
You will balance a meter stick with a known mass and an unknown mass. You will compute the mass of the unknown.
PROCEDURE:
STEP1: Balance the meterstick horizontally with nothing hanging from it. Record the position of the CG of the meter stick.
Position of meter stick CG (center of gravity) = ______________________
Balance the meter stick on a knife-edge at the CG.
Using a string or rubber band, attach an object of unknown mass, such as a rock, at the 90-cm mark of the meter stick, as shown below. Place a known mass on the other side of the meter stick to balance the meter stick.
STEP2:Compute the distances from the fulcrum (knife-edge) to each object.
distance from fulcrum to unknown mass ______________________
distance from fulcrum to known mass _______________________
ANALYSIS
1) These two distances as known as lever arms. The lever arm is the distance from the fulcrum to the place where the force acts. In the following space, write an equation for balanced torques, first in words and then with the known values. Compute the unknown mass.
mass computed = __________________________
2) using a spring scale, measure the unknown mass. mass true = ___________________________
3) Calculate the percentage difference (% error) = (computed - true) / true x 100 = _______________ (positive number)
PART 2
PURPOSE: We will use the same idea to compute the mass of the meter stick.
PROCEDURE:
STEP1: Place the fulcrum exactly on the 85cm mark. Balance the meter stick using a single mass hung between the 85cm and 100cm marks. Record the mass used and its position:
pub google
ANALYSIS
1) the weight that you hung balances the weight of meter stick located at the CG (computed above around 50cm mark).
Draw a lever diagram: Draw an horizontal line for the meter stick and draw the 2 forces acting on it. Don't forget to draw the fulcrum as a triangle ∆. label your diagram
2) Compute the mass of the meter stick using:
torque exerted by the weight of the meter stick = torque exerted by the weight of the mass.
mass computed __________________________
3) Find the true mass of the meter stick: true mass ________________
4) Compute the % error ___________________
GOING FURTHER
1) A 45 kg girl is sitting on a seesaw 0.6m from the balance point (fulcrum). How far, on the other side, should a 60kg boy sit so that the seesaw will remain in balance ?/
2) You pen the lab door but that time your force makes a 30 degrees angle with the door:
Let's trace an X,Y coordinate system. F is attached to the origin. The X-axis is along the lever arm and the Y-axis is perpendicular to the lever arm.
A) Trace in green or blue of x-component of F (Fx) and the y-component of F (Fy).
hint: first trace Fx from the origin to right , then Fy connects the head of Fx to the head of F.
Only Fy is producing the torque that opens the door: τ = Fy x L .Fy is perpendicular of the lever arm (the door)
L is the distance between the axis of rotation and the origin (where the force is applied) = lever arm.
If F= 5N, L = 80cm and angle = 30 find the y-component of Fy = _______________ (use sine and F=5N)
. τ = _____________ (hint: use τ = Fy x L don't forget to convert cm to m first)
If now you open the dorr with a 5N force but that time the force is perpendicular to the door. (the angle is 90 degrees).
τ = _____________ (hint : use τ = F x L. In that case, Fy = F)
conclusion __________________________________________________________
hint: if you want to open a door, it is more efficient to apply the force __________________________
B) advanced physics: (optional)
A uniform ladder of length lm and weight 100N rests against a smooth vertical wall. The coefficient of static friction between the bottom of the ladder and the floor is 0.5. Draw a free-body diagram. Find the minimum angle that the ladder can make with the floor so that the ladder will not slip.
3) A uniform meter stick (1kg) is hanging from a thread at its midpoint. A block of 3 kg hangs from the left end of the meter stick. (mark 0cm). Another block, of unkown mass M, hangs below the 80cm mark. The meter stock remains at rest in an horizontal position. Find the unkown mass. M.
4) optional. (even more advanced)
In the figure below, what is the torque about the pendulums suspension point produced by the weight of the bob, given that the lengh of the pendulum, L, is 80cm and m = 0.5kg. ? The angle between the thread and the ceiling is 60 degrees.
A uniform ladder of length lm and weight 100N rests against a smooth vertical wall. The coefficient of static friction between the bottom of the ladder and the floor is 0.5. Draw a free-body diagram. Find the minimum angle that the ladder can make with the floor so that the ladder will not slip.
3) A uniform meter stick (1kg) is hanging from a thread at its midpoint. A block of 3 kg hangs from the left end of the meter stick. (mark 0cm). Another block, of unkown mass M, hangs below the 80cm mark. The meter stock remains at rest in an horizontal position. Find the unkown mass. M.
4) optional. (even more advanced)
In the figure below, what is the torque about the pendulums suspension point produced by the weight of the bob, given that the lengh of the pendulum, L, is 80cm and m = 0.5kg. ? The angle between the thread and the ceiling is 60 degrees.
pub google
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