Objective To use the principle of balanced torques to find the value of an unknown distance and to investigate the conce

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Objective To Use The Principle Of Balanced Torques To Find The Value Of An Unknown Distance And To Investigate The Conce 1 (176.65 KiB) Viewed 16 times

Objective To use the principle of balanced torques to find the value of an unknown distance and to investigate the concept of center of gravity. Theory First condition of equilibrium An object doesn't move. Therefore, the vector sum of all forces exerted on the object must be equal to zero. ΣF = 0 (1) Second condition of equilibrium The resting object also doesn't rotate. Therefore, the sum of all torques exerted on it is zero. Στ = 0 0 t = Fr sin e (2) r is the distance from the point where the forse exerted to the axis of rotation. F is the force acting on the object at point r. O is an angle between F and r. An object balances when all torques on it add up to zero. In this sum, the torques tending to rotate the object in the chosen positive direction should be taken with the sign “plus” whereas the torques tending to rotate the object in the negative (opposite) direction should be taken with the sign "minus". Earth's gravity pulls on every part of an object. It pulls stronger on the more massive parts and weaker on the less massive parts. The sum of all these pulls is the weight of the object. The weight is exerted on the object at its center of gravity, or C... In this experiment, you will balance a uniform stick of mass M, on a pin with two known values (M and M2) to check the conditions of equilibrium experimentally.
A. Change the pivot point on stick cm30 2011 cm50 cm70 பபபா Click and hold (purple circle). Move your mouse left or right to change pivot point. Check Xpin for pivot point at the top left corner VIII wuy Libya Ipin = 0.456 N=95 Tnet = -4.18 cm 30 cm 50 cm70 ***** B. Change mass value and position Xq=0.139 X2=0.827 Click and hold (top circle). Changes the mass value. (Up or down) cm 30 cm50 vu cm70 299.2 m=256 Click and hold (bottom circle). Changes the position. (left or right)
EXPERIMENT Note: the center of gravity of a uniform stick is at its geometric center (50cm mark) PART 1: PIVOT POINT AT THE CENTER OF GRAVITY (c.g) -20 cm M = 200kg c.g. M2 = 100kg 1. Set the pivot point at the center of the stick Xpin =0.5 (or 50cm) and choose the stick mass Ms = 100kg. 2. Place My = 200 kg mass at x1= 0.3 (30cm) 3. Find the position where M2 = 100 kg will produce equilibrium (zero net torque) 4. Determine the distance X between the M, and the pivot point. Xexp Analyzing the data L= 20cm c.g. M200 = 200kg * g M100 = 100kg*g If we choose the clockwise direction of rotation around the pivot point as a positive direction of rotation the equation for balanced torques takes the form (see the diagram and check the "Equilibrium" lecture on how to derive this equation) M100X - M200 L = 0 Find the theoretical value of x from this equation: Xtheory = and determine the percentage error
%error = Xexp-Xtheory Xtheory x 100% = PART 2: PIVOT POINT AT 40 CM MARK (10 CM TO THE LEFT OF THE CENTER OF GRAVITY) X 20 cm - 10 cm c.g. (@ 40cm mark) Weight of Stick M2 = 100kg M = 200kg 1. Set the pivot point at the mark Xpin=.4 (or 40cm) and choose the stick mass M = 100 kg 2. Place M1 = 200 kg mass at x1= 0.2 (20cm) 3. Find the position where M2 = 100 kg will produce equilibrium (zero net torque) 4. Determine the distance X between the M2 and the pivot point. Xexp =. Analyzing the data X d-20 cm -1 c.g. (a 40cm mark) M200 = 200kg *g Ms = 100kg *g M100 = 100kg *g If we choose clockwise direction of rotation around the pivot point as a positive direction of rotation the equation for balanced torques takes the form (see the diagram and check the "Equilibrium" lecture on how to derive this equation) M100X + Ms.L-M200.d = 0
Find the theoretical value of X from this equation: | Xtheory and determine the percentage error %error = Xexp-Xtheory Xtheory X 100% = Questions 1. How well did your experiment check the two conditions of equilibrium? Explain 2. What is the impact of each condition of equilibrium on the motion of a rigid body?