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The passage reads:
"A laboratory pan balance is constructed as shown in Figure 1.
Figure 1
The rod has a mass of 0.5 kg. The counterweight has a mass of 0.01 kg. With nothing on the pan, the rod is balanced at x = 1 cm. As low-mass items such as chemical samples are added to the pan, the counterweight can be moved to balance out the torques and in doing so determine the weight of the item added to the pan."
8. What is the mass of the pan?
A. 0.1kg
B. 0.5 kg
C. 1.0 kg
D. 5.0 kg
Choice B is the best answer. With the rod balanced, the net torque on the rod is zero, so the torque on the left side is equal to the torque on the right side. The picture below shows the balanced system with an empty pan. You may note that the counter-weight is trivial in terms of mass and moment arm relative to the pan and rod, so the empty pan is essentially balanced by the asymmetric positioning of the rod on the fulcrum. Both the empty pan and rod's center of mass are 10 cm from the fulcrum, so the system is essentially balanced if the pan has the same mass as the rod. This means the best answer is the one that is closest to the rod's mass, 0.50 kg.
We can verify the answer we chose using visualization by applying torque math. We simply need to set all of the magnitudes of torque on the right side equal to the magnitude of torque on tiie left side. Choosing the fulcrum as the pivot point, we calculate the net torque about this point. Note that the weight of the rod exerts a torque on the rod. The rod's center of mass is 10 cm away from the fulcrum. Let the mass of the pan be m. Then:
Solving for m we get:
(10 cm)mg = (1 cm)(0.01 kg)(g) + (10 cm)(0.5 kg)(g)
This confirms that the mass of the pan must be essentially equal to the mass of the rod. You may note that this particular system can only measure small masses, because the counterweight is so light The best answer is choice B.
In general on questions like this how come the weight of the rod is only considered on one side of the question? Is this because you consider the center of the mass the only point in which the force is acting so you only take it into account on the side of the equation that has the center of mass on one side of the fulcrum?
"A laboratory pan balance is constructed as shown in Figure 1.
Figure 1
The rod has a mass of 0.5 kg. The counterweight has a mass of 0.01 kg. With nothing on the pan, the rod is balanced at x = 1 cm. As low-mass items such as chemical samples are added to the pan, the counterweight can be moved to balance out the torques and in doing so determine the weight of the item added to the pan."
8. What is the mass of the pan?
A. 0.1kg
B. 0.5 kg
C. 1.0 kg
D. 5.0 kg
Choice B is the best answer. With the rod balanced, the net torque on the rod is zero, so the torque on the left side is equal to the torque on the right side. The picture below shows the balanced system with an empty pan. You may note that the counter-weight is trivial in terms of mass and moment arm relative to the pan and rod, so the empty pan is essentially balanced by the asymmetric positioning of the rod on the fulcrum. Both the empty pan and rod's center of mass are 10 cm from the fulcrum, so the system is essentially balanced if the pan has the same mass as the rod. This means the best answer is the one that is closest to the rod's mass, 0.50 kg.
We can verify the answer we chose using visualization by applying torque math. We simply need to set all of the magnitudes of torque on the right side equal to the magnitude of torque on tiie left side. Choosing the fulcrum as the pivot point, we calculate the net torque about this point. Note that the weight of the rod exerts a torque on the rod. The rod's center of mass is 10 cm away from the fulcrum. Let the mass of the pan be m. Then:
Solving for m we get:
(10 cm)mg = (1 cm)(0.01 kg)(g) + (10 cm)(0.5 kg)(g)
This confirms that the mass of the pan must be essentially equal to the mass of the rod. You may note that this particular system can only measure small masses, because the counterweight is so light The best answer is choice B.
In general on questions like this how come the weight of the rod is only considered on one side of the question? Is this because you consider the center of the mass the only point in which the force is acting so you only take it into account on the side of the equation that has the center of mass on one side of the fulcrum?
