Answer Happy

OBJECTIVE: Students will use a meter stick and adjust the positions of weights on the meter stick to find the position of equilibrium. They will then compare those positions to the theoretical values found using Newton's 2nd Law for Rotation. APPARATUS: Meter stick, weights, demonstration balance, knife-edged clamps, string, triple beam balance INTRODUCTION: In the beginning of the semester, we learned about kinematics and motion in a straight line. There were several variables involved in this motion, including Force, F, speed, v, acceleration, a, and displacement, Ax or Ay. If an object is rotating, there are analogous variables that represent the rotation. For example, represents the angular distance the object has rotated, and is analogous to the displacement, Ax or Ay. The velocity with which the object rotates (angular velocity, @) is analogous to the linear (or translational) velocity, v, and the angular acceleration, a, is analogous to the linear (or translational) acceleration, a. A torque, T, causes the object to rotate instead of a force (although torque is related to force). Newton's 2nd Law for rotation states "the sum of the torques is equal to the moment of inertia, I, times the angular acceleration, a." In general, @ = 40/At, a = Aw/At, and t = Flcos0, where / is the perpendicular distance from a line through which the force acts to the point of rotation. In this lab, we will be investigating the situation of equilibrium. In the case, the sum of torques, the sum of forces in the x-direction, and the sum of forces in the y-direction are all equal to zero. We will balance a meter stick on a demonstration balance, and then experimentally add weights at different distances to determine a new equilibrium point. PROCEDURE: 1. Begin by determining the center of mass of the meter stick using a demonstration balance and knife-edged clamp. Place the meter stick in the clamp and then the pair on the demonstration balance. Find and record the location where the meter stick is in equilibrium. That will be your pivot point and will not change. Why must the rod be level? Where do you expect the center of mass to be? If it is not where you expect, what may be the reason?
2. Place a 10 g mass on the meter stick 15 cm to the left of the pivot point. Now slide a 5 g mass along the portion of the meter stick to the right of the pivot point until you find the location where the meter stick and masses are in equilibrium. Record this distance (use the center of the weight as the position), and sketch the situation, including the masses of the weights, their positions, the meter stick, and the pivot. 3. Place the 5 g and 10 g masses at different, random locations on the meter stick to the right of the pivot. Experimentally determine where a 20 g mass must be placed in order to balance the meter stick and masses. Record the position of the center of the weights and corresponding weights, as well as make a sketch of the situation. 4. Your turn! Choose your own set of masses & positions (at least 3) & try to balance the system. Don't use masses & positions that we have used previously. 5. Now determine the mass of the meter stick. Move the meter stick off-center from the pivot so that the point of rotation is not the same as the center of mass of the meter stick. Determine the location of a 5 g, 10 g, or 20 g mass that balances the system. (You choose the mass). 6. Determine the exact mass of your meter stick using the triple beam balance. ANALYSIS 1. Using the conditions for equilibrium, theoretically determine the location of the 5 g mass in step 2, the 20 g mass in step 3, and your chosen mass in step 4. (Hint: use Newton's 2nd law for rotation). 2. Find the % error between the theoretical position and the experimental position in each of the above cases. What is a possible cause for this error? 3. Using the data from procedure step 5, and the conditions for equilibrium, determine the mass of the meter stick. 4. What is the % difference between the calculated mass and the measured mass?
BALANCING ACT 1. Meter stick at equilibrium = 49.5 cm 2. 10g mass at 34.5cm = 5g mass at 65 cm 3. MASS LOCATION 65 cm 5g 76 cm (found experimentally) 11cm Mass Location Mass of meter Location of the meter stick stick 5g 31.5cm 39cm 6. The exact mass of meter stick = 78.5g ANALYSIS 1. Using the conditions for equilibrium, theoretically determine the location of the 5 g mass in step 2, the 20 g mass in step 3, and your chosen mass in step 4. (Hint: use Newton's 2nd law for rotation). 2. Find the % error between the theoretical position and the experimental position in each of the above cases. What is a possible cause for this error? 3. Using the data from procedure step 5, and the conditions for equilibrium, determine the mass of the meter stick. 4. What is the % difference between the calculated mass and the measured mass 10g 20g 4. 5.