Question 7.CE.5: Balancing a bread knife You balance a bread knife by laying ......
Balancing a bread knife You balance a bread knife
by laying the flat side across one finger, as shown below. Where is the center of mass of the knife? How does the mass of the knife on the left side of the balance point compare to the mass of the knife on the right side of the balance point?
Sketch and translate We choose the knife as the system and orient a vertical y-axis upward.
Simplify and diagram Two objects exert forces on the knife: the finger exerts an upward normal force and Earth exerts a downward gravitational force. Since the knife is rotationally stable, these two forces must both pass through the axis of rotation at the location of the finger. If not, there would be an unbalanced torque exerted on the knife and it would tip. You can assume that the gravitational force is exerted at the knife’s center of mass. Thus, the To determine how the mass on the right side of the balance point compares to the mass on the left side, we model the knife as two small spheres of mass m_1 and mass m_2 , connected by a massless rod. The spheres are located at the center of mass of the respective sides of the knife. When the knife is balanced, there is less distance between sphere 1 and the balance point than between sphere 2 and the balance point. Thus, the mass of the handle end must be greater than the mass of the cutting end.
Try it yourself: A barbell has a 10 kg plate on one end and a 5-kg plate on the other end. Where is the center of mass of the barbell, which is also the balance point for the barbell? Ignore the mass of the 1.0-m-long rod that connects the plates on the ends.
Answer: The center of mass is 0.33 m from the 10-kg end and 0.67 m from the 5-kg end. center of mass must be directly above the finger.
