You are standing at rest on the ramp shown in the figure below. Is the magnitude of the normal force acting on your bottom foot greater than, less than, or equal to the magnitude of the normal force acting on your top foot?
Figure12.10.1.A person standing on a ramp.
Tip1.
A relevant representation is often helpful in both constructing and communicating your explanation. For a situation like this one, try using an extended free-body diagram to help guide your reasoning.
Tip2.
Once you have drawn an extended free-body diagram, a good starting point is the fundamental physical law relating torques and angular acceleration.
A*R*C*S12.10.2.Massive Pulley.
Two massive blocks are shown in the figure below, connected to each other by a rope over a pulley with nonzero mass. Find the acceleration of both masses and of the pulley.
Figure12.10.2.Two massive blocks connected to a massive pulley.
Tip1.
Analyze and Represent: Sketch and label free-body diagrams for each object. When you choose a coordinate system for each object, make sure to describe the direction of the acceleration for each object using that coordinate system.
Tip2.
Calculate: In this situation, it can be a good idea to let your free-body diagrams do a lot of work for you. For each free-body diagram, try to find an equation (or more than one) that quantitatively relates known quantities and unknown quantities.
Tip3.
Sensemake: Use a special-case analysis and the fact that you may have solved this problem previously when the pulley is massless.
Activity12.10.3.Metacognitive Reflection.
Choose an object from your everyday experience, different from any of the situations you encountered so far in physics, that has at least one non-zero torque (it can have many, and the net torque can even be zero) and give a brief description of all the forces and torques on it. Sketch a free-body diagram for the object and explain how your diagram is consistent with both the Law of Motion and the Angular Law of Motion.
