Question

A hanging potted plant is suspended by a cord from a hook in the ceiling. Draw an FBD for each of these: (a) the system consisting of plant, soil, and pot; (b) the cord; (c) the hook; (d) the system consisting of plant, soil, pot, cord, and hook. Label each force arrow using subscripts (for example, \(\overrightarrow{\mathbf{F}}_{\mathrm{ch}}\) would represent the force exerted on the cord by the hook).

Short answer

Question: Draw free body diagrams (FBD) for each case in the hanging potted plant system, and identify the forces acting on each component. a) Plant, soil, and pot b) The cord c) The hook d) The entire system (plant, soil, pot, cord, and hook) Answer: a) The plant, soil, and pot FBD has tension force (\(\overrightarrow{\mathbf{F}}_{\mathrm{t}}\)) acting upward and gravitational force (\(\overrightarrow{\mathbf{F}}_{\mathrm{g}}\)) acting downward. b) The cord FBD has the force exerted by the hook on the cord (\(\overrightarrow{\mathbf{F}}_{\mathrm{hc}}\)) acting upward, and the tension force (\(\overrightarrow{\mathbf{F}}_{\mathrm{t}}\)) acting downward. c) The hook FBD has the force exerted by the ceiling on the hook (\(\overrightarrow{\mathbf{F}}_{\mathrm{ch}}\)) acting upward and the force exerted by the cord on the hook (\(\overrightarrow{\mathbf{F}}_{\mathrm{hc}}\)) acting downward. d) The entire system FBD has the gravitational force (\(\overrightarrow{\mathbf{F}}_{\mathrm{g}}\)) acting downward and the force exerted by the ceiling on the hook (\(\overrightarrow{\mathbf{F}}_{\mathrm{ch}}\)) acting upward.

Step-by-step solution

Case (a): Plant, soil, and pot

To draw the FBD for the system consisting of plant, soil, and pot, we need to consider the following forces acting on the system: 1. Gravitational force (\(\overrightarrow{\mathbf{F}}_{\mathrm{g}}\)) acting on the system which is equal to the mass of plant, soil, and pot times acceleration due to gravity (\(m_{p}\times g\)). 2. Tension force in the cord (\(\overrightarrow{\mathbf{F}}_{\mathrm{t}}\)) acting upward, which balances the gravitational force. The free body diagram for the plant, soil, and pot will include the tension force acting upward and the gravitational force acting downward.

Case (b): The cord

To draw the FBD for the cord, we need to consider the following forces acting on the cord: 1. The force exerted by the hook on the cord (\(\overrightarrow{\mathbf{F}}_{\mathrm{hc}}\)) acting upward. 2. The tension force acting in the cord (\(\overrightarrow{\mathbf{F}}_{\mathrm{t}}\)) acting downward (equal and opposite to \(\overrightarrow{\mathbf{F}}_{\mathrm{hc}}\)). The free body diagram for the cord will have two equal and opposite forces acting on it: the force exerted by the hook on the cord and the tension force.

Case (c): The hook

To draw the FBD for the hook, we need to consider the following forces acting on the hook: 1. The force exerted by the ceiling on the hook (\(\overrightarrow{\mathbf{F}}_{\mathrm{ch}}\)) acting upward. 2. The force exerted on the hook by the cord (\(\overrightarrow{\mathbf{F}}_{\mathrm{hc}}\)) acting downward (equal and opposite to \(\overrightarrow{\mathbf{F}}_{\mathrm{ch}}\)). The free body diagram for the hook will have two equal and opposite forces acting on it: the force exerted by the ceiling on the hook and the force exerted by the cord on the hook.

Case (d): Plant, soil, pot, cord, and hook (entire system)

To draw the FBD for the entire system, we need to consider the following forces acting on the system: 1. Gravitational force (\(\overrightarrow{\mathbf{F}}_{\mathrm{g}}\)) acting on the plant, soil, and pot which is equal to the mass of plant, soil, and pot times acceleration due to gravity (\(m_{p}\times g\)). 2. The force exerted by the ceiling on the hook (\(\overrightarrow{\mathbf{F}}_{\mathrm{ch}}\)) acting upward (equal and opposite to the gravitational force). The free body diagram for the entire system will have two equal and opposite forces acting on it: the gravitational force acting downward and the force exerted by the ceiling on the hook acting upward.