Force — Question 1

Question 1

A force requires both an agent and a recipient

A hand pushes a box across a horizontal table. Earth attracts the box, the table supports it and a measured horizontal table resistance acts opposite the motion. Ignore air.

1. Name each force on the box by agent and recipient.

2. Is the force of the box on the hand another force on the box?

3. Which listed interactions are contact interactions?

Question 1 - Solution

A force requires both an agent and a recipient

(a) Keep one recipient.

$$\vec F_{\mathrm{box}}=\vec F_{H\to B}+\vec F_{E\to B}+N\hat y-f\hat x$$ The forces on the box are hand on box, Earth on box, table’s normal on box and table’s tangential resistance on box. Normal and tangential labels distinguish components of the table interaction.

(b) Do not exchange the recipient.

$$\vec F_{B\to H}=-\vec F_{H\to B},\quad\text{recipient}(\vec F_{B\to H})=H$$ Box on hand acts on the hand and belongs on a hand diagram. Adding it to the box diagram would mix two bodies and double-count the interaction incorrectly.

(c) Classify by physical contact.

$$\boxed{\vec F_{\mathrm{contact}}=\vec F_{H\to B}+N\hat y-f\hat x},\quad\vec F_g=-mg\hat y$$ Hand and table forces require contact in this model. Earth’s gravitational attraction does not require local material contact with the box. A force is an interaction, not a property stored in a moving object.