Physics for Life Sciences I – Lecture 10: Forces, Ropes & Pulleys, Circular Motion, and Gravitation

Recap: Forces – Weight, Friction, and Drag

Weight

The weight of an object is the force due to gravity acting downward on its mass.

• Definition: $\vec{w} = m\vec{g}$, where $m$ is mass and $\vec{g}$ is the acceleration due to gravity.

• Direction: Always vertically downward.

Friction

Friction is a force that opposes the relative motion between two surfaces in contact.

• Static friction: $\vec{f}_s = (0 \text{ to } \mu_s n)$, acts to prevent motion.

• Kinetic friction: $\vec{f}_k = \mu_k n$, acts opposite to the direction of motion.

• General friction: $\vec{f} = \mu n$, where $\mu$ is the coefficient of friction and $n$ is the normal force.

Drag

Drag is a resistive force experienced by objects moving through a fluid (air or liquid).

• Reynolds number: $\text{Re} = \frac{\rho v^2 L^2}{\eta L v}$, compares inertial to viscous forces.

• High Reynolds number ($\text{Re} > 1000$): Drag force $\vec{D} \propto v^2$.

• Low Reynolds number (Stokes' law): $\vec{D}_{\text{sphere}} = 6\pi \eta r v$, drag is proportional to velocity.

Terminal Velocity

When a falling object reaches terminal speed, the drag force exactly balances the weight, resulting in zero acceleration.

• Condition: $\vec{D} = \vec{w}$ and $\vec{a} = 0$.

• Application: Skydivers reach terminal velocity when air resistance equals their weight.

Section 5.8: Ropes and Pulleys

Massless Strings and Ropes

In many physics problems, ropes and strings are assumed to be massless to simplify calculations.

• Massless approximation: $m_{\text{rope}} = 0$.

• Tension force: The tension $\vec{T}$ in a massless rope transmits force undiminished from one end to the other.

• Newton's Second Law for Rope: $F_{\text{box on rope}} = F = T = m_{\text{rope}} a_x = 0$.

Properties of Tension in Massless Ropes

• Force transmission: If you pull one end of a rope with force $F$, the other end pulls with the same magnitude $F$.

• Uniform tension: The tension is the same throughout the rope.

Pulleys

Ideal pulleys are assumed to be massless and frictionless, which means they do not change the tension in the rope passing over them.

• Property: Tension in the string is the same on both sides of the pulley.

• Application: Used in problems involving connected masses and mechanical advantage.

Tactics for Working with Ropes and Pulleys

• If a force pulls on one end of a rope, the tension equals the magnitude of the pulling force.

• If two objects are connected by a rope, the tension is the same at both ends.

• If the rope passes over a pulley, the tension remains unaffected.

Situation	Tension Property
Force on one end	Tension equals pulling force
Two objects connected	Same tension at both ends
Rope over pulley	Tension unaffected

Example: In a system where two masses are connected by a massless rope over a frictionless pulley, both masses experience the same tension force.

*Additional info: The notes above are expanded from the provided slides and include definitions, equations, and applications relevant to introductory college physics, especially for life sciences majors. The table is inferred from the "Tactics Box" slide and general principles of tension in ropes and pulleys.*