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2.5 Newton’s Second Law

Syllabus
2024
Topic
2.5
Level
—

Learning objectives

2.5A—Describe the conditions under which a system’s velocity changesDescribe the conditions under which a system’s velocity changes.• Unbalanced forces are a configuration of forces such that the net force exerted on a system is not equal to zero.• Newton’s second law of motion states that the acceleration of a system’s center of mass has a magnitude proportional to the magnitude of the net force exerted on the system and is in the same direction as that net force. Relevant equation:• The velocity of a system’s center of mass will only change if a nonzero net external force is exerted on that system. TOPIC 2.6 Gravitational Force | AP Physics 1: Algebra-Based Course and Exam Description

Net external force changes velocity

Recognize unbalanced forces

Forces are unbalanced when their vector sum is not zero. A system's center-of-mass velocity changes only when a nonzero net external force acts on the system.

Connect force, mass, and acceleration

a⃗sys=∑iF⃗imsys=F⃗netmsys\vec a_{\text{sys}}=\frac{\sum_i \vec F_i}{m_{\text{sys}}}=\frac{\vec F_{\text{net}}}{m_{\text{sys}}}

Calculate and interpret

Worked example: choose right as positive. A 4.0 kg4.0\,\text{kg} cart has a 12 N12\,\text{N} force right and a 4.0 N4.0\,\text{N} force left.

Fnet=+12−4.0=+8.0 NF_{\text{net}}=+12-4.0=+8.0\,\text{N}

a=Fnetm=+8.0 N4.0 kg=+2.0 m/s2a=\dfrac{F_{\text{net}}}{m}=\dfrac{+8.0\,\text{N}}{4.0\,\text{kg}}=+2.0\,\text{m/s}^2.

The positive result means the cart's velocity changes by 2.0 m/s2.0\,\text{m/s} toward the right each second.

Predict proportional changes

Change Acceleration consequence
Double ∣F⃗net∣|\vec F_{\text{net}}| at fixed mass Double ∣a⃗∣|\vec a|
Double msysm_{\text{sys}} at fixed net force Halve ∣a⃗∣|\vec a|
Reverse F⃗net\vec F_{\text{net}} Reverse a⃗\vec a

Separate acceleration from velocity

Acceleration points with the net force, but velocity need not. If the cart is initially moving left while the net force points right, it first slows down. For a multi-object system, sum external forces and use the total system mass to describe the center-of-mass acceleration; internal forces do not enter that external-force sum.