State and apply Newton's second law, $F_{net} = ma$, to calculate net force, mass or acceleration, and analyze situations with several forces by finding the net force first.

What this topic is asking

Newton's second law is the most-used equation in Regents mechanics. The Physical Setting/Physics course asks you to relate the net force on an object to its acceleration and mass through $F_{net} = ma$, and to use it both ways: to find the acceleration from the forces, and to find a force from a known acceleration. The exam tests it on single objects, in multi-force situations where you must compute the net force first, and in qualitative items about the proportionalities.

Newton's second law

The law makes two intuitions precise: a larger net force produces a larger acceleration, and a more massive object is harder to accelerate. The net force is the single force equivalent to all the forces acting, found by adding them as vectors. This is why the first step in almost every problem is to combine the forces, not to plug a single force into the equation.

The two proportionalities

These relationships let you answer many Regents items without a calculator. If a problem triples the net force on a cart, the acceleration triples; if it loads the cart so the mass doubles under the same force, the acceleration halves. Recognizing the proportional reasoning is often quicker than a full calculation.

Finding the net force first

In a multi-force situation, the forces must be combined before the second law is applied. Along one line, add forces in the direction of motion and subtract those opposing it. A box pushed with $40$ N against $10$ N of friction has a net force of $30$ N, and it is this $30$ N, not the $40$ N push, that goes into $F_{net} = ma$. Using the applied force alone, forgetting friction, is the single most common error.

The same logic extends to vertical and horizontal directions separately. Often the vertical forces balance (no vertical acceleration), giving the normal force, while the horizontal forces give the net force that accelerates the object.

Reference Tables note

The equation $F_{net} = ma$ is printed in the Mechanics section of the Reference Tables, along with the weight relation $F_g = mg$ (which is itself the second law applied to gravity, since $a = g$). The friction relation $F_f = \mu F_N$ is also printed and supplies one of the forces you combine. You provide the strategy of summing forces to get the net force before substituting.

Try this

Q1. A net force of $18$ N acts on a $6.0$ kg object. Calculate its acceleration. [2 points]

• Cue. $a = \dfrac{F_{net}}{m} = \dfrac{18}{6.0} = 3.0$ m/s squared.

Q2. State what happens to an object's acceleration if the net force on it is halved while its mass is unchanged. [1 point]

• Cue. The acceleration halves (it is proportional to the net force at fixed mass).