Formula
The force acting on a body equals the product of its mass and acceleration: F = ma.
ENT-level problem
A block of mass $m = 5$ kg slides down an inclined plane that makes an angle $\alpha = 30°$ with the horizontal. The coefficient of friction between the block and the plane is $\mu = 0.2$. Find the acceleration of the block. The acceleration due to gravity is $g = 10$ m/s².
Resolve the weight into components: along the plane $mg\sin\alpha$, perpendicular to the plane $mg\cos\alpha$. The normal force is $N = mg\cos\alpha$, the friction force is $F_f = \mu N = \mu mg\cos\alpha$.
By Newton's second law along the plane:
$$ma = mg\sin\alpha - \mu mg\cos\alpha$$
$$a = g(\sin\alpha - \mu\cos\alpha) = 10(0.5 - 0.2 \cdot 0.866) \approx 3.27 \text{ m/s}^2$$
Newton's second law links three quantities: force F, mass m and acceleration a. The acceleration always points along the force, and for a constant force it is inversely proportional to the mass.
Given any two of them, the third follows from this formula — the calculator above shows the steps. SI units: newton (N), kilogram (kg), metre per second squared (m/s²).
Divide the force by the acceleration: m = F / a. For F = 20 N and a = 2 m/s² the mass is 10 kg.
In an inertial frame of reference with constant mass. Near the speed of light Newtonian mechanics is no longer accurate.
Embed on your site
Paste the code — the page will only show the calculator for this formula:
<iframe src="https://physlabo.com/embed/en/newton-second-law/" width="100%" height="380" style="border:0" loading="lazy" title="Newton's second law calculator"></iframe>
Practice the topic “Newton's second law”
9 more solved problems with animations
Go to problems