Newton's 2nd Law & Free-Body Diagram
Push a block with forces and watch the free-body diagram and acceleration resolve.
About this simulation
Apply a force at an angle to a block on a surface and every force is drawn as a labelled arrow — applied, weight, normal, friction and the net — while the block accelerates by ΣF = ma. A lift mode shows apparent weight change. Builds the habit of drawing the free-body diagram before writing the equation.
How to use it
- In the Push scene, raise the Applied force slider slowly and watch the block stay still until the push beats static friction.
- Change the Push angle and see the normal force arrow N shrink as part of the push lifts the block.
- Set Friction to zero with the 'Frictionless floor' preset and see the net force arrow ΣF lie right over the applied force arrow F, because nothing now opposes the push.
- Switch Scene to Lift and move the Lift acceleration slider: the N reading on the scale is the apparent weight.
- Watch the a = … line at the top of the stage, the ΣF, N and f values under it, and the arrows, as you change each control.
What to notice
- The block's acceleration always equals the net force divided by the mass, and the thick ΣF arrow is the only arrow that sets the motion.
- Static friction matches the horizontal push exactly while the block is at rest, so increasing the push at first changes friction, not the motion.
- Pushing at an upward angle reduces the normal force to mg − F sin α, which also reduces the maximum friction.
- In a lift accelerating upward the scale reads more than mg, and accelerating downward it reads less.
The formulas
- ΣF = ma
- The net force on the block equals its mass times its acceleration.
- N = mg − F sin α
- Normal force on the floor when a force F is applied at angle α above the horizontal; f ≤ μN limits the friction.
- N = m(g + a)
- Apparent weight in a lift with acceleration a, taken positive when upward.
Questions
What is a free-body diagram and why is it drawn?
A free-body diagram shows one object on its own with every force acting on it drawn as an arrow from the object: weight, normal force, friction, applied forces and tensions. It is drawn so that you can add the forces correctly before writing ΣF = ma. In the simulation, the block carries labelled arrows for F, mg, N, f and the net force ΣF.
Why does a block not move when a small force is applied to it?
Static friction is a self-adjusting force. It grows to match the applied push, up to a maximum of μN. Until the push is larger than μN, the net force is zero and the block stays at rest. In the simulation, raise the applied force from zero with the 'Won't budge' preset and watch the friction arrow grow with the push until the block breaks free.
Why is it easier to pull a box at an angle than to push it?
When you pull upward at an angle, the vertical part of your force lifts the box slightly, so the normal force becomes mg − F sin α and friction μN becomes smaller. When you push down at an angle, the normal force increases and so does friction. In the simulation the force acts upward at the push angle, so increasing the angle visibly shortens the normal force arrow.
Why do you feel heavier in a lift that is accelerating upward?
What you feel as your weight is the normal force from the floor. For you to accelerate upward, the floor must push harder than gravity pulls: N − mg = ma, so N = m(g + a). When the lift accelerates downward, N = m(g − a) and you feel lighter. In the simulation's Lift scene, the scale reading changes with the lift acceleration while mg stays the same.
