Forces and friction lab
An open lab for the whole forces unit. Move any slider, or grab any dashed circle and drag it: arrow tips set the size and direction of a force, rope ends and ramp corners set angles, and graph markers set values. Every diagram, graph and equation updates as you go, and arrows are drawn to scale within each diagram.
How to use this lab
- Work through the five tabs in order, or jump to the topic you are studying.
- In Free-body diagrams, try Predict first: choose the forces yourself, then check your diagram.
- In the Inclined plane lab, pick a problem, predict the answer, then press Hide answers to test yourself before you release the block.
Free-body diagrams
Choose a situation. Its free-body diagram, on the right, shows every force acting on the object and nothing else, with all arrows starting from one point. Explore freely, or switch to Predict first, choose the forces yourself and check.
Apply Newton’s second law along each axis (up and right are positive)
Drawing a free-body diagram
- Sketch the object alone, as a point or a small box.
- Add a field force for gravity, then a contact force for each thing touching the object: floors, ropes, hands, air.
- Draw every force as an arrow leaving the object in the direction it acts, longer for bigger forces.
- Name each arrow. Leave out forces the object exerts on other things; they belong on those objects' diagrams.
Newton’s three laws
The normal force
A surface pushes on whatever rests on it, at right angles to the surface. That push, the normal force, does not have to equal the weight. It takes whatever value stops the object from sinking into the surface.
Static and kinetic friction
Slowly increase your push on a resting box. Static friction cancels the push exactly, but only up to \(\Fsmax = \mu_s \Fn\). When the box starts to slide, friction drops to the steady kinetic value \(\Fk = \mu_k \Fn\).
Inclined plane lab
Line up the \(x\)-axis with the slope and the \(y\)-axis at right angles to it; then the weight is the only force you need to break into components. Pick a problem, or set up your own, make a prediction, and release the block.
Step-by-step solution
Questions to explore
Free-body diagrams
In the "Sign hanging from two cables" situation, make one cable steeper. Which cable's tension grows, and why must both tensions grow when the cables become flatter?
Show answer
The sign is in equilibrium, so the vertical parts of the two tensions must add up to the weight. A flatter cable has a smaller vertical part per newton of tension, so it needs more tension to hold up its share. The steeper cable carries more of the weight.
Newton's first law
Shove the block on several surfaces with different masses. Does the stopping distance depend on the mass? Explain with \(F_k = \mu_k mg\) and \(a = F/m\).
Show answer
No. Friction is \(\mu_k mg\), so the deceleration is \(a = \mu_k mg / m = \mu_k g\). The mass cancels, and for the same launch speed the block stops in the same distance.
Normal force
Put the box on the scale in the elevator. What does the scale read while the elevator speeds up going up, and while it slows down going up?
Show answer
Speeding up while going up, the acceleration is upward, so \(F_n = m(g + a)\) and the scale reads more than the weight. Slowing down while going up, the acceleration is downward, so \(F_n = m(g - a)\) and it reads less.
Inclined plane
On the Moon, does a crate start to slide at a different angle than on Earth? Use the lab to check, then explain.
Show answer
No. The crate starts to slide when \(\tan\theta = \mu_s\), which contains neither \(g\) nor \(m\). Once it slides, its acceleration \(g(\sin\theta - \mu_k\cos\theta)\) is smaller on the Moon, because \(g\) is smaller.
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