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Upper secondary foundations · Newton's laws · Contact friction · Work and heat

Pull the platform. Does the block follow?

Change only the pull or its target in one apparatus to compare moving together, relative sliding and frictional heating.

The problem

A 2 kg platform, 2 m long, rests on a smooth horizontal floor. A 1 kg block, 0.4 m long, is centered on it. The contact has static friction coefficient 0.3 and kinetic coefficient 0.2. Starting from rest, pull the platform rightward with 6 N for 0.6 s. Repeat from rest with 12 N on the platform, then with 3 N on the upper block instead.

Assumptions and boundaries
  • Use gravity 9.80665 m/s² and a frictionless floor. Ignore air resistance and rotation.
  • Each experiment restarts at rest with the block centered. Forces stay constant during a run; the animation does not switch the pull halfway through.
  • The block must remain fully supported. Partial support, tipping and falling are not modeled.

Questions to explore

  1. Why does the block stick with a 6 N pull? Is static friction at its maximum?
  2. What changes with a 12 N pull? Which distance determines the heat?
  3. Does friction reverse if a 3 N force pulls the upper block instead?
Edit the code in Studio →
Stacked bodies: contact and friction Scientific model diagram Static friction: both bodies accelerate together Static friction: both bodies accelerate together parcel (1 kg) parcel (1 kg) cart (2 kg) cart (2 kg) f = 2 N f = 2 N f = 2 N f = 2 N F = 6 N F = 6 N a(parcel) = 2 m/s² | a(cart) = 2 m/s² a(parcel) = 2 m/s² | a(cart) = 2 m/s² N = 9.807 N | Floor normal = 29.42 N | f(max) = 2.942 N N = 9.807 N | Floor normal = 29.42 N | f(max) = 2.942 N External work = total kinetic energy gained + frictional heat External work = total kinetic energy gained + frictional heat 0.6 s: W = 2.16 J | K = 2.16 J | Q = 0 J 0.6 s: W = 2.16 J | K = 2.16 J | Q = 0 J Starts at rest; smooth floor; no rotation; one horizontal scale Starts at rest; smooth floor; no rotation; one horizontal scale
time 0s driver displacement 0m response displacement 0m contact slip 0m external work 0J kinetic energy 0J frictional heat 0J Playback speed is adjusted; time readouts still show physical time.
Diagram description

Animated physics diagram: stacked_blocks; showing time, driver displacement, response displacement, contact slip, external work, kinetic energy, frictional heat.

Unpack one connected process

First assume common motion, find acceleration for the whole system, and check the required static friction. If it exceeds the limit, apply Newton's law to each body separately. Contact forces are equal and opposite; heat depends on relative travel.

ma_block = F_block + f; Ma_platform = F_platform − f; Wexternal = ΔKtotal + Q

1. Why does the block stick with a 6 N pull? Is static friction at its maximum?

Common acceleration would be 6/(2+1) = 2 m/s², requiring only 2 N of friction on the block. This is below the static limit of about 2.942 N. Both travel 0.360 m in 0.6 s. The largest platform pull without slipping is about 8.826 N. Static friction adjusts to the required force; it is not always at its maximum.

2. What changes with a 12 N pull? Which distance determines the heat?

The 4 N friction needed for common acceleration exceeds the static limit. The block slides left relative to the platform. Kinetic friction is about 1.961 N; block and platform accelerations are about 1.961 and 5.019 m/s². In 0.6 s they travel 0.353 m and 0.903 m, giving 0.550 m of relative sliding and Q ≈ 1.080 J. Applied work, about 10.842 J, equals total kinetic energy, about 9.762 J, plus heat.

3. Does friction reverse if a 3 N force pulls the upper block instead?

Both accelerate rightward at 1 m/s². Friction on the upper block is 2 N to the left; friction on the platform points right. These are an interaction pair. Friction opposes the tendency to slide relative to the contact, not necessarily motion over the ground. With no relative sliding in this run, no frictional heat is generated.

Test your prediction in code

Change the pull from 6 N to 12 N. Watch the block slip relative to the platform and produce frictional heat.

scene stacked_blocks

surface floor orientation=horizontal friction=smooth
body cart mass=2kg width=2m
surface deck orientation=horizontal friction=static mu_static=0.3 mu_kinetic=0.2
body parcel mass=1kg width=0.4m
force pull 6N direction=right on cart

deck attached to cart
cart on floor
parcel on deck

simulate 0.6s playback=3s
show forces motion acceleration energy heat
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