Motion & Force · MotionLab

Paper tape & v-t graph

A hanging mass pulls the cart with a string, and the cart drags a paper tape through the ticker timer. The timer marks a dot every 0.02 s, so the tape records the cart's position at each instant.

After the run, open the Tape tab in the data dock. Take one counting point every 5 dots (T = 0.1 s) and measure the spacings x₁, x₂, x₃… between adjacent counting points.

vₙ = (xₙ + xₙ₊₁) / 2T a = Δx / T²

The difference Δx between adjacent spacings stays nearly constant, showing that the cart moves in uniformly accelerated linear motion. Plot a v-t graph from the velocities at each counting point; the slope of the line is the acceleration.

Measuring speed with photogates

Air blown out of the air track lifts the glider, so friction is almost zero. The glider carries a flag of width d; as it passes a photogate it blocks the beam, and the digital timer records the blocking time Δt.

v ≈ d / Δt

The narrower the flag, the shorter Δt, and the closer the measured average speed is to the glider's instantaneous speed at the photogate.

Measure the speeds v₁ and v₂ at the two photogates and the distance L between them to find the acceleration:

a = (v₂² − v₁²) / 2L

You can drag the photogates in the scene to change their positions.

Free fall

The electromagnet is switched off and the ball is released from rest. A strobe light flashes every 0.05 s, leaving a trail of ghost images: the gaps grow larger further down.

h = ½gt² v = gt

Measure v₁ and v₂ with the two photogates to calculate the gravitational acceleration g ≈ 9.8 m/s².

Try a ping-pong ball or a feather: air resistance F = ½ρCdAv² grows with speed, and the feather soon reaches terminal velocity. Once Newton's tube is evacuated, the feather and the steel ball fall equally fast.

Newton's second law

To study how acceleration depends on force and mass, control the variables: keep the cart mass M fixed and vary the pulling force, or keep the force fixed and vary M. After each run, press Record data.

① Compensate for friction: raise the left end of the track so that the component of the cart's weight along the incline cancels friction.

② Use the hanging weight mg in place of the string tension. In fact

T = Mmg / (M + m) < mg

They are approximately equal only when m ≪ M. With more than 100 g of hanging mass, the a-F graph bends downward; turn on the force sensor to measure the tension directly and the graph becomes a straight line again.

a = F / M

Sliding friction

A motor pulls the wooden block at constant speed through a spring scale. At first the block stays put while the reading keeps rising — this is static friction. The block starts to move the moment the reading reaches its maximum.

Once the block slides, the reading drops back and holds steady, equal to the sliding friction:

f = μN

Add weights to the block to increase the normal force N, or cover the track with a towel, rubber mat or felt to change the contact surface. Record the steady reading and plot an f-N graph; its slope is the coefficient of kinetic friction μ.

Changing the pulling speed leaves the sliding friction almost unchanged.

Inclines & resolving forces

Resolve the weight G along and perpendicular to the incline:

G∥ = G sinθ G⊥ = G cosθ = N

At small angles, static friction balances G∥ and the block stays at rest. Drag the red knob on the left support to raise the angle gradually. When

G sinθ > μs G cosθ i.e. tanθ > μs

the block starts sliding with acceleration a = g(sinθ − μcosθ). Note that the critical angle does not depend on the block's mass.

Apparent weight gain & loss

A 5 kg mass sits on a platform scale inside an elevator. The scale reads the normal force the mass exerts on the pan. By Newton's second law:

N − mg = ma ⇒ N = m(g + a)

When the acceleration points up (speeding up going up, or slowing down going down), N > mg — apparent weight gain (overweight). When it points down, N < mg — apparent weight loss. If the cable snaps, a = −g and the reading is 0: complete weightlessness.

During apparent weight gain or loss the object's weight mg does not change; only the "apparent weight" changes.

Conservation of mechanical energy

The glider slides from rest down the raised track, converting gravitational potential energy into kinetic energy:

mgh = ½mv²

On the air track friction is negligible, so Ek + Ep stays constant, and after hitting the spring at the right end the glider returns almost to its starting height.

Turn off the air pump to use an ordinary track: friction does negative work and part of the mechanical energy becomes internal energy Q:

WG − fs = ΔEk

This is the work–energy theorem.

Conservation of momentum

Two gliders collide on the air track. The net external force is zero, so the system's momentum is conserved:

m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′

· Fit spring bumpers: an elastic collision, so kinetic energy is also conserved; with equal masses the gliders swap velocities.· Fit rubber blocks: an ordinary collision with some loss of kinetic energy.· Fit Velcro: the gliders stick together — a perfectly inelastic collision with the greatest loss of kinetic energy.

You can also grab a glider and fling it; its speed when you let go is the initial velocity.

Free lab

Every component is available: switch the air track, adjust the angle, hang masses, add a second cart, fit photogates and the ticker timer, and design your own experiment.

You can interact with the scene directly:

· Drag the cart: set its start position, or fling it to give it an initial velocity· Drag a photogate: change where it measures· Drag the red knob on the left: change the angle· Click the hanging mass or the slotted-mass box on the table: remove / add 10 g