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Why does a full shopping cart feel so much harder to get moving than an empty one?

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By the end of this video, you'll understand Newton's second law, how to use F equals m times a, and why heavy and light objects fall at the same rate.

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Push an empty shopping cart and it speeds up quickly.

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Push a full one just as hard, and it speeds up much more slowly.

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Newton's second law explains why:

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how quickly velocity changes depends on the net force and the object's mass.

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Here's the law itself.

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Acceleration is directly proportional to the net force, so more force means more acceleration.

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It's inversely proportional to mass, so more mass means less acceleration.

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And the acceleration always points in the same direction as the net force.

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In symbols, F net equals m times a.

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F net is the total force in newtons;

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if several forces act, add them as vectors first.

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Mass is in kilograms, and acceleration is in metres per second squared.

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One newton is the net force that gives one kilogram an acceleration of one metre per second squared.

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Now keep the net force fixed at 60 newtons and change the mass.

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A 10 kilogram cart accelerates at 6 metres per second squared.

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Double the mass to 20 kilograms and the acceleration halves to 3.

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At 30 kilograms, it drops to just 2.

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Try a real problem:

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a student pushes a 40 kilogram crate with 200 newtons, while friction pushes back with 80.

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First find the net force:

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200 minus 80 is 120 newtons.

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Then divide by the mass:

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120 over 40 gives 3 metres per second squared.

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The common mistake here is plugging the 200 newton push straight into the formula.

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That ignores friction, which is a force too.

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The law needs the net force, so always total up every force before you divide by mass.

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The law works in reverse too.

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A 1,200 kilogram car goes from rest to 15 metres per second in 6 seconds.

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Its acceleration is change in velocity over time:

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15 divided by 6, or 2.5 metres per second squared.

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Multiply by the mass, and the net force is 3,000 newtons.

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So why do heavy and light objects fall at the same rate?

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Gravity pulls harder on a heavier object, with a force of m times g.

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But that object also has more mass to speed up.

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Divide force by mass, the mass cancels, and without air resistance everything falls at about 9.8 metres per second squared.

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Here's a big misconception:

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a moving object needs a force to keep it moving.

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Not true.

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An object moving at constant velocity has zero net force.

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You only need a force to change velocity:

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to speed up, slow down or turn.

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Another one:

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a bigger force always means a bigger speed.

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Not quite.

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Force sets the acceleration, which is the rate at which velocity changes.

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It doesn't set the speed itself.

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Let's check what you learned.

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Why do heavy and light objects fall at the same rate, ignoring air resistance?

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The mass cancels, so they share the same acceleration, g.

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What is the net force on an object moving at constant velocity?

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Zero.

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The same net force acts on a 2 kilogram ball and a 6 kilogram ball.

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How does the heavier ball's acceleration compare?

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It's one third as large.

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Great work today, and see you next lesson!