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Motion and Forces overview

Topic 5 of 6

Apply all three Newton laws

Identify the body before applying a law. The resultant force describes the combined effect of forces on that body; an interaction pair acts on two different bodies.

Use an approximately inertial laboratory frame for these models. A free-body diagram helps keep the recipient of every force explicit.

First law: zero resultant preserves velocity

A body at rest stays at rest, and a moving body continues at constant velocity, unless a resultant external force acts on it.

Zero resultant does not mean that no forces act. For example, the weight and support on a gliding object may balance vertically while horizontal resistance is negligible. It can continue moving horizontally without a forward resultant force.

When a vehicle brakes, a passenger tends to continue with the previous velocity. A restraint or another contact supplies the force needed to change the passenger's motion. The tendency to continue is inertia, not evidence of an extra forward force.

Second law: resultant force changes momentum

The rate of change of momentum is proportional to the resultant force and is in its direction. With consistent SI units, the instantaneous relationship is:

Fresultant = dp/dt

Average resultant force = Δp/Δt

Here dp/dt means the local rate of change of momentum. The interval expression gives the average force over the stated interval; it does not by itself establish the force at every instant.

Worked average force

Use the full momentum change

A 1.20 kg body changes velocity from +3.0 to -2.0 m/s in 0.50 s. Its momentum change is 1.20(-2.0 - 3.0) = -6.0 kg m/s.

Average resultant force = -6.0/0.50 = -12 N.

The negative sign gives the force direction. The body initially moved positively, but its momentum changed negatively. The result does not show that the force was -12 N throughout the interval.

Third law: interaction partners are simultaneous

If body A exerts a force on body B, body B simultaneously exerts a force of equal magnitude and opposite direction on body A. The pair describes one interaction and acts on different bodies.

The partner is not a later response. It can exist whether or not either body is moving. When drawing the forces on B, include A's force on B; B's force on A belongs on A's diagram.

The contact pair acts on two different skaters

These are separate horizontal interaction views. Vertical weight and support forces are omitted. Both contact forces exist at the same instant.

Equal contact forces give different accelerationsThe upper view selects the forty-kilogram skater: the sixty-kilogram skater exerts a 120-newton leftward force on this body. The lower view selects the sixty-kilogram skater: the forty-kilogram skater exerts a 120-newton rightward force on this different body. The two purple force arrows have equal lengths. With other horizontal forces neglected, the forty-kilogram body accelerates left at three metres per second squared and the sixty-kilogram body right at two. The green acceleration arrows use a separate common scale, with lengths in the ratio three to two; they are not extra forces.Force from the 60 kg skater120 N40 kg bodya = 3.0 m/s2 leftForce from the 40 kg skater120 N60 kg bodya = 2.0 m/s2 right

Purple arrows compare forces on one scale; green arrows compare accelerations on another. The pair's forces are equal. The accelerations differ because the masses differ.

The two 120 N contact forces act simultaneously on different skaters. This pair-only view omits their vertical forces. Equal contact forces need not produce equal accelerations when the masses differ.

Equal forces, different accelerations

Two skaters push each other

A 40 kg skater is pushed left and a 60 kg skater right by a pair of 120 N contact forces. Other horizontal forces are negligible.

Their accelerations are 120/40 = 3.0 m/s2 left and 120/60 = 2.0 m/s2 right. The different responses follow from their different masses, not from unequal partner forces.

A stationary book's weight and table support both act on the book. They can balance, but they are not a third-law pair. Earth's pull on the book is paired with the book's pull on Earth. The table's force on the book is paired with the book's force on the table.

Equal and opposite is not enough to identify a third-law pair. Name both source and recipient and check that the forces are the two sides of the same interaction.

Optional check A 40 kg skater pushes a 60 kg skater rightward with 120 N. Other horizontal forces are negligible. Which statement describes the simultaneous interaction?
A 40 kg skater pushes a 60 kg skater rightward with 120 N. Other horizontal forces are negligible. Which statement describes the simultaneous interaction?