Unit 2: Force and Translational Dynamics

21 terms. Say what each one means, then open the card to check.

• System

  The object or group of objects you choose to study. Forces from outside it are external; forces between its parts are internal and cancel in pairs.

  Example. If a car and the trailer it tows are the system, the hitch force between them is internal; road friction and gravity are external.

• Center of mass

  The mass-weighted average position of a system, $x_{cm} = \sum m_ix_i / \sum m_i$. The net external force accelerates this point as if all the mass were there.

  Example. A hammer tossed end over end spins in a complicated way, but its center of mass follows a smooth parabola.

• Free-body diagram

  A sketch of one object or system showing every external force on it as an arrow, labeled by its type and by what exerts it.

  Example. A free-body diagram of a hanging lamp has two arrows: the cord’s tension pulling up and Earth’s gravitational force pulling down.

• Normal force

  The push a surface exerts on an object touching it, perpendicular to the surface. Its size adjusts to keep the object from moving into the surface.

  Example. On a level floor a box’s normal force equals its weight, but if someone presses down on the box the normal force grows.

• Tension

  The pull a rope, string or cable exerts on an object tied to it, directed along the rope away from the object. A light rope pulls equally hard at both ends.

  Example. A rope tying a boat to a dock pulls the boat toward the dock and pulls the dock toward the boat.

• Net force

  The vector sum of all the external forces on an object or system.

  Example. A 10 N push to the right and a 4 N friction force to the left give a net force of 6 N to the right.

• Newton’s first law

  An object keeps its velocity, staying at rest or moving in a straight line at constant speed, unless a nonzero net force acts on it.

  Example. When a car brakes hard, a cup on the dashboard slides forward: the car slows, but the cup keeps moving, because the small friction from the dashboard cannot slow it as quickly.

• Newton’s second law

  The acceleration of an object or system equals the net external force divided by the mass, $\vec a = \vec F_{\text{net}}/m$, in the direction of the net force.

  Example. A net force of 600 N on a 300 kg snowmobile gives it an acceleration of 2 m/s² in the direction of that force.

• Newton’s third law

  When object A exerts a force on object B, B exerts a force of the same size in the opposite direction on A. The two act on different objects, so they cannot cancel each other on either object.

  Example. When a swimmer pushes backward on the water, the water pushes forward on the swimmer just as hard.

• Equilibrium

  The state of an object with zero net force on it, so it is at rest or moving at constant velocity.

  Example. A skydiver falling at a steady terminal speed is in equilibrium: air drag upward balances gravity downward.

• Weight

  The gravitational force a planet or moon exerts on an object, $F_g = mg$ near its surface. Mass is the same everywhere; weight depends on where you are.

  Example. A 10 kg backpack weighs about 98 N on Earth and about 16 N on the Moon, but its mass is 10 kg in both places.

• Gravitational field strength

  The gravitational force per kilogram at a location, $g = F_g/m$, in N/kg. It equals the free-fall acceleration there.

  Example. Near Earth’s surface a 2.0 kg mass feels about 19.6 N of gravity, so the field strength is 9.8 N/kg.

• Universal gravitation

  Any two masses attract with a force $F_g = Gm_1m_2/r^2$, where r is the distance between their centers, so doubling r cuts the force to one quarter.

  Example. Moving a satellite from 2 to 6 Earth radii from Earth’s center makes Earth’s pull on it one ninth as large.

• Apparent weight

  The reading on a scale, which is the normal force on you. It differs from your true weight whenever you accelerate up or down.

  Example. In an elevator that starts upward, a scale briefly reads more than your weight, because it must hold you up and also speed you up.

• Static friction

  The friction between surfaces that are not sliding. It takes whatever value prevents sliding, up to a maximum of $\mu_sF_N$.

  Example. When someone leans gently on a parked car with its brakes on, static friction at the tires grows just enough to match the push, and the car stays put.

• Kinetic friction

  The friction between surfaces sliding past each other, $f_k = \mu_kF_N$, directed against the sliding. It is usually smaller than the maximum static friction.

  Example. A heavy dresser is hard to get moving but takes less force to keep sliding across the floor.

• Coefficient of friction

  A number with no units that describes how strongly two surfaces grip each other: $\mu_s$ for surfaces at rest relative to each other and $\mu_k$ for sliding ones.

  Example. Rubber on dry concrete has a coefficient near 1, while a steel skate blade on ice has one of only a few hundredths.

• Spring force

  An ideal spring pushes or pulls with a force proportional to its stretch or compression, $F_s = kx$, directed back toward its relaxed length; k is the spring constant.

  Example. A spring with k = 50 N/m that is stretched 0.10 m pulls back with 5 N.

• Centripetal acceleration

  The acceleration of an object moving in a circle at constant speed, $a_c = v^2/r$, always pointing toward the center of the circle.

  Example. A train taking a curve of radius 500 m at 20 m/s has a centripetal acceleration of 0.8 m/s² toward the center of the curve.

• Net inward force

  The sum of the force components pointing toward the center, which must equal $mv^2/r$. Real forces such as tension, friction, gravity or a normal force supply it.

  Example. For a car turning on a flat road, static friction from the road on the tires supplies the whole net inward force.

• Period

  The time for one full trip around a circle. At constant speed, $v = 2\pi r/T$.

  Example. A carousel horse 4.0 m from the center that goes around once every 16 s moves at about 1.6 m/s.