Forces Movement Shape And Momentum

change in speed; change in direction; change in shape

the force changes the ball’s speed (from stationary to moving); the force changes the ball’s shape (the ball is compressed/deformed during contact)

electrostatic force

gravitational and electrostatic forces act at a distance / do not require contact between bodies; friction is a contact force that requires surfaces to be touching

a scalar has magnitude only; a vector has both magnitude and direction

distance = 400 m; displacement = 0 m (the runner returns to the starting point, so the straight-line distance from start to finish is zero)

force is a vector quantity; it must have both magnitude and direction stated, so “50 N to the right” or similar direction is needed

Taking forward as positive, with: $${F}_{\text{thrust}}=+2500\text{ N}$$ $${F}_{\text{water}}=-1800\text{ N}$$ $${F}_{\text{wind}}=-350\text{ N}$$ Finding the resultant force $${F}_{\text{resultant}}=(+2500)+(-1800)+(-350)$$ $${F}_{\text{resultant}}=+350\text{ N}$$ The resultant force is 350 N forward.

the body is in equilibrium; if stationary it remains stationary, if moving it continues at constant velocity (no change in speed or direction)

a force that opposes motion between surfaces in contact

friction acts to the left, opposing the motion of the crate; the applied force to the right must equal the friction force; so the resultant force is zero and the crate moves at constant velocity (Newton’s first law)

from F = ma, acceleration is directly proportional to force when mass is constant; so doubling the resultant force doubles the acceleration

Converting velocity to SI units $${v}_{\text{initial}}=\frac{108}{3.6}$$ $${v}_{\text{initial}}=30{\text{ m s}}^{-1}$$ Finding the acceleration Taking the direction of travel as positive: $$a=\frac{v-u}{t}=\frac{0-30}{12}$$ $$a=-2.5{\text{ m s}}^{-2}$$ Finding the braking force $$F=m\times a=1400\times (-2.5)$$ $$F=-3500\text{ N}$$ The braking force is 3500 N, opposing the direction of travel. The negative sign indicates the force acts opposite to the direction of travel, as expected for a braking force.

mass is a measure of the quantity of matter in an object, measured in kg, and is a scalar; weight is the gravitational force on an object, measured in N, and is a vector acting downward

Finding the mass on Earth $$m=\frac{W}{g}=\frac{240}{9.8}$$ $$m=24.49\text{ kg}$$ Finding the weight on the new planet The mass is the same on the new planet (mass is constant). $$W=m\times g=24.49\times 4.2$$ $$W=102.9\text{ N}$$ The weight on the new planet is approximately 103 N (downward) (3 s.f.).

stopping distance = thinking distance + braking distance

doubling speed doubles the thinking distance (because the car travels twice as far during the same reaction time); doubling speed quadruples the kinetic energy (KE = ½mv²); so the brakes must do four times as much work to stop the car, approximately quadrupling the braking distance; the total stopping distance therefore more than doubles

alcohol/drugs slow the driver’s nervous system, so reaction time increases; tiredness/fatigue reduces alertness, so the driver takes longer to respond; in both cases, the longer reaction time means the vehicle travels further before brakes are applied, increasing the thinking distance and therefore the total stopping distance

weight acts downward on the skydiver; as speed increases, drag/air resistance increases; the resultant downward force decreases, so acceleration decreases; eventually drag equals weight, so the resultant force is zero and acceleration is zero — the skydiver falls at constant (terminal) velocity

the graph starts at the origin (speed = 0 at time = 0); the line rises steeply at first because acceleration is large; the gradient decreases as drag increases; the line becomes horizontal when terminal velocity is reached (constant speed, zero acceleration)