CQ 1 If a car suddenly stops, the contents continue to move forward unless acted upon by an external force such as seatbelts or normal force of the dashboard. CQ 6 Friction on wheels pushes car forward. The engine pushes back on the ground, so by Newton's 3rd law, the ground pushes forward on the tire. CQ 7 Each car is in motion, so by N1L, continues in straight-line motion until acted upon by an external force, the other car, which slows the car down. Change velocity at finite acceleration takes time, Δt = Δv/a so even if the cars only have to go from 5m/s (~11mph) to 0m/s at 10g's, ~100m/s/s, Δt = (-5m/s) / (-100m/s/s) = .05s = 50ms Because cars are not truly rigid bodies, the front-end stops before the back-end. CQ 9 The scale measures the spring force inside the scale, which is the normal force the scale exerts up on the person. This equals the weight of the person ONLY if the person is not accelerating up or down. CQ 12 The acceleration is downward at 9.8 m/s/s the ENTIRE time the object is falling (up, top, or down). If air resistance is negligible, the answer is still the same - b/c the force is that of gravitation and that is straight down always. CQ 13 Even though the force of you on the wagon equals the force of the wagon on you, you can accelerate and the wagon can accelerate. What is required is a third body, the ground, to exert a net force, a push, on your feet forward (the action-reaction pair to you pushing backward on the ground). CQ 12 g downward because the velocity is constantly changing, even it momentarily stopped CQ 14 (a) scale reads the same as when stopped because a=0 so W=N (b) moving up with incr. speed implies upward a>0 implies N>W (c) in free fall, N=0! CQ 16 Equal. N3L P 2(and what is its mass) 19.8N *(1 lb / 4.448 N) = 4.45 lb m = W/g = 19.8N / 9.8m/s/s = 2.02 kg P 16 Net force in vert dir = Fair up on wings -mg = by N2L = ma = 0 b/c bird is hovering. thus mg = .3N P17 Forces are air pushin upward on bird and weight of bird (downward), so net upward force = Fair - mg but Fnet = 0 if bird is motionless, so Fair = mg = 0.30N [Since mg=0.3N, m = (0.3N) / (9.8m/s/s) = 0.031kg = 31 gm] P22 2010kg elevator accelerates upward at 1.5m/s/s, thus the net force is ma=3015N. The cables exert an upward tension while the Earth pulls down with W=mg=19698N. Fnet = T-W = T - 19698, but N2L says Fnet = ma = 3015N, thus 3015N = T-19700N, so T=22713N or 22700N or 22.7kN. P 25 2kg stone (weight mg = 19.6N ) lifted upward at constant upward acceleratio = 1.5m/s/s. Net force in vert dir = Fhand up on mass - mg = = by N2L = ma , so Fhand up on mass = mg + ma = m*(g+a) = (2kg)*(9.8+1.5m/s/s) = 22.6 N. P 30 650N skydiver falls at constant speed (a=0). Parachute pulls up with 620N, thus there must be another 30N upward force, air drag. P 31 FNET on HER = Ffloor up on HER_feet + 2*Farmrest up on HER_arms +Fseat up on HER_body - WEarth on HER = Ffloor up on HER_feet +2*25 + 500 - 600 = 0 because a=0 and by N2L, Fnet=0, thus Ffloor up on HER_feet = 600-500-50=50N. P 32 N3L action-rxn pairs: a=-b, (Earth down on bike) = -(bike up on Earth). N1L: hook up on bike = -(earth down on bike) - both on bike so Fnet=0 P61 (a) Force of hand on book plus opposing force of table on book (friction) plus vertical forces (normal=table up on bk and weight=earth down on bk)(b) After I stop pushing the book, the forces are exaclty the same as in (a) except for force of hand on book (c) After book stops sliding, only normal and weight act on book (d) The net force is non-zero in (a) provided you're speeding the book up and also in (b) because the friction is the only horizontal force, so the book is slowing down. (e) m=0.5kg => mg=4.9N and also N=4.9N b/c ay=0 so Fnety,y=0 If friction coeff, mu, is 0.4, then f=0.4*(4.9N)=1.96N, which is the only force acting in the horizontal direction, so the net force is 1.96N backwards. (f) If mu=0, then the only forces in part 9b) would be normal and weight, which cancel, so the net force would be zero, so the book would move at constant velocity (constant speed in straight line). P64 The net force on the sleigh is zero (by N2L b/c the velo is constant) The physical forces add up to give Fnet of (T-friction) horizontally and (Normal-weight) vertically. Both add to zero, so T=friction and N=m*g. (b) friction = mu*N, but T=friction = mu*N = mu*m*g, so T=mu*m*g OR mu = T/(m*g) P83 Fnet,horizontal on both masses = T2 and N2L says = (m1+m2)*a Fnet,horizontal on m2 = T2 - T1 and N2L says = m2*a Fnet,horizontal on m1 = T1 and N2L says = m1*a So the first gives T2 = (m1+m2)*a while the third, T1 = m1*a. Dividing these two equations T1 / T2 = m1*a / ((m1+m2)*a) = m1 / (m1+m2) P90 1400kg car (weight mg=13720N) is pulled with a rope that breaks at 2500N. If there is no friction, then the tension in the rope is the only horizontal force, so m*ax = 2500N at the breaking point. Thus the maximum horizontal acceleration, ax = 2500N/1400kg = 1.786m/s/s.