fisica1-youn-e-freedman-exercicios-resolvidos

5.109: a) For the same rotation rate, the magnitude of the radial acceleration is
proportional to the radius, and for twins of the same mass, the needed force is
proportional to the radius; Jackie is twice as far away from the center, and so must hold
on with twice as much force as Jena, or 120 N.
2
b) ∑ F = mv r.
Jackie
v =
(120 N) (3.6 m)
30 kg
= 3.8 m s.
5.110: The passenger’s velocity is v = 2 π R t = 8.80 m s. The vertical component of the
seat’s force must balance the passenger’s weight and the horizontal component must
provide the centripetal force. Therefore:
F sin θ = mg = 833 N
seat
2
mv
Fseat
cos θ = = 188 N
R
Therefore tan θ = 833 N 188 N = 4.43; θ = 77. 3°
above the horizontal. The magnitude of
the net force exerted by the seat (note that this is not the net force on the passenger) is
2
2 ⎛ mv ⎞
2
2
Fseat
= ( mg)
+
⎜
⎟ = (833 N) + (188 N)
⎝ R ⎠
= 854 N
(b) The magnitude of the force is the same, but the horizontal component is reversed.
5.111: a)
2
b) The upward friction force must be equal to the weight, so
2 2
µ n = m(4π
R T ) ≥ mg and
s
µ s
2
2
2
gT (9.80 m s ) (1s 0.60 rev)
µ
s
> =
= 0.28.
2
2
4π
R 4π (2.5 m)
c) No; both the weight and the required normal force are proportional to the rider’s
mass.