fisica1-youn-e-freedman-exercicios-resolvidos

1 2 1 2
7.24: From kx = mv , the relations between m, v, k and x are
2
2
2 2
kx = mv , kx = 5mg.
2
v
Dividing the first by the second gives x = , and substituting this into the second gives
2
mg
k = 25 , so a) & b),
2
v
5g
2
(2.50 m s)
x =
= 0.128 m,
2
5(9.80 m s )
(1160 kg)(9.80 m s )
k = 25
2
(2.50 m s)
2
2
= 4.46 × 10
5
N m.
7.25: a) Gravity does negative work, − (0.75 kg)(9.80 m s )(16 m) = −118
J. b)
Gravity does 118 J of positive work. c) Zero d) Conservative; gravity does no net work
on any complete round trip.
2
7.26: a) & b) − (0.050 kg)(9.80 m s )(5.0 m) = −2.5
J.
2
c) Gravity is conservative, as the work done to go from one point to another is pathindependent.
7.27: a) The displacement is in the y-direction, and since F r has no y-component, the
work is zero.
b)
2
P2
x2
2 12 N/m 3 3
∫ F
r
⋅ dl
r
= −12∫
x dx = − ( x2
− x1
) = −0.104 J.
P1
x1
3
3
c) The negative of the answer to part (b), 0 .104 m d) The work is independent of
path, and the force is conservative. The corresponding potential energy is
U =
(12 N
2 3
m ) x
3
3
= (4 N m ) x .
2