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5.101: a) The rock is released from rest, and so there is initially no resistive force and<br />

2<br />

a = (18.0 N) (3.00 kg) 6.00 m s .<br />

0<br />

=<br />

2<br />

b) (18.0 N − (2.20 N ⋅ s m) (3.00 m s)) (3.00 kg) = 3.80 m s . c) The net force must be<br />

1.80 N, so kv = 16.2 N and v = ( 16.2 N) (2.20 N ⋅ s m) = 7.36 m s.<br />

d) When the net<br />

force is equal to zero, and hence the acceleration is zero, kv<br />

t<br />

= 18.0 N and<br />

v = (18.0 N) (2.20 N ⋅ s m) 8.18 m s. e) From Eq. (5.12),<br />

t<br />

=<br />

⎡ 3.00 kg<br />

y = (8.18 m s) ⎢(2.00 s) −<br />

(1 − e<br />

⎣ 2.20 N ⋅s<br />

m<br />

= + 7.78 m.<br />

From Eq. (5.10),<br />

−((2.2 N⋅<br />

s m)<br />

v = (8.18 m s)[1−<br />

e<br />

= 6.29 m s.<br />

From Eq. (5.11), but with a<br />

0<br />

instead of g,<br />

2 −((2.20 N⋅s<br />

m)<br />

a = (6.00 m s ) e<br />

.<br />

f)<br />

v<br />

1−<br />

= 0.1 = e<br />

v<br />

t<br />

(3.00 kg))(2.00 s)<br />

−(<br />

k m)<br />

t<br />

m<br />

t = ln (10) = 3.14 s.<br />

k<br />

,<br />

−((2.20 N⋅s<br />

m) (3.00 kg))(2.00 s)<br />

(3.00 kg))(2.00 s)<br />

so<br />

]<br />

= 1.38 m s<br />

2<br />

.<br />

⎤<br />

) ⎥<br />

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