fisica1-youn-e-freedman-exercicios-resolvidos

4.42: a) The velocity of the spacecraft is downward. When it is slowing down, the
acceleration is upward. When it is speeding up, the acceleration is downward.
b)
speeding up: w > F and the net force is downward
slowing down: w < F and the net force is upward
c) Denote the y-component of the acceleration when the thrust is F
1
by a
1
and the y-
component of the acceleration when the thrust is F
2
by a
2
. The forces and accelerations
are then related by
F , .
1
− w = ma1
F2
− w = ma2 Dividing the first of these by the second to eliminate the mass gives
F1
− w a1
= ,
F2
− w a2
and solving for the weight w gives
a1F2
− a2F1
w = .
a1
− a2
In this form, it does not matter which thrust and acceleration are denoted by 1 and which
by 2, and the acceleration due to gravity at the surface of Mercury need not be found.
Substituting the given numbers, with + y upward, gives
w =
2
3
( 1.20 m / s
3
3
2
)(10.0×
10 N) − ( −0.80 m / s )(25.0 × 10
2
2
1.20 m / s − ( −0.80 m / s )
N)
= 16.0 × 10
In the above, note that the upward direction is taken to be positive, so that a
2
is negative.
Also note that although a
2
is known to two places, the sums in both numerator and
denominator are known to three places.
N.