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6.94:
a) The number of cars is the total power available divided by the power needed per
car,
,
177
m/s)
N)(27
10
8
.
2
(
W
10
4
.
13
3
6
=
×
×
rounding down to the nearest integer.
b)
To accelerate a total mass
M
at an acceleration
a
and speed
v
, the extra power
needed is
Mav
. To climb a hill of angle
α
, the extra power needed is
.
sin
v
Mg
These
will be nearly the same if
;
sin
~
g
a
if
,
m/s
10
.
0
~
tan
~
sin
2
g
g
the power is
about the same as that needed to accelerate at
.

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**Unformatted text preview: **m/s 10 . 2 c) MW. 2.9 m/s) 27 )( 010 . )( m/s kg)(9.80 10 10 . 1 ( 2 6 = × d) The power per car needed is that used in part (a), plus that found in part (c) with M being the mass of a single car. The total number of cars is then , 36 m/s) 27 ))( 010 . )( m/s kg)(9.80 10 (8.2 N 10 8 . 2 ( W 10 9 . 2 W 10 4 . 13 2 4 3 6 6 = × + × ×-× rounding to the nearest integer....

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