Physics 151 Class Exercise: Net Force
In the sequence of images that follow, Bob Costas is shown riding on
an elevator while standing on a scale that illustrates his apparent weight. In
the image to the immediate right, Bob is shown standing in the elevator
stopped at the 6th floor. Determine the acceleration of the elevator in each of
the four images. (Hint: You should begin by drawing a FBD and specifying
your coordinate system.)
a1 = 0 m/s2
W = mg
W
700 N
=
= 71.4 kg
g=
m⎞
g ⎛
⎜ 9.81 2 ⎟
s ⎠
⎝
ΣFy = N − mg = ma
a2 =
N − mg (1000 N ) − ( 700 N )
m
=
= 4.2 2
m
s
( 71.4kg )
ΣFy = N − mg = ma
a3 =
N − mg ( 400 N ) − ( 700 N )
m
=
= −4.2 2
m
s
( 71.4kg )
ΣFy = N − mg = ma
a4 =
N − mg ( 0 N ) − ( 700 N )
m
=
= −9.8 2
m
s
( 71.4kg )
T
mg
2.
Wally is dragging a 300 N crate across a smooth
floor by pulling with a 65 N force on a roped at a 30º
above the horizontal. (Hint: You should begin by
drawing a FBD and specifying your coordinate system.)
(a)
Calculate the acceleration of the crate.
W = mg
m=
( 300 N ) = 30.6 kg
W
=
m⎞
g ⎛
⎜ 9.81 2 ⎟
s ⎠
⎝
ΣFx = FA cos 30° = max
ax =
FA cos 30° ( 65 N ) cos 30°
=
m
( 30.6 kg )
(b)
N
FA
Calculate the value of the normal force exerted by the floor on the crate.
30º
N = mg − FA sin 30°
= ( 300 N ) − ( 65 N ) sin 30°
mg
= 268 N
(c)
Calculate the value of the force Wally must apply to have the crate accelerate at 0.75 m/s2.
ΣFx = FA cos 30° = max
FA =
max
=
cos 30°
( 30.6kg ) ⎛⎜ 0.75
⎝
cos 30°
m⎞
⎟
s2 ⎠
= 26.5 N