Download 5.60. Model: The ball hanging from the ceiling of the truck by a string

5.60. Model: The ball hanging from the ceiling of the truck by a string is represented as a particle.
Visualize:
Solve: (a) You cannot tell from within the truck. Newton’s first law says that there is no distinction between “at
rest” and “constant velocity.” In both cases, the net force acting on the ball is zero and the ball hangs straight down.
(b) Now you can tell. If the truck is accelerating, then the ball is tilted back at an angle.
(c) The ball moves with the truck, so its acceleration is 5 m/s2 in the forward
direction.
r
(d) The free-body diagram shows that the horizontal component of T provides a net force in the forward direction.
This is the net force that causes the ball to accelerate in the forward direction along with the truck.
(e) Newton’s second law for the ball is
ax =
( Fnet ) x
m
=
Tx T sin 10°
=
m
m
a y = 0 m 2 /s 2 =
( Fnet ) y
m
=
Ty + w y
m
We can solve the second equation for the magnitude of the tension:
T=
(1 kg)(9.8 m/s 2 )
mg
=
= 9.95 N
cos10°
cos10°
Then the first equation gives the acceleration of the ball and truck:
T sin 10° (9.95 N ) sin 10°
=
= 1.73 m /s 2
m
m
The truck’s velocity cannot be determined.
ax =
=
T cos10° − mg
m