At the instant the displacement of a 2.00 kg object relative to the origin is d → = ( 2.00 m ) i ^ + ( 4 .00 m ) j ^ − ( 3.00 m ) k ^ , its velocity is v → = − ( 6.00 m/s ) i ^ + ( 3 .00 m/s ) j ^ + ( 3.00 m/s ) k ^ and it is subject to a force F → = ( 6.00 N ) i ^ − ( 8 .00 N ) j ^ + ( 4.00 N ) k ^ . Find (a) the acceleration of the object, (b) the angular momentum of the object about the origin, (c) the torque about the origin acting on the object, and (d) the angle between the velocity of the object and the force acting on the object.
At the instant the displacement of a 2.00 kg object relative to the origin is d → = ( 2.00 m ) i ^ + ( 4 .00 m ) j ^ − ( 3.00 m ) k ^ , its velocity is v → = − ( 6.00 m/s ) i ^ + ( 3 .00 m/s ) j ^ + ( 3.00 m/s ) k ^ and it is subject to a force F → = ( 6.00 N ) i ^ − ( 8 .00 N ) j ^ + ( 4.00 N ) k ^ . Find (a) the acceleration of the object, (b) the angular momentum of the object about the origin, (c) the torque about the origin acting on the object, and (d) the angle between the velocity of the object and the force acting on the object.
At the instant the displacement of a 2.00 kg object relative to the origin is
d
→
=
(
2.00
m
)
i
^
+
(
4
.00 m
)
j
^
−
(
3.00
m
)
k
^
, its velocity is
v
→
=
−
(
6.00
m/s
)
i
^
+
(
3
.00 m/s
)
j
^
+
(
3.00
m/s
)
k
^
and it is subject to a force
F
→
=
(
6.00
N
)
i
^
−
(
8
.00 N
)
j
^
+
(
4.00
N
)
k
^
. Find (a) the acceleration of the object, (b) the angular momentum of the object about the origin, (c) the torque about the origin acting on the object, and (d) the angle between the velocity of the object and the force acting on the object.
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
Part C
Find the height yi
from which the rock was launched.
Express your answer in meters to three significant figures.
Learning Goal:
To practice Problem-Solving Strategy 4.1 for projectile motion problems.
A rock thrown with speed 12.0 m/s and launch angle 30.0 ∘ (above the horizontal) travels a horizontal distance of d = 19.0 m before hitting the ground. From what height was the rock thrown? Use the value g = 9.800 m/s2 for the free-fall acceleration.
PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems
MODEL: Is it reasonable to ignore air resistance? If so, use the projectile motion model.
VISUALIZE: Establish a coordinate system with the x-axis horizontal and the y-axis vertical. Define symbols and identify what the problem is trying to find. For a launch at angle θ, the initial velocity components are vix=v0cosθ and viy=v0sinθ.
SOLVE: The acceleration is known: ax=0 and ay=−g. Thus, the problem becomes one of…
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
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