Question

A 4.71 kg mass moving in space according to v=
(6.00t^{2} - t)i + (15.0t^{2})j +(t^{3} +
3.14t)k (relative to the origin), with v in meter/second and t in
seconds. At t= 1.57s (a) what are the magnitude and direction of
the force acting on the mass (b) what is the angle between the
acceleration and velocity vector (c) what is the average velocity?
(d) What is the mass angular momentum relative to the origin? (e)
What is the torque acting on the mass relative to the origin? (f)
What is the work done by this force from t=0 s to t=1.57 s? (g)
What is the instantaneous power at t= 1.57 s?

Answer #1

The position ? of a particle moving in space from (t=0 to 3.00
s) is given by ? = (6.00?^2− 2.00t^3 )i+ (3.00? − ?^2 )j+ (7.00?)?
in meters and t in seconds. Calculate (for t = 1.57 s): a. The
magnitude and direction of the velocity (relative to +x). b. The
magnitude and direction of the acceleration (relative to +y). c.
The angle between the velocity and the acceleration vector. d. The
average velocity from (t=0 to 3.00 s)....

At time t = 0, a 4.0 kg particle with velocity v with arrow =
(5.0 m/s) i hat − (6.0 m/s) j is at x = 4.0 m, y = 2.0 m. It is
pulled by a 6.0 N force in the negative x direction. (a) What is
the angular momentum of the particle about the origin? (Express
your answer in vector form.) (b) What torque about the origin acts
on the particle? (Express your answer in vector form.)...

At the instant the displacement of a 2.00 kg object relative to
the origin is ? ⃗ = (2.00 ?)?̂ + (4.00 ?)?̂ − (3.00 ?)? ̂ its
velocity is ? ⃗ = −(6.00 ? ? )?̂ + (3.00 ? ? )?̂ − (3.00 ? ? )? ̂
and it is subject to a force ? ⃗ = (6.00 ?)?̂ − (8.00 ?)?̂ + (4.00
?)? ̂. Find (a) the acceleration of the object, (b) the angular
momentum of the...

Consider a particle moving through space with velocity v(t) =
cos(t)i−sin(t)j + tk.
(i) Determine its acceleration vector.
(ii) Determine the position vector, supposing the
particle starts at position (3,−2,3) at time t = 0.

A force F= (3.14t)i+ 6.28j + (1.57t^2)k N acts on a mass of
0.785 kg in space, with initial velocity v= 7.21i + 9.76j + 3.25k
(m/s). At t = 1.71 s, (a) What are the magnitude and direction of
the acceleration? (relative to +z axis) (b) What are the magnitude
and direction of the velocity? (relative to +y axis) (c) What are
the magnitude and direction of the displacement? (relative to +x
axis) (d) The angle between the velocity...

At the instant the displacement of a 2.00 kg object relative to
the origin is
= (2.00 m) + (4.00 m) - (3.00 m) , its velocity is = - (1.70
m/s) + (9.57 m/s) + (2.99 m/s) and it is subject to a force = (5.04
N) - (9.13 N) + (7.38 N) . Find the acceleration of the object
((a), (b) and
(c) for , and components respectively), the
angular momentum of the object about the origin
((d),...

A 3.65 kg particle with velocity v→=(8.97m/s)î-(4.43m/s)ĵ is
at x = 7.38 m, y = 5.02 m. It is pulled by a 2.09
N force in the negative x direction. About the origin,
what are (a) the particle's angular momentum,
(b) the torque acting on the particle, and
(c) the rate at which the angular momentum is
changing?

A particle of mass 2.00 kg moves with position r(t) = x(t) i +
y(t) j where x(t) = 10t2 and y(t) = -3t + 2, with x and y in meters
and t in seconds.
(a) Find the momentum of the particle at time t = 1.00 s.
(b) Find the angular momentum about the origin at time t = 3.00
s.

At time t, r→ = 8.60t2
î - (4.90t + 6.10t2) ĵ gives the
position of a 3.0 kg particle relative to the origin of an
xy coordinate system ( r→ is in meters and t is
in seconds). (a) Find the torque acting on the
particle relative to the origin at the moment 4.50 s
(b) Is the magnitude of the particle’s angular
momentum relative to the origin increasing, decreasing, or
unchanging?

At time t, r→ = 1.70t2
î - (7.60t + 7.80t2) ĵ gives the
position of a 3.0 kg particle relative to the origin of an
xycoordinate system ( r→ is in meters and t is in
seconds). (a) Find the torque acting on the
particle relative to the origin at the moment 6.50 s
(b) Is the magnitude of the particle’s angular
momentum relative to the origin increasing, decreasing, or
unchanging?

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