Show that for any central force, a particle moving in a curved path and acted upon...
Show that for any central force, a particle moving in a curved path and acted upon by that central force has constant angular momentum about the force center.
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Show that for any central force, a particle moving in a curved
path and acted upon...
A particle moving along the x axis is acted upon by a single force F =...
A particle moving along the x axis is acted upon by a single force F = F0e–kx, where F0 and k are constants. The particle is released from rest at x = 0. It will attain a maximum kinetic energy of:
1.14) A particle of mass m is acted upon by a net force F. As a...
1.14) A particle of mass m is acted upon by a net force F. As a result of the force, the particle starts from rest and moves along a curved path for which the acceleration relative to an inertial Cartesian coordinate system with an origin at the location where the particle is at rest is given by a - with At, B+Ct, and constants. You may assume that the units associated with t are seconds and = D where A,...
(b) Suppose that a particle of mass m travels along a path r(t) with velocity t)...
(b) Suppose that a particle of mass m travels along a path r(t) with velocity t) according to Newton's second law, F(t)ma(t), where a-is the acceleration. Then the angular momentum C of the particle about the origin is defined as while the torque of the force F about the origin is Show that the rate of change of the angular momentum is given by C()-T What happens to the momentum if the force F is a central force field, .e.,...
A 4.2 kg particle moving along the x-axis is acted upon by the force whose functional...
A 4.2 kg particle moving along the x-axis is acted upon
by the force whose functional form appears below. The velocity of
the particle at x = 0 is v = 6.6 m/s.
(a) Find the particle's speed (in m/s) at x = 2.0
m.
____ m/s
(b) Find the particle's speed (in m/s) at x = 5.0
m.
____ m/s
(c) Find the particle's speed (in m/s) at x = 10.0
m.
____ m/s
(d) Does the particle turn...
An object, moving along the circumference of a circle with radius R, is acted upon by a force of constant magnitude F....
An object, moving along the
circumference of a circle with radius R, is acted upon by a force
of constant magnitude F. The force is directed at all times at a 30
angle with respect to the tangent to the circle as shown in the
figure .
Determine the work done by this force when
the object moves along the half circle from A to B.
Express your answer in terms of the
variables , , and appropriate constants.
A particle is acted on by two torques about the origin: has a magnitude of 9.3...
A particle is acted on by two torques about the origin: has a magnitude of 9.3 N.m and is directed in the positive direction of the x axis, and has a magnitude of 3.1 Nm and is directed in the negative direction of the y axis. In unit-vector notation, find déldt , where is the angular momentum of the particle about the origin. Number Units
A particle is acted on by two torques about the origin: 71 has a magnitude of...
A particle is acted on by two torques about the origin: 71 has a magnitude of 9.8 N-m and is directed in the positive direction of the x axis, and 7 2 has a magnitude of 9.8 N-m and is directed in the negative direction of the y axis. In unit-vector notation, find déldt, where is the angular momentum of the particle about the origin. Number Î Units
A particle of mass 3.2 kg is acted on by a non-constant force of F=3x2 (N/m2)....
A particle of mass 3.2 kg is acted on by a non-constant force of
F=3x2
(N/m2). When x=3 meters it has a speed of 7.5 m/s. How
fast is it moving at x = 8 meters?
You observe a 2.0 kg particle moving at a constant speed of 3.6 m/s in a...
You observe a 2.0 kg particle moving at a constant speed of 3.6 m/s in a clockwise direction around a circle of radius 4.0 m. (a) What is its angular momentum about the center of the circle? kg·m2/s (b) What is its moment of inertia about an axis through the center of the circle and perpendicular to the plane of the motion? kg·m2 (c) What is the angular velocity of the particle? rad/s
A particle of mass M = 7.5 kg is at a position r = (-3 i...
A particle of mass M = 7.5 kg is at a position r = (-3 i + 8 j)m, has velocity v = (-1 i -2 j)m/s and is being acted upon by a force 98 i + 2j)N. Calculate (a) the particle's angular momentum vector and (b) the torque vector acting upon it about the origin.
1.14) A particle of mass m is acted upon by a net force F. As a result of the force, the particle starts from rest and moves along a curved path for which the acceleration relative to an inertial Cartesian coordinate system with an origin at the location where the particle is at rest is given by a - with At, B+Ct, and constants. You may assume that the units associated with t are seconds and = D where A,...
(b) Suppose that a particle of mass m travels along a path r(t) with velocity t) according to Newton's second law, F(t)ma(t), where a-is the acceleration. Then the angular momentum C of the particle about the origin is defined as while the torque of the force F about the origin is Show that the rate of change of the angular momentum is given by C()-T What happens to the momentum if the force F is a central force field, .e.,...
A 4.2 kg particle moving along the x-axis is acted upon
by the force whose functional form appears below. The velocity of
the particle at x = 0 is v = 6.6 m/s.
(a) Find the particle's speed (in m/s) at x = 2.0
m.
____ m/s
(b) Find the particle's speed (in m/s) at x = 5.0
m.
____ m/s
(c) Find the particle's speed (in m/s) at x = 10.0
m.
____ m/s
(d) Does the particle turn...
An object, moving along the
circumference of a circle with radius R, is acted upon by a force
of constant magnitude F. The force is directed at all times at a 30
angle with respect to the tangent to the circle as shown in the
figure .
Determine the work done by this force when
the object moves along the half circle from A to B.
Express your answer in terms of the
variables , , and appropriate constants.
A particle is acted on by two torques about the origin: has a magnitude of 9.3 N.m and is directed in the positive direction of the x axis, and has a magnitude of 3.1 Nm and is directed in the negative direction of the y axis. In unit-vector notation, find déldt , where is the angular momentum of the particle about the origin. Number Units
A particle is acted on by two torques about the origin: 71 has a magnitude of 9.8 N-m and is directed in the positive direction of the x axis, and 7 2 has a magnitude of 9.8 N-m and is directed in the negative direction of the y axis. In unit-vector notation, find déldt, where is the angular momentum of the particle about the origin. Number Î Units
A particle of mass 3.2 kg is acted on by a non-constant force of
F=3x2
(N/m2). When x=3 meters it has a speed of 7.5 m/s. How
fast is it moving at x = 8 meters?
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