Question
In: Physics
A point particle slides frictionlessly down a sphere, starting from rest a the top(θ=0). Show that...
A point particle slides frictionlessly down a sphere, starting from rest a the top(θ=0). Show that the particle leaves the sphere when cos θ= 2/3. Use lagrange multiplier instead of newtonian mechanics
Solutions
genius_generous answered 2 years agoRelated Solutions
A student, starting from rest, slides down a water slide. On the way down, a kinetic...
A student, starting from rest, slides down a water slide. On the
way down, a kinetic frictional force (a nonconservative force) acts
on her. The student has a mass of 62.0 kg, and the height of the
water slide is 12.4 m. If the kinetic frictional force does -5.72 ×
103 J of work, how fast is the student going at the bottom of the
slide?
A student, starting from rest, slides down a water slide. On the way down, a kinetic...
A student, starting from rest, slides down a water slide. On the
way down, a kinetic frictional force (a nonconservative force) acts
on her. The student has a mass of 77 kg, and the height of the
water slide is 12.9 m. If the kinetic frictional force does -7.1 ×
103 J of work, how fast is the student going at the bottom of the
slide?
8. A cart slides down an inclined plane with the angle of the incline θ starting...
8. A cart slides down an inclined plane with the angle of the
incline θ starting from rest. At the moment the cart begins to
move, a ball is launched from the cart perpendicularly to the
incline.
(a) Choosing an x-y-coordinate system with the x-axis along the
incline and the origin at the initial location of the cart, derive
the equation of the trajectory that the ball assumes from the
perspective of this coordinate system.
(b) Determine where the maximum...
A uniform marble rolls down a symmetric bowl, starting from rest at the top of the...
A uniform marble rolls down a symmetric bowl, starting from rest
at the top of the left side. The top of each side is a distance h
above the bottom of the bowl. (a) How far up the right side of the
bowl will the marble go if the interior surface of the bowl is
rough so that the marble rolls without slipping? (b) How high would
the marble go if the bowl's surface were frictionless? (c) For
which case...
An object of mass m1 = 0.435 kg starts from rest at point and slides down an...
An object of mass m1 = 0.435 kg
starts from rest at point and slides down an incline
surface that makes an angle θ = 36.0°
with the horizontal as shown. The coefficient of kinetic
friction between the object and the incline surface is 0.395. After
sliding down a distance d = 5.60 m, it makes a perfectly inelastic
collision with an object of mass m2 =
0.650 kg at point .
a) Find the speed of m1 at point just
before...
An object of mass m1 = 0.415 kg starts from rest at point and slides down an...
An object of mass
m1 = 0.415 kg
starts from rest at point and slides down an incline
surface that makes an angle
θ = 36.0°
with the horizontal as shown. The coefficient of kinetic
friction between the object and the incline surface is 0.455. After
sliding down a distance d = 5.80 m, it makes a perfectly inelastic
collision with an object of mass
m2 = 0.645 kg
at point .
(a) Find the speed of
m1
at point just before...
Q2: A particle is moving in a constant force field starting at rest from some point...
Q2: A particle is moving in a constant force
field starting at rest from some point (x1,
x1’) to some higher point
(x2, x2’). The
potential energy is mgx, where
g is the acceleration imparted by the
force. Find the path that allows the particle to accomplish the
transit in the least possible
time.
A 0.200 kg ball starting from rest rolls down an inclined plane with θ=30°. a)Find the...
A 0.200 kg ball starting from rest rolls down an inclined plane
with θ=30°.
a)Find the acceleration of the ball, and the magnitude of normal
force exerted by the plane.
b) If it starts from rest a height h = 30.0 cm above its
position at the bottom of the incline (measured between the center
of the ball at each position), what is the speed of the ball vf at
that bottom point, and how long did it take to...
A 4.5 kg box slides down a 4.2-m -high frictionless hill, starting from rest, across a...
A 4.5 kg box slides down a 4.2-m -high frictionless hill,
starting from rest, across a 2.3-m -wide horizontal surface, then
hits a horizontal spring with spring constant 480 N/m . The other
end of the spring is anchored against a wall. The ground under the
spring is frictionless, but the 2.3-m-long horizontal surface is
rough. The coefficient of kinetic friction of the box on this
surface is 0.26.
What is the speed of the box just before hitting the...
Starting from rest, a 4.20-kg block slides 2.30 m down a rough 30.0° incline. The coefficient...
Starting from rest, a 4.20-kg block slides 2.30 m down a rough
30.0° incline. The coefficient of kinetic friction between the
block and the incline is μk =
0.436.
(a) Determine the work done by the force of gravity.
J
(b) Determine the work done by the friction force between block and
incline.
J
(c) Determine the work done by the normal force.
J
(d) Qualitatively, how would the answers change if a shorter ramp
at a steeper angle were...
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