Prove for all n\inN
2n= (\stackrel{n}{0})+(\stackrel{n}{1})+...+(\stackrel{n}{n})
So I used mathematical induction
base case: n=0 so 20=1 and (\stackrel{0}{0})=1
induction step: Let n\inN be given, assume as induction hypothesis that 2n=...
Homework Statement
A uniform flat plate of metal with a circular hole, where it is a rectangle starting from -6 to 7 from the length, and the height is -3 to 3.
The circle has a radius of 2, and it starts at 1 to 5.
Calculate the x-coordinate of the center of
mass xcm of the metal plate...
Homework Statement
An m2 = 1.2 kg can of soup is thrown upward with a velocity of v2 = 4.6 m/s. It is immediately struck from the side by an m1 = 0.63 kg rock traveling at v1 = 7.9 m/s.
The rock ricochets off at an angle of α = 65◦ with a velocity of v3 = 5.5 m/s.
(a)What is the angle of...
Homework Statement
A 4.39 g particle is moving at 4.15 m/s toward a stationary 9.64 g particle.
(a)With what speed does the heavier particle approach the center of mass of the two particles?
Answer in units of m/s.
(b) What is the magnitude of the momentum of the lighter particle...
Homework Statement
A spring with a spring-constant 2.5 N/cm is compressed 35 cm and released. The 4 kg mass skids down the frictional incline of height 37 cm and inclined at a 20◦ angle. The acceleration of gravity is 9.8 m/s2 . The path is frictionless except for a distance of 0.5 m along the...
Homework Statement
A 3.2 kg particle moves along the direction
under the influence of a force described by the
potential energy function U = a k~xk, where
a = 5.48 J/m and x is the position of the
particle in meters measured from the origin
as in Figure.
The total energy of the particle...
Homework Statement
A(n) 2300 g block is pushed by an external
force against a spring (with a 14 N/cm spring
constant) until the spring is compressed by
19 cm from its uncompressed length. The
compressed spring and block rests at the bot-
tom of an incline of 33◦ .
The acceleration of...
Homework Statement
A poorly designed playground slide begins with a straight section and ends with a circular arc as shown in the figure below.
[PLAIN]http://img716.imageshack.us/img716/8381/25746193.jpg [Broken]
A child starts at point P and slides down both sections of the slide. At some...
Homework Statement
A crate is pulled by a force (parallel to the incline) up a rough incline. The crate has an initial speed shown in the figure below. The crate is pulled a distance of 5.94 m on the incline by a 150 N force.
The acceleration of gravity is 9.8 m/s2 ...
Homework Statement
Hint: W = ~S · ~F .
Consider a force ~F with components Fx =28 N, Fy = 57 N, and Fz = 99 N, as illustrated in the figure below. Work is done when a particle moves up the vertical z-axis a distance of 4 m.
[PLAIN]http://img691.imageshack.us/img691/5594/problem4e.jpg...
Homework Statement
A civil engineer is asked to design a curved
section of roadway that meets the following
conditions:
With ice on the road, when the coefficient of
static friction between the road and rubber is
0.1, a car at rest must not slide into the ditch
and a car traveling less...
Homework Statement
A pulley is massless and frictionless. 3 kg, 2 kg, and 6 kg masses are suspended on a pulley.
(a)What is the tension T1 in the string between the two blocks on the left-hand side of the pulley?
(b)What is the magnitude of the acceleration of the lower left-hand block...
Homework Statement
A 33.5 kg person stands on a 67 kg platform.
He pulls on the rope that is attached to the
platform via the frictionless lower-right pul-
ley. He pulls the rope at an angle of 35◦ to the
horizontal, as shown in the figure below.
Assume: g = 9.8 m/s2 . Ignore friction...
Homework Statement
The suspended 2.29 kg mass on the right is
moving up, the 1.3 kg mass slides down the
ramp, and the suspended 7.7 kg mass on the
left is moving down. There is friction between
the block and the ramp.
The acceleration of gravity is 9.8 m/s2 . The
pulleys are massless...
Homework Statement
Three blocks in contact with each other are
pushed across a rough horizontal surface by a
75 N force as shown.
The acceleration of gravity is 9.8 m/s2 .
[PLAIN]http://img178.imageshack.us/img178/6198/007ow.png [Broken]
If the coefficient of kinetic friction between...
Homework Statement
A force of 23.52 N pushes and pulls to blocks
as shown in the figure below. The vertical
contact surfaces between the two blocks are
frictionless. The contact between the blocks
and the horizontal surface has a coefficient of
friction of 0.29.
The acceleration of...
Homework Statement
A pulley is massless and frictionless. 3 kg, 2 kg (on the left), and 6 kg (on the right) masses are suspended
(a)What is the tension T1 in the string between the two blocks on the left-hand side of the pulley?
(b) What is the magnitude of the acceleration of the lower...
1. (a)A train slows down at a constant rate as it
rounds a sharp circular horizontal turn. Its
initial speed is not known. It takes 16.6 s to
slow down from 86 km/h to 30 km/h. The
radius of the curve is 162 m.
As the train goes around the turn, what is
the magnitude of the tangential...
1. (a)The speed of the tip of the minute hand on a
town clock is 0.00136 m/s.
What is the speed of the tip of the second
hand of the same length?
Answer in units of m/s.
(b)What is the centripetal acceleration of the tip
of the second hand?
Answer in units of m/s2.
Homework...
1. Before throwing a 0.821 kg discus, an ath-lete rotates it along a circular path of radius1.19 m. The maximum speed of the discus is18.7 m/s.Determine the magnitude of its maximumradial acceleration.Answer in units of m/s2
Homework Equations
atotal = sq rt (a2 radial + a2 tangential)...
1. A home run is hit such a way that the baseballjust clears a wall 27 m high located 147 mfrom home plate. The ball is hit at an angleof 37◦ to the horizontal, and air resistance isnegligible. Assume the ball is hit at a heightof 1 m above the ground.The acceleration of gravity is 9.8 m/s2...
1.
(a) A particle has ~r(0) = (4 m)j and ~v(0) =
(2 m/s)i.
If its acceleration is constant and given by
~a = −(2 m/s2) (i+j), at what time t does the
particle first cross the x axis?
Answer in units of s.
(b) At what time t is the particle moving parallel to the y axis; that is, in the...
A ball is thrown from the top of a building
upward at an angle of 47 ◦ to the horizontal
and with an initial speed of 23 m/s, as in
the figure. The ball is thrown at a height of
46 m above the ground and hits the ground
82.0127 m from the base of the building.
The acceleration of gravity...
f(x,y)=(x)/ (1-y2), y does not equal 1 or -1
Is it possible to define a new function g(x,y) that is defined and continuous for all (x,y) in R2, and such that g(x,y)=f(x,y) for all (x,y) in the domain of f? If so, find such a function. If not, explain why.
I really don't know where to...