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=...
Yes I meant minus on the bottom
the 7 is from how far away the cicle is from the begin on the rectangle
sorry I don't have the picture but the shapes are on a coordinate system and inside the rectangle (that goes from (-6,0) to (7,0) ) the circle lies at (1,0) to (5,0).
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...
would it be
1/2kx2=mgh
h=kx2/2mg
well i tried and did 1400(.19)2/(2*2.3*9.8)
h=1.12112m
then sin33=o/h
h=o/sin30
h=2.05846
2.05846-.19 m=1.8684m
which is 186.84 cm which is wrong
well I reread the problem and it says when it is uncompressed so .57 m
I misused 2.05846-.57=1.48846
which is...
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...
okay, so Ncos\theta=mg => N= mg/cos\theta
and the normal radial force is Nsin\theta right?
so Nr= mg/cos\theta*sin\theta= tan\thetamg
which can be tan\theta= v2/gr
but now I'm stuck because there are two unknowns...
So (Kf+Uf)-(Ki+Ui)=0 =>Kf+Uf)=(K[/SUB]i+Ui) ?
then if so, 1/2 mvf2+0=0+mg2r
At what point on the slide do I draw the fbd, so I can find out all the forces?
Thanks for the symbol help!
So ∆KE + ∆PE= (Kf+Uf)-(Ki+Ui) <- is that what you mean by constant?
So if U uses the difference in height, like mgh=mg2r?
Vf is the speed at which the reaction force is zero?
could you explain what the reaction force is in this problem?
I would think it was...
So for the conservation of energy, should I use the equations:
Delta K + Delta U= (Kf+Uf)-(Ki+Ui) = Delta Emech ?
where Kf= 1/2 mvf^2
and Ki= 1/2mvi^2 (which isn't this zero since its starting at rest?)
not sure what Ui equals
but Uf is zero right?
and for the centripetal acc =...
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...