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    Prove 2^n possibly with the binomial theorem

    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=...
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    Flat plate, circular hole center of mass

    thanks so much for all your help! if you wouldn't mind looking at my other problem: https://www.physicsforums.com/showthread.php?t=439084
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    Flat plate, circular hole center of mass

    yes the center of the circle is (3,0) so what is x1...? is it 1/2?
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    Flat plate, circular hole center of mass

    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).
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    Angle and speed of can after collision

    Please, anyone? Am I even on the right track?
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    Flat plate, circular hole center of mass

    alright, is this right: 13*6(1/2)-(7)(22\Pi/ (13*6+ 4\Pi)
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    Flat plate, circular hole center of mass

    this is probably a dumb question, but how do you find the mass of the rectangle and circle? and is the x1 and x2 the coordinates?
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    Flat plate, circular hole center of mass

    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...
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    Angle and speed of can after collision

    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...
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    Magnitude of Momentum, relative to the center of mass

    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...
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    Length along ramp from end of spring, picture included

    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...
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    Distance of particle travels from origin, and maximum speed, picture included

    I'm still confused... what part is Uf and what part is Ui and I don't know how to calculate kinetic energy without velocity
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    Final velocity of spring down incline with fricition

    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...
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    Length along ramp from end of spring, picture included

    So Wnc= 1/2kx2+mgh is k the 19cm (.19m)? and do I figure out the height from the angle? and if so how?
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    Distance of particle travels from origin, and maximum speed, picture included

    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...
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    Length along ramp from end of spring, picture included

    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...
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    Hat height from the ground will the child become airborne? picture included

    I have no idea how to find the radial component i know that radial acc= v2/r Fc=mac= m v2/r
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    Hat height from the ground will the child become airborne? picture included

    So the radial direction is perpendicular to the normal force? Ftotal = Ncos\theta-mg ???
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    Hat height from the ground will the child become airborne? picture included

    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...
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    Hat height from the ground will the child become airborne? picture included

    Well \sum Fy= N-mg+Fsin\theta \sum Fx= Fcos\theta maybe?
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    Hat height from the ground will the child become airborne? picture included

    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?
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    Hat height from the ground will the child become airborne? picture included

    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...
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    Hat height from the ground will the child become airborne? picture included

    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 =...
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    Hat height from the ground will the child become airborne? picture included

    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...
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    Angle between Fz and S, picture included

    Oh, I see now. Thanks so much!
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    Angle between Fz and S, picture included

    So, Fzk=99k W= 99k * S= mag (99k*S)costheta theta=arccos( 99k*S)/mag (99k*S) but how do I get S?
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    Angle between Fz and S, picture included

    So the direction is in the z direction... so does this mean I only need to care about Fzk(which is also S) and F?
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