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  1. G

    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

    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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    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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    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

    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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    Crate pulled up incline, kinetic energy and speed; picture included

    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 ...
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    Angle between Fz and S, picture included

    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...
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    What is the minimum radius of curvature of the curve?

    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...
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    Three masses suspended on pulley

    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...
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    Raising a platofrm at an angle

    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...
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    Three blocks, two pulleys, on a incline

    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...
  15. G

    Force pushes three blocks, find mag of force exerted on last two blocks

    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...
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    Force pushes and pulls two blocks at an angle

    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...
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    Pulley with three masses what is T1?

    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...
  18. G

    Train turning, tangential acceleration and total acceleration

    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...
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    Town clock seconds hand speed and centripetal acceleration

    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...
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    Determine the magnitude of its maximumradial acceleration

    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)...
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    Finding the initial speed of the baseball?

    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...
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    What time t does the particle first cross the x axis?

    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...
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    What is the speed of the ball just before it strikes the ground?

    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...
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    Function, using two-path test, finding limits

    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...
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