2. Consider the curve ø(t) = (t² – 4t + 2, cos(t²), ' sin(t²)) for t e (0, 1). (a) Find the work required to bend a straight rod into ø, assuming a stiff- ness of M = 2. (b) Find the work required to bend a straight rod into ø, assuming a stiff- ness of M(x, y, z) = /1+ x² + y² + z².
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- A painter (of mass 75 kg) needs to reach out from a scaffolding to paint the side of a building, so he lays a plank across two bars of the scaffolding, and puts a heavy bucket of mass 72 kg directly over one of the bars (see figure). You can assume the plank is massless, and is long enough to reach to the other building. If the bars are separated by a distance 2.6 m, how far, d, from the bar on the the right can the painter walk before the plank starts to fall? d =Find the cross product →A × →C for (a) A = 2.0 ^i − 4.0 ^j + ^k and C = 3.0 ^i + 4.0 ^j + 10.0 ^k (b) A = 3.0 ^i + 4.0 ^j + 10.0 ^k and →C = 2.0 ^i − 4.0 ^j + ^k (c) A = −3.0 ^i − 4.0 ^j and →C = −3.0 ^i + 4.0 ^j (d ) →C = −2.0 ^i + 3.0 ^j + 2.0 ^k and A = −9.0 ^j Answer a and bNote: Make sure your calculator is in radian mode for this problem, and that you switch it back after this problem. There are two particles (1 and 2) that are moving around in space. The force that particle 2 exerts on 1 is given by: F→21(t)=Fxe−(t/T)ı^+Fysin(2πt/T)ȷ^ Where the parameters have the values: Fx=14.2 N, Fy=89 N, T=55 s.We will consider a time interval that begins at ti=0 s and ends at tf=96 s. Find the x component of the impulse from 2 on 1 between ti and tf.
- • Problem 3.22 The potential energy between the atoms of an hydrogen molecule can be modelled by means of the Morse potential -2(r – ra) (r V (r) = V exp 2 еxp where Vo = 7 × 10 12 erg, ) = 8 x 10-º cm and a = 5 x 10-º em.Find the answer for the given: Let L be the length. Let M be the mass. A rod that has L and M was hunged from the one end of a frictionless pivot, and it was hanged vertically at rest (intially) A person fired one small ball of clay with mass (m) to the rod with a speed V(initial) and stuck to the end of the non pivoted area. Find the angle Of greatest rotation for the rod/clay system? M M,L V(initial)let's consider the three atoms composing the molecule have different masses and coordinate, while the axis of rotation is still y-axis. The first atom has a mass of 8.61 kg, with x coordinate at 3.063 m and y coordinate at 3.826 m. The second atom has a mass of 63.048 kg, with x coordinate at 87.738 m and y coordinate at 51.326 m. The third atom has a mass of 26.317 kg, with x coordinate at 42.334 m and y coordinate at 23.115 m. What is the moment of inertia in the unit of kg m2 with respect to the y axis?
- (a) What does the quadrupole formula (P) = = = (Qij Q³ ³) compute? Reason the answer. (b) A point mass m undergoes a harmonic motion along the z-axis with frequency w and amplitude L, x(t) = y(t) = 0, z(t) = L cos(wt). Show that the only non-vanishing component of the quadrupole moment tensor is = Im L² cos² (wt). (c) Use the quadrupole formula to compute the power radiated by the emission of gravitational waves. (Hint: recall that (cos(t)) = (sin(t)) = 0 and (cos² (t)) = (sin² (t)) = ½½ for a given frequency 2.)I need help with this physics question.