SSM At time t = 0, force
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Fundamentals Of Physics
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- A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass ml = 48.0 kg travels in the positive x-direction at 12.0 m/s, and a second piece of mass m2 = 62.0 kg travels in the xy-plane at an angle of 105 at 15.0 m/s. The third piece has mass m3 = 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities, (b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m1, m2, m3, v1, v2 and v3 and the sines and cosines of the angles, taking to be the unknown angle, (c) Calculate the final x-components of the momenta of m1 and m2. (d) Calculate the final y-components of the momenta of m1 and m2. (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m3. (f) Solve the two momentum equations for v3 cos and v3 sin , respectively, and use the identity cos2 + sin2 = 1 to obtain v3. (g) Divide the equation for v3 sin by that for v3 cos to obtain tan , then obtain the angle by taking the inverse tangent of both sides, (h) In general, would three such pieces necessarily have to move in the same plane? Why?arrow_forwardCES Chapter 13, Problem 010 GO Two dimensions. In the figure, three point particles are fixed in place in an xy plane. Particle A has mass m, = 5 g, particle B has mass 2.00ma, and particle C has mass 3.00mA. A fourth particle D, with mass 4.00ma, is to be placed near the other three particles. What (a) x coordinate and (b) y coordinate should particle D be placed so that the net gravitational force on particle A from particles B, C, and D is zero (d = 17 cm)? em em BO plem 1.5d blem oblem roblem Units (a) Number Problem Units (b) Number Problem Click if you would like to Show Work for this question: Open Show Workarrow_forwardAt time t= 0, force F1 = (- 6.3li + 6.70j) N acts on an initially stationary particle of mass 3.21 × 10³ kg and force %3D F2 = (2.69i – 4.74j) N acts on an initially stationary particle of mass 3.00 x 10-3 kg. From time t = 0 to t = 4.46 ms, what are the (a) magnitude and (b) angle (relative to the positive direction of the x axis) of the displacement of the center of mass of the two-particle system? (c) What is the kinetic energy of the center of mass at t = 4.46 ms? (a) Number 6.59 Units mm (b) Number i 151 Units ° (degrees) (c) Number i 0.0268 Units J-sarrow_forward
- A proton with mass 1.67 x 10^-27 kg, moving with the speed of 4.80 x 10^6 m/s. the earth ( mass =5.98 x 10^24 kg) moving with an orbital speed equal to 2.98 x 10^4 calculate the magnitude of the linear momentum for the following cases.arrow_forwardA man (weighing 915 N) stands on a long railroad flatcar (weighing 2415 N) as it rolls at 18.2 m/s in the positive direction of an x axis, with negligible friction.Then the man runs along the flatcar in the negative x direction at 4.00 m/s relative to the flatcar. What is the resulting increase in the speed of the flatcar?arrow_forwardAn unstable atomic nucleus of mass 1.60 x 102 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.10 x 10 27 kg, moves in the y direction with a speed of 6.00 x 10 m/s. Another particle, of mass 8.42 x 10 kg, moves in the x direction with a speed of 4.00 x 10 m/s. x 1)m/s (b) Find the total kinetic energy increase in the process. 576.69-15 ✔3 (a) Find the velocity of the third particle. -13.560-21 X112.34e-21arrow_forward
- Bryce, a mouse lover, keeps his four pet mice in a roomy cage, where they spend much of their spare time joyfully scampering about on the cage's floor. Bryce tracks his mice's health diligently and just now recorded their masses as m₁ = 0.0145 kg, m2 = 0.0141 kg, m3 = 0.0245 kg, and m4 = 0.0105 kg. At this very instant, the x and y components (Ux, U,) of the mice's velocities are, respectively, (U₁x, U₁₁y) = (0.591 m/s, -0.425 m/s,) (v2.x, U2,y) = (-0.605 m/s, -0.933 m/s,) (v3,x, U3,y) = (0.259 m/s, 0.305 m/s), and (V4x, V4,y) = (-0.211 m/s, 0.569 m/s). Calculate the x and y components px and py of Bryce's mice's total momentum. Px = kg.m/s Py = kg.m/sarrow_forwardThere are two particles (1 and 2) that are moving around in space. The mass of particle 1 is 4.1 kg and the mass ofparticle 2 is 4.51 kg. The particles are isolated so that only the forces between the particles are significant. The forcethat 2 exerts on 1 is given by: F21(t) = Fxe−(t/tx )ˆi + Fy sin(2πt/T)ˆj The initial time is t = 0 s and the final time is t = 5.9 s The y-component of the impulse from 1 on 2 is: I12,y = 50.28 N s Fx = 17.4 N, Fy = -28.8 N, tx = 6.5 s, T = 60.7 s what is the x component of the impulse from 1 on 2? What is the y-component of the change in momentum for particle 1? what is the y componentof the average force from 1 on 2arrow_forwardMomentum, P = (2.0 kg m/sec)î – (7.0 kg m/sec)ĵ acts on a particle with position vector 7 = (3.0 m)î – (1.0 m)ĵ. If ř and P are working in Y and – Z direction respectively, what would be the direction of force?arrow_forward
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