Problem 4: An ice skater of mass M = 56 kg has two snowballs thrown at them at q = 49.9 degrees from each other, as shown in the figure (view from the top). The two snowballs have identical masses of m = 0.291 kg and identical speeds of vo = 5.59 m/s. The snowballs stick to the skater. The skater is initially at rest and you may consider the ice skater to be standing on a frictionless surface. Note: this is a linear momentum problem, not an angular momentum problem. skater V= X Part (c) Calculate the magnitude of the velocity (the speed) of the system (skater + snowballs) v immediately after the snowballs strike the skater. Numeric: A numeric value is expected and not an expression. Part (d) Calculate the angle in degrees at which the system (skater + snowballs) will move with respect to the x-axis after the collision. Numeric A numeric value is expected and not an expression. 0=

Problem 4: An ice skater of mass M = 56 kg has two snowballs thrown at them at q = 49.9 degrees from each other, as shown in the figure (view from the top). The two snowballs have identical masses of m = 0.291 kg and identical speeds of vo = 5.59 m/s. The snowballs stick to the skater. The skater is initially at rest and you may consider the ice skater to be standing on a frictionless surface. Note: this is a linear momentum problem, not an angular momentum problem. skater V= X Part (c) Calculate the magnitude of the velocity (the speed) of the system (skater + snowballs) v immediately after the snowballs strike the skater. Numeric: A numeric value is expected and not an expression. Part (d) Calculate the angle in degrees at which the system (skater + snowballs) will move with respect to the x-axis after the collision. Numeric A numeric value is expected and not an expression. 0=

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter8: Momentum And Collisions

Section: Chapter Questions

Problem 1OQ

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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?
A rocket has total mass Mi = 360 kg, including Mfuel = 330 kg of fuel and oxidizer. In interstellar space, it starts from rest at the position x = 0, turns on its engine at time t = 0, and puts out exhaust with relative speed ve = 1 500 m/s at the constant rate k = 2.50 kg/s. The fuel will last for a burn time of Tb = Mfuel/k = 330 kg/(2.5 kg/s) = 132 s. (a) Show that during the burn the velocity of the rocket as a function of time is given by v(t)=veln(1ktMi) (b) Make a graph of the velocity of the rocket as a function of time for times running from 0 to 132 s. (c) Show that the acceleration of the rocket is a(t)=kveMikt (d) Graph the acceleration as a function of time. (c) Show that the position of the rocket is x(t)=ve(Mikt)ln(1ktMi)+vet (f) Graph the position during the burn as a function of time.
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Figure P9.59a shows an overhead view of the configuration of two pucks of mass In on frictionless ice. The pucks are tied together with a string of length 1' and negligible mass. At time t = 0, a constant force of magnitude F begins to pull to the right on the center point of the string. At time t, the moving pucks strike each other and stick together. At this time, the force has moved through a distance 4 and the pucks have attained a speed v (Fig. P9.59b). (a) What is v in terms of F, d, e, and in? (b) How much of the energy transferred into the system by work done by the force has been transformed to internal energy?
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