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- (a) What is the momentum of a 2000-kg satellite orbiting at 4.00 km/s? (b) Find the ratio of this momentum to the classical momentum. (Hint: Use the approximation that at low velocities.)The four masses shown in the diagram are connected by massless, rigid rods. The mass of the A particle is 400 g, the mass of the B particle is 650 g, the mass of the C particle is 700 g, and the mass of the D particle is 550 g. The length of the rods is 40 cm. Consider the A particle to be the origin of the coordinate system. The x coordinate of the center of mass (in cm) is ...Problem 3 A hollow sphere of mass m and radius R has its center of mass at rest as it spins at a given wo. Two point masses, each of mass m, travel with exactly opposite velocities and collide simultaneously at mirror image angles as drawn. Given the angle a, find an expression for the angle between the spin vectors just before and just after the collision. Two mZv 8 before Lom % m Zw after
- A BO Two objects with identical masses m are tied to each other with a string of length L. The figure shows the situation at the initial time t = 0. At that instant, the string is tight, B is at rest, A is moving with velocity i A = i - vo . We will call the reference frame in which the problem is stated as the lab frame. It is easier to investigate the motion and answer the following questions in the center of mass frame. For this reason, first we express the initial conditions in this frame. (a) Find the initial velocity of A and B relative to the center of mass frame. Note: you should enter the unit vectors i,j, k as ihat, jhat and khat. %3D (b) Find the tension in the string Tension = (C) Find the period of the motion in the center of mass frame. tperiod (d) Suppose that half a period has passed, i.e, the time is nowt = tperiod/2. Find the velocities of A and B in the lab frame at that time. %3DA thin empty frame is hung along side A (see figure). Side A is 1.19 m long and side B is 0.957 m long. Side C is hit by a bullet with a mass of 26.0 g, an initial velocity of 148.08 m/s and a final velocity of −118 m/s. Calculate the energy loss during the impact if the frame rotates frictionlessly around the z-axis and the frame's moment of inertia around this axis is 1,885 kg · m². Assume that the ball bounces straight back after the impact.A 0.25 kg mass of clay is moving with a horizontal velocity of v when it collides and sticks to a 5 kg object hanging from the end of a 1 meter long rod. Find the minimum velocity v so that the objects will make one complete revolution.
- In 1977 the planet Alderaan, with a mass of 3 × 1024 kg, exploded. Assume it was initially at rest and experienced no external interactions. Problem 3.2. Consider instead that the planet instead blew apart into three pieces, with 30% of its mass flying away at 3, 000 km/s, and 20% of its mass flying away at 5, 000 km/s at an angle of 120o relative to the velocity direction of the first fragment. Draw a diagram of this situation. What velocity did the rest of the planet have? Report the direction by specifying its angle relative to the velocity direction of the first fragment.Find the total mass of a mass distribution of density o in a region T in space. o = e*-)-<,T the tetrahedron with vertices (0,0, 0), (2,0, 0), (0, 2,0), (0, 0, 2) -x-y-z Round your answer to 2 decimal places. odxdydz = i TQuestion 9: A half uniform annulus of inner and outer radii R1 and R2 has a non- uniform surface mass density given by o = oor where oo is a positive constant and r is the radial distance from the origin (radial coordinate in the cylindrical coordinates) as shown in Figure 6. Find i) the mass of the half annulus, and ii) the position of the center of mass, i.e., (xem, Yem) the center of mass in terms of R1 and R2. R2 M Figure 6
- A typical geosynchronous spacecraft requires 15 m/s/yr for orbital stationkeeping and momentum dumping. The satellite must last 10 years, and has a dry mass of 4000 kg. What is the fuel budget for monopropellant hydrazine with Isp = 220 s? %3Da particle with a mass of m1 slides down a frictionless road from point A to the stationary state. This particle hits another m2=3m1-mass stationary particle at point B. The observed orbit is horizontal at point B. a) Find the range of values that the collision coefficient e can take to move the m1 mass particle upwards (B to A) after impact. b) To e=0.5, find the h* height of the m1 mass particle and the w distance that the m2 mass will take horizontally.Consider two particles A and B of masses m and 2m at rest in an inertial frame. Each of them are acted upon by net forces of equal magnitude in the positive x direction for equal amounts of time t. Moment of the particles A and B in centre of mass frame respectively are?