The vector position of a 3.45 g particle moving in the xy plane varies in time according to i, - (3i + 35)t + 2jr? where t is in seconds and is in centimeters. At the same time, the vector position of a 5.20 g particle varies as i,- 31 - zir? - 6jt. (a) Determine the vector position (in cm) of the center of mass of the system at t = 2.90 s. x cm cm (b) Determine the linear momentum (in g cm/s) of the system at t = 2.90 s. 9. cm/s (e) Determine the velocity (in cm/s) of the center of mass at t = 2.90 s. cm/s (4) Determine the acceleration (in cm/s) of the center of mass at t = 2.90 s. cm/s? (e) Determine the net force (in µN) exerted on the two-particle system at t = 2.90 s. UN net

(3î + 3j)t + 2ĵt² where t is in seconds andr is in centimeters. At the same The vector position of a 4.00 g particle moving in the xy plane varies in time according tor, time, the vector position of a 5.55 g particle varies as r, = 3î - 2ît? - 6jt. (a) Determine the vector position (in cm) of the center of mass of the system at t = 2.60 s. cm cm (b) Determine the linear momentum (in g · cm/s) of the system at t = 2.60 s. p = g· cm/s (c) Determine the velocity (in cm/s) of the center of mass at t = 2.60 s. cm/s cm (d) Determine the acceleration (in cm/s2) of the center of mass at t = 2.60 s. a cm/s? cm (e) Determine the net force (in µN) exerted on the two-particle system at t = 2.60 s. µN net

a shape is on an x-y axis, beginning at x = 0.  The bottom of the shape is 25 cm long and it reaches a height of 20 cm.  The shape weights 450 g.   The shape has a triangular form, like a wedge.    If shape has a uniform density and a uniform width in the z-direction, find the x-component of the center-of-mass.

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A set of three masses is arranged as shown below. Calculate the position of the center of mass of the system, i.e., find the coordinates (xcm, Ycm) in units of meters. У (m) 2.00 2.00 kg 5.00 kg 1.00 10.00 kg + x (m) 1.00 2.00

kg, 4. (a) The masses of the Earth and the Moon are 5.98 × 1024 kg and 7.35 x 1022 respectively, and their centers are separated by 3.84 × 108 m. Where is the center of mass of this system located? (b) Consider two objects with masses mA = 35 kg and mp = 25 kg. They have velocities (in m/s) đA = 12î – 16j and õB of the center of mass of the system. -20î + 14j. Determine the velocity

Problem Two. A rod of length L = 2.0 m is placed on the x-axis from x = 0 to x = L. The rod has a mass density given by 2 = 2] 1+- x- where 2, = 2.0k. L' Find the location of the center of mass of the rod in meters. 4.) (A) 1.5 (B) 1.3 (С) 1.1 (D) 1.7 (E) 0.45 Consider if the rod is subjected to an applied force given by F = Aî +Bx²j , where A=10 N and B = 25 N2 . If the end of the rod at x = 0 is attached to a hinge, find the angular acceleration of the rod in rad/s². m 5.) (A) 0.68 (B) 0.92 (C) 0.26 (D) 0.34 (E) 0.45 Find the direction of the net torque vector acting on the rod. 6.) (A) +z (В) —х (C) +x (D) –z (E) -у

Enet = The vector position of a 3.80 g particle moving in the xy plane varies in time according tor, = (3î + 3j)t + 2ĵt2 where t is in seconds and r is in centimeters. At the same time, the vector position of a 5.35 g particle varies as 2 sr, = 3î – 2ît? - 6jt. (a) Determine the vector position (in cm) of the center of mass of the system at t = 2.40 s. rcm 4.744i – 7.38j cm (b) Determine the linear momentum (in g• cm/s) of the system at t = 2.40 s. p = 11.4i – 35.58j g• cm/s (c) Determine the velocity (in cm/s) of the center of mass at t = 2.40 s. 1.245i – 3.888j cm/s = cm (d) Determine the acceleration (in cm/s2) of the center of mass at t = 2.40 s. 0.6775j cm/s? = cm (e) Determine the net force (in µN) exerted on the two-particle system at t = 2.40 s. µN

Problem 3: A particle with mass ma = 3.00 kg is located at ra = (2.50 i + 3.50 j) m, and a second particle of mass m2B = 5.00 kg is located at rB = (1.50 i - 3.00 j) m. Find the location of the center of mass of the system relative to the point (1,1).

A block of mass 10.0 kg is moving east at 2.0 m/s and another block, of mass 4.0 kg is moving north at 4.0 m/s. The velocity of the center of mass of this two-block system is 2.0 m/s at an angle of 51 degrees south of east 1.8 m/s at an angle of 39 degrees north of east 6.0 m/s at an angle of 51 degrees west of north 1.8 m/s at an angle of 39 degrees east of north 2.0 m/s due west