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Homework Problems

 

HW#25   Ch 9: Center of Mass and Linear Momentum

Instructions: Be sure to write formulas and show substitutions to earn full credit.

1.    Three point masses are located at coordinates (1.0m, −3.0m), (3.0m, 2.0m) and (−2.0m, −4.0m), respectively. a) Find the center of mass of the system if M1 = 2 kg, M2 = 5 kg and M3 = 1 kg. b) What is the acceleration of the center of mass if a force of \(\vec F = \left( {16N} \right)\hat i\) is applied to the 2 kg point mass?

2.    What are the (a) x-coordinates and (b) y-coordinates of the center of mass of the plate shown, if the dimension L = 10 cm?

Plate mass diagram

3.    Krish decides to bake some cookies, so he rolls the dough into a rectangular sheet with a horizontal dimension of 32 cm. Using a cookie cutter, he cuts seven circular holes of radius 4 cm in the dough, which has uniform thickness (see figure below). The holes are cut so that each circle touches another circle at one point without overlapping. If the bottom left corner of the cookie dough is placed at the origin, what are the coordinates of the center of mass?

Cookie dough with circular holes

4.    A male Canadian goose of mass 5.7 kg is flying with a velocity \({\vec v_m} = \left( {12.2\frac{m}{s}} \right)\hat i + \left( {13.1\frac{m}{s}} \right)\hat j\) while a female Canadian goose of mass 5.0 kg is flying with a velocity \({\vec v_f} = \left( { - 22.1\frac{m}{s}} \right)\hat i + \left( {3.50\frac{m}{s}} \right)\hat j\). What is the velocity of their center of mass?

5.    Two masses of 5 kg and 10 kg are connected by a compressed spring and rest on a frictionless table. After the spring is released, the smaller mass has a velocity of 8 m/s to the left. What is the velocity of the larger mass?