1)A child leaps on a skateboard: A 35 kg girl is running at a speed of 2.8 m/s when she jumps on a stationary skateboard. If the system consisting of the girl and the skateboard begins rolling at a speed of 2.6 m/s, what is the mass of the skateboard?

2) 2D Center of Mass of Three Objects:

Three masses located in the x-y plane have the following coordinates:

a 5kg mass has coordinates given by (2, -3) m; a 4kg mass has coordinates 

(-4, 2) m; a 2 kg mass has coordinates (3, 3) m. Find the coordinates of the center of mass to two significant figures.

Expert Answers

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The coordinate `R_(cm)` of the center of mass of a system composed by n particles is defined as a vector by the relation:

`M*R_(cm) = sum_(i=1)^n (m_i*r_i)`

where `M` is the total mass of the system, and `m_i`(respectively   `r_i`) is mass (respectively the position vector), of the i component of the system.

Thus on components we have on the X axis:

`X_(cm) = (1/M)(m_1*x_1 +m_2*x_2+m_3*x_3)`

`X_(cm) =1/(5+4+2)*(5*2+4*(-4) +2*3) =1/11 * 0 =0 m`

On the y axis:

`Y_(cm) =1/(5+4+2)*(5*(-3) +4*2 +2*3) =1/11 *(-1) =-1/11 m`

Answer: the coordinates of the center of mass are `(0,-1/11) m`
or equivalent (0,-0.091) m

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