TP 5.29

Given:

A = 115 N

a = 0.725 m/s²

Find: (a) m - ?

 Let's find components of the forces acting on the suitcase: 

A_x = A cos(q_A) = (115 N) cos(90.0^o) = 0

A_y = A sin(q_A) = (115 N) sin(90.0^o) = 115 N

  w_x = w cos(q_w) = w cos(-90.0^o) = 0

 w_y = w sin(q_w) = w sin(-90.0^o) = w = m g

Applying second Newton's Law: 

SF_x = m a _x    0 = 0 (trivial result, since no forces act in x-direction)

 SF_y = m a _y      A_y + w_y = m a _y     

A_y - m g  = m a _y     

A_y =  m g  + m a _y  = m (g + a _y)

m = A_y /(g + a _y)

m =  (115 N)/ (9.81 m/s² + 0.725 m/s²) = 10.9 kg

a =  (V - V₀)/t

a = ((12.0 m/s) - 0)/ (4.00 x 10^-3 s) = 3 x 10³ m/s²

F_net = m a = (0.530 kg)(3 x 10³ m/s²) = 1.59 x 10³ N