TP 8.40

Given:

m = 1.80 kg

V_i = 2.00 m/s, V_f = 0 m/s

x_i = 0 m, x_f = 0.110 m

m_k = 0.560

Find: k - ?

W_nc= f_k Dx cos(q) = m_k n Dx cos(180^o) = - m_k m g Dx

W_nc= (K_f + U_sf) - (K_i + U_si)

K_f = 0, U_si = 0

W_nc= U_sf - K_i = 1/2 k x_f² - 1/2 m V_i²

- m_k m g Dx = 1/2 k x_f² - 1/2 m V_i²

1/2 k x_f² =  1/2 m V_i²- m_k m g Dx

 k x_f² =  m V_i²- 2 m_k m g Dx

k  =  (m V_i²- 2 m_k m g Dx)/ x_f²

k = 415 N/m