Question #bdbbe
1 Answer
Newton's second law of motion can be written as
#F=ma# .......(1)
Let
Force of static friction between penguin and sled is
#F_s=mu_sm_pg# .......(2)
Using (1), acceleration of penguin when it does not slide from the sled be
#a = µ_s g# .......(3)
The sled must also accelerates at the same rate. In such a case net force on the sled is
#F_"net" = (m_p + m_s)a#
Using (3)
#F_"net" = (m_p + m_s)xxmu_s g#
#=>F_"net" = (m_pg + m_sg) xx mu_s #
#=>F_"net"= (w_p + w_s)mu_s# ......(4)
The force of kinetic friction required to be overcome is
# F_k = µ_k (m_pg + m_sg)#
# =>F_k = µ_k (w_p + w_s)# ........(5)
The maximum applied force so that penguin does not slide from the sled and force of kinetic friction is also overcome is
#F_max = F_"net" + F_k #
Using (4) and (5)
#F_max= (w_p + w_s)µ_s + (w_p + w_s)µ_k#
#F_max = (µ_s + µ_k)(w_p + w_s)#