Question

Question #bdbbe

Answer 1

Newton's second law of motion can be written as

`F=ma` .......(1)

Let `m_p` be mass of penguin, `m_s` be mass of sled and `g` be acceleration due to gravity.

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)`