Question

A sled of mass 26 kg has an 18 kg child on it. If big brother is pulling with a 30 N force to the right and 10 N up, and big sister is pushing with a 40 N force to the right and 16 N down, what is the normal force?

Answer 1

Given data:

* The mass of the sled is m_1 = 26 kg.

* The mass of the child is m_2 = 18 kg.

* The force in the upwards direction by the big brother is F_1 = 10 N.

* The force in the downwards direction by the big sister is F_2 = 16 N.

Solution:

The net mass on the sled along with the child is,

`\begin{gathered} m=m_1+m_2 \\ m=26+18 \\ m=44\text{ kg} \end{gathered}`

The net weight of the sled along with the child is,

`\begin{gathered} w=mg \\ w=44*9.8 \\ w=431.2\text{ N} \end{gathered}`

The weight of the sled along the child is acting on the sled in the downwards direction.

Thus, the normal force acting on the sled (taking upward force as negative and downward force as positive) is,

`\begin{gathered} N=w+F_2-F_1 \\ N=431.2+16-10 \\ N=437.2\text{ newton} \end{gathered}`

Thus, the normal force acting on the sled is 437.2 N.