Question

Hi, we are stuck on this question. I've attached a diagram. Find the force exerted by the surface on the point of contact with the hammer head. Assume that the force the hammer exerts on the nail is parallel to the nail.

Answer 1

2024.87 N

Explanation:

Given:

L = 32 cm = 0.32 m

θ = 31°

F = -216 N

l = 3.79 cm = 0.0379 m

We must first calculate the force exerted by hammer claws on the nail, just like this:

`\begin{gathered} F\cdot L+f_{}\cdot l\cdot\cos \theta=0 \\ \text{ Replacing and solving for f:} \\ -216\cdot0.32+f\cdot0.0379\cdot\cos 31=0 \\ f=(216\cdot0.32)/(0.0379\cdot\cos 31) \\ f=2127.64\text{ N} \end{gathered}`

Now, we calculate the force in each component to then calculate the resulting force by means of the Pythagorean theorem, like this:

For x-component:

`\begin{gathered} x=-2127.64\cdot\sin \: 31-\mleft(-216\mright) \\ x=-2127.64\cdot\sin \: 31+216 \\ x=-879.82\text{ N} \end{gathered}`

For y-component:

`\begin{gathered} y=2127.64\cdot\cos 31 \\ y=1823.74\text{ N} \end{gathered}`

Now, the resultant force is calculated by means of the Pythagorean theorem:

`\begin{gathered} r^2=x^2+y^2 \\ r=\sqrt[]{x^2+y^2} \\ \text{ Replacing:} \\ r=\sqrt[]{(-879.82)^2+(1823.74)^2} \\ r=2024.87\text{ N} \end{gathered}`