The figure below shows a claw hammer being used to pull a nail out of a horizont
ID: 2041006 • Letter: T
Question
The figure below shows a claw hammer being used to pull a nail out of a horizontal board where ? = 34.2°. The mass of the hammer is 1.00 kg. A force of 120 N is exerted horizontally as shown, and the nail does not yet move relative to the board. Assume the force the hammer exerts on the nail is parallel to the nail.
(a) Find the force exerted by the hammer claws on the nail.
___kN
(b) Find the force exerted by the surface on the point of contact with the hammer head.
(___ î +___ ?) N
___kN
direction ___° above the horizontal 16 30.0 cm ii Single point of contact 5.00 cmExplanation / Answer
a)
As the harmer is in equilibrium net force and net torque acting on the hammer must be zero.
let F' is the magnitude of force exerted by the nail on hammer and force exerted by hammer on nail.
net torque about contact point = 0
F'*5*sin(90-theta) - 30*F*sin(90) = 0
F'*5*sin(90- 34.2) - 30*120 = 0
F' = 30*120/(5*sin(55.8))
= 871 N
= 0.871 kN
direction : 55.8 degrees above +x axis
b) let Fx and Fy are the components of forces exerted by the surface.
Apply, Fnetx = 0
F - F'*sin(34.2) + Fx = 0
Fx = F'*sin(34.2) - F
= 871*sin(34.2) - 120
= 370 N
Apply, Fnety = 0
m*g - F'*cos(34.2) + Fy = 0
Fy = F'*cos(34.2) - m*g
= 871*cos(34.2) - 1*9.8
= 711 N
so, force exerted by the surface on the point of contact with the hammer head = Fx i + Fy j
= (370 i + 711 j) N
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