Surfing,
like many other water related sports depends on two major forces acting on the
surfer and the board. These two forces are gravity and buoyancy. These two
forces enable to surfer to ride to float before and during their ride. Gravity
is the pull on a mass towards to center of earth. F

_{mg}=mg the acceleration due to gravity if 9.8m/s^{2}. Buoyancy is the upward force of water onto the board. The force of buoyancy is the density of the fluid times the volume of the fluid displaced times the acceleration due to gravity. F_{B}=pVg. Gravity acts on the center of mass of the person and buoyancy acts on the center of mass of the board. There is gravity acting on the 3.0kg board and gravity acting on the 60.0 kg person on the board. There is a force of buoyancy on the board and a normal force on the surfer. Based on the summation of the forces and the lack of acceleration on the system the normal force the person exerts on the board is equal to the force of gravity of the person. So there is not net acceleration and the person and the board are floating on the water. Since there are only two forces acting on the board and the person:
∑F=ma

F

_{Bb}+F_{N}-_{Fmgp}-F_{mgb}=ma
ma=0

F

_{Bb}+F_{N}-F_{mgp}-F_{mgb}=0
pVg+F

_{N}-mg_{p}-mg_{b}=0
(m

_{b}/V)(V)(9.8m/s^{2})+F_{N}-m_{b}g-m_{p}g=0
(m

_{b})(9.8)+F_{n}-mg-mg=0
F

_{N}=m_{p}(9.8m/s^{2})
When the
surfer is balancing on the board the positioning of the person on the board and
balance is very important. If the surfer is not properly positioned on the
board they will likely “nosedive” or the tip of the board becomes submerged and
the whole board flip. This is due to the forces acting on the board causing a
toque resulting in a flip of the board in a circular motion. The acceleration
is only zero on the system if the force of buoyancy acting upward on the center
of the board is acting on the same position as the force of gravity of the
person. If the person is too far forward on the board then the force of gravity
will act downward some distance away from the force of buoyancy acting upward
resulting in a toque on the board. Torque is a twisting force that tends to
cause rotation. T=rFsinθ. The force of buoyancy acting on the center of mass of
the board so it is slightly behind the center of the board because the back of
the board is heavier. Therefore, the axis of rotation is located at the center
of mass at the center of the board. If the surfer is 0.6 m from the center of
the board this will result in a torque and most likely a nosedive. The angle of
force is 90 degrees because the person’s gravity acts on a right angle from the
board.

T=rFsinθ

T=(0.6m)(mg)sinθ

T=(0.6m)(60kg)(9.8m/s

^{2})(1)
T=352.8 Nm

The toque acting on the board would be 352.8 Nm.

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