Why Is the Buoyant Force Added to the Decelerating Force in Diving Physics?

[2710]

There is a diver of mass 72Kg who stands 2.4m away from the pivot of the diving board, 3.2m above the water.

"The water brings the diver to rest when his centre of mass is 1.6 m below the surface of the
water. Calculate the average total upward force acting on the diver which brings his vertical
velocity to zero."

I calculate the speed as he enters the water to be 7.92 which is correct.

u=7.92
v=0
a=?
s=1.6

a comes out to be -19.6m/s^2

F=ma

F= 72x |19.6| = 1411N

Yet, in the answers, it says that you have to plus 706 to this to get the total upward force. I understand that 706 comes from the mass(72) x g(9.8).

It tells me that 1411 is the decelarating force, and that 2117N is the toal upward force. Can I just ask, why is the extra 706 needed? Is it to do with Newtons first law, stating that every force has an equal and opposite force? But even so, doesn't the F=Ma in my calculation take care of that force?

Thanks

 

[ImAnEngineer]

There is a diver of mass 72Kg who stands 2.4m away from the pivot of the diving board, 3.2m above the water.

"The water brings the diver to rest when his centre of mass is 1.6 m below the surface of the
water. Calculate the average total upward force acting on the diver which brings his vertical
velocity to zero."

I calculate the speed as he enters the water to be 7.92 which is correct.

u=7.92
v=0
a=?
s=1.6

a comes out to be -19.6m/s^2

F=ma

F= 72x |19.6| = 1411N

Yet, in the answers, it says that you have to plus 706 to this to get the total upward force. I understand that 706 comes from the mass(72) x g(9.8).

It tells me that 1411 is the decelarating force, and that 2117N is the toal upward force. Can I just ask, why is the extra 706 needed? Is it to do with Newtons first law, stating that every force has an equal and opposite force? But even so, doesn't the F=Ma in my calculation take care of that force?

Thanks

Big hint:
|F_net|=|F_upwards - F_gravitation|= m |a|

:)

 

[nlightner]

for your question. It is great to see you are thinking critically about the problem and trying to understand the concept behind the answer.

The extra 706N is needed because it represents the buoyant force acting on the diver. When the diver enters the water, the water exerts an upward force on him, which helps to bring him to a stop. This force is equal to the weight of the water displaced by the diver's body, according to Archimedes' principle.

In this case, the diver's body displaces a volume of water with a weight of 706N, which is equal to his weight on land. This buoyant force helps to reduce the total downward force acting on the diver, making it easier for the upward force to bring him to rest. Therefore, the total upward force needed is the decelerating force (1411N) plus the buoyant force (706N), giving a total of 2117N.

You are correct in saying that F=ma takes care of the equal and opposite force, but in this case, there are multiple forces acting on the diver (gravity, buoyancy, and the force from the water), so we need to consider all of them to get the total upward force acting on the diver.

I hope this helps to clarify the concept. Keep up the good work in your scientific thinking and problem-solving skills!