Swimmer off tower: Velocity and Force

[Wanting to Learn]

Problem:
A 65kg swimmer jumps off a 10.0m tower.
a. Find the swimmer's velocity on hitting the water.
b. The swimmer comes to a stop 2.0m below the surface. Find the net force exerted by the water.
Given & Equations:
v₀ = 0m/s
a = 9.8m/s²
d = 10m
v_f = __m/s

F = __N

v_f² = v₀² + 2ad
F = ma

Work:
v_f² = v₀² + 2ad
v² = 0 + 2•9.8•10
v² = 196
v = 14

F = m•a
F = 65•9.8
F = 137.2

Conclusion:
So I got
a. = 14m/s
b. = 137.2N

Is this correct? I just started learning force so have no idea whether that seems to be a reasonable amount of force.
Thank you in advance.

 

[kuruman]

Part b is not correct. The swimmer is no longer in free fall therefore his/her acceleration is not 9.8 m/s². You need to find what acceleration is needed to change the velocity from 14 m/s to zero over 2 meters.

 

[Wanting to Learn]

So would acceleration be -7m/s ?
In that case I would get F = 7*14 = 98, but what would I do with the negative, or is it irrelevant?

 

[kuruman]

So would acceleration be -7m/s ?

How did you get this number? BTW, acceleration has units m/s².
Also, assuming that a = 7 m/s², why is F = 7*14? What equation are you thinking of?
The negative is not irrelevant; it denotes a direction opposite to the one you assumed is positive.

On edit: As far as having an intuitive feeling for force is concerned, 1 Newton is approximately the weight of a 1/4 lb. stick of butter.

 

[haruspex]

Find the net force exerted by the water.

The question ought to tell you to pretend that the force is constant during the deceleration, otherwise there is no way to solve it with the information provided.

 

[jbriggs444]

So would acceleration be -7m/s ?

That is the acceleration required to go from 14 m/s to 0m/s in two seconds. The question at hand is how much acceleration to go from 14 m/s to 0 m/s in two meters.

 

[Wanting to Learn]

I looked in the textbook, found a similar problem, and followed its format (yes I know I should have done that before but because we do not normally use the textbook I hadn't thought to), so I got the following (continued from my earlier work):
v_f² = v₀² + 2a(x-x₀)
0 = 14² + 2a(2-0)
-196 = 4a
a = -49m/s²

F = m•a
F = 65•-49
F = -3185N

Is this correct?

 

[Wanting to Learn]

As far as having an intuitive feeling for force is concerned, 1 Newton is approximately the weight of a 1/4 lb. stick of butter.

Thank you for this.

 

[jbriggs444]

I looked in the textbook, found a similar problem, and followed its format (yes I know I should have done that before but because we do not normally use the textbook I hadn't thought to), so I got the following (continued from my earlier work):
v_f² = v₀² + 2a(x-x₀)
0 = 14² + 2a(2-0)
-196 = 4a
a = -49m/s²

F = m•a
F = 65•-49
F = -3185N

Is this correct?

Almost. The acceleration is correct. The force is correct. But there is a gotcha. Go back and re-read the question.

In F=ma, the F is the total force on the object from all sources. The question asks for the net force by the water on the swimmer. Can you think of something that you've missed?

 

[Wanting to Learn]

Almost. The acceleration is correct. The force is correct. But there is a gotcha. Go back and re-read the question.
In F=ma, the F is the total force on the object from all sources. The question asks for the net force by the water on the swimmer. Can you think of something that you've missed?

Thanks.

I'm not sure, is there force being exerted on the swimmer by something other than the water? Or does that calculation include force other than just what is on the swimmer? Or does it have something to do with how there is both the force the water exerts on the swimmer and that the swimmer exerts on the water?
(This is a new concept and the first homework set we have had on it so I'm not entirely certain about the concepts.)

Edit: Does this have to do with gravity? How would I take that into account?

 

[kuruman]

Does this have to do with gravity? How would I take that into account?

Yes, it has to do with gravity.
1. The net force is the sum of all the forces.
2. The net force is mass times acceleration.
3. There are two forces acting on the swimmer, gravity and water friction.
4. Put it together.

 

[Wanting to Learn]

So -49 is total acceleration and -9.8 is the acceleration due to gravity, so does that mean that -39.2 is the acceleration due to the water?
This would make F_water = 65•-39.2 = -2,548N

 

[jbriggs444]

So -49 is total acceleration and -9.8 is the acceleration due to gravity, so does that mean that -39.2 is the acceleration due to the water?

F=ma.
You know the acceleration -- 49 m/s^2 downward.
You know the mass -- 65 kg.
You already calculated the total force -- 3185N.

What you have not calculated is the force due to the water alone.

 

[kuruman]

So -49 is total acceleration and -9.8 is the acceleration due to gravity, so does that mean that -39.2 is the acceleration due to the water?
This would make Fwater = 65•-39.2 = -2,548N

Say positive is "up" and negative is "down".
In what direction is the net force, up or down?
In what direction is the force of gravity, up or down?
In what direction is the force of the water, up or down?

 

[Wanting to Learn]

Thanks jbriggs444 for the idea to just say downward instead of trying to use negatives since all the forces I'm dealing with in this are downwards, I find that easier to think about than negatives.

 

[Wanting to Learn]

What you have not calculated is the force due to the water alone.

So would this be the way to calculate only the force from the water, without including gravity?

F_total = 3185N downward
F_gravity = 65•9.8 = 637N downward

F_total- F_gravity = F_water
3185 - 637 = 2,548

Answer:
F_water = 2,548N downward

 

[kuruman]

If all the forces are downward and the swimmer is already moving in a downward direction, the speed will increase will it not? To stop something from moving in a given direction, you need to apply a force in the opposite direction. Please reconsider my post #14.

On edit: Perhaps you are confusing velocity and acceleration.
When the acceleration and the velocity point in the same direction, the speed is increasing regardless of whether that direction is positive or negative.
When the acceleration and the velocity point in opposite directions, the speed is decreasing regardless of which is positive and which is negative.
The converse is also true.

 

[Wanting to Learn]

If all the forces are downward and the swimmer is already moving in a downward direction, the speed will increase will it not? To stop something from moving in a given direction, you need to apply a force in the opposite direction. Please reconsider my post #14.

So is the force of the water upward?

Say positive is "up" and negative is "down".
In what direction is the net force, up or down?

Is net force up? I'm confused trying to think about this because the swimmer is going down, but I think the force is pushing up because if it was pushing down then the swimmer would just keep going more down.

In what direction is the force of gravity, up or down?

Gravity would be down.

In what direction is the force of the water, up or down?

Reference my first replies, is the water force pushing up?

I'm not sure how to apply all this into the calculations if some things should be positive and some negative.

 

[kuruman]

Is net force up?

Facts
1. The net force is always in the direction of the acceleration.
2. The velocity is down in this case.
3. The speed is decreasing because the swimmer eventually comes to a stop.
4. When the speed is decreasing, the acceleration is opposite to the velocity.
So ... in what direction is the net force?

'm not sure how to apply all this into the calculations if some things should be positive and some negative.

The net force is the sum of all the forces. What's up is positive and what's down is negative. As you said earlier
F_total = F_water + F_gravity
Just put the numbers in with the appropriate sign in front of each force and solve.

 

[Wanting to Learn]

in what direction is the net force?

Therefore the net force is upward.

What's up is positive what's down is negative.

F_total = + 3185
F_gravity = - 637
F_water = + ____

F_total- F_gravity = F_water

Should be the same thing as

F_total = F_water + F_gravity

I just need to be really careful about the signs, so:
F_total = F_water + F_gravity
+3185 = +F_water + -637
+3185 +637 = +F_water + -637 +637
+3,822 = +F_water
So that makes final answer:
F_water = +3,822

(upward)​

 

[kuruman]

Yey! It's all very logical.

 

[Wanting to Learn]

Yey! It's all very logical.

Thank you!