Question

It is weigh-in time for the local under 85 kg rugby team. The bathroom scale used to assess eligibilty can be described by Hooke's law, which is depressed 0.65 cm for its maximum load of 115 kg. What is the spring's effective spring constant?

A player stands on the scale, and it depresses by 0.39cm. What is the mass of the player?

Answer 1

Do you know the Hooke's Law equation for springs?

Answer 2

No

Answer 3

F = kx

Where F is the force that is experienced and k is the spring constant. "x" is the amount of displacement that is experienced with the given force (F)

Answer 4

You are also dealing with constant of gravity (9.81 m/s^2)

Answer 5

ok.

Answer 6

I am not sure where to plug what though

Answer 7

Well the first question asks us what the spring constant is, we can solve this by using what I already gave you. We know the mass that displaced the "0.65cm" or "0.0065m". I'm going to use the meters conversion since are constant of gravity is in units of meters.

The weight of a player also known as pounds can be expressed in Newtons as "force" since they're expressing force on the scale by standing on it right? To get a weight of a player, we take their mass which was expressed in (kg) and times it by the constant of gravity (9.81 m/s^2):
\[weight=(9.81 \frac{ m }{ s^2 })(115kg)\]do that now and tell me what you get.

Answer 8

weight = 1128.15

Answer 9

Awesome. Now we have the amount of Force that is upon the scale to displace it 0.0065m. We then plug these two information into our Hooke's Law equation

1128.15 N = k (0.0065m)

Solve for "k" and show me your answer

Answer 10

173561.5385 = k

Answer 11

Awesome. That is the spring's effective constant. It has a high constant meaning the springs are really REALLY tight. To measure even the slightest change of mass of a player.

Since we have the spring constant, we can now solve your 2nd question. The displacement "x" is 0.39 cm or 0.0039 meters. Use the meters and the spring constant you found and plug it into the hooke's Law equation and find the amount of "force" that the player has put upon the scale.

Answer 12

676.89?

Answer 13

That answer was not correct, but I am not sure if that is in the correct units of kg?

Answer 14

Yup! So 676.89 Newtons (N) of force was put on the scale by the player. All we need to do now is find the mass of the player. Earlier we found the amount of weight of the player by just having the mass. How do you get the mass by having the weight?

Answer 15

Which answer is not correct?

Answer 16

Ok I stopped to early. After 676.89 I should plug into what?

Answer 17

Read my above statement.

Answer 18

Remember weight could also be represented in Newtons. (that is your hint)

Answer 19

The weight is the mass.

Answer 20

No. Weight and mass are totally different things. Weight is in definition depends on the gravity that we are experiencing, which is Earth's gravity constant.

Mass is the amount of matter we have without having external gravitational interactions or external accelerations.

Answer 21

Ok. I am not sure what you asking then.

Answer 22

The second quesiton is asking you the mass of the player, meaning it should be expressed in __kg or kilograms. Earlier I asked you to find the weight of a player by just having their mass (kg).

You now have the weight(Newtons) of a player, how do you find their mass(kilograms)

Answer 23

I do not know.

Answer 24

Scroll up to the 4th post I put in this thread and you'll find your equation.

Answer 25

F=kx

Answer 26

That's my 2nd post not my 4th.

Answer 27

Okay do I multiply it by 9.81

Answer 28

No. Look where the weight is placed and where the mass (kilogram) was placed in the equation.

Answer 29

They're on the opposite sides of the equal sign. The mass is multiplied to the 9.81m/s^2 (our gravity)

Answer 30

Oh ok divide by 9.81, which gives the answer 68.9 kg

Answer 31

Thank you.

Answer 32

Yup! Which is below 85kg which is the limit to be in that certain rugby team weight.