How Does the Tension in a Child's Neck Muscles Change on a Water Slide?

[nate9519]

Homework Statement

A child lying on her back experiences 55 N tension in the muscles on both sides of her neck when she raises her head to look past her toes. Later, sliding feet first down a water slide at terminal speed 5.7 m/s and riding high on the outside wall of a horizontal curve of radius 2.4 m, she raises her head again to look forward past her toes. Find the tension in the muscles on both sides of her neck while she is sliding.

Homework Equations

F = ma
CF = (mv^2)/r

The Attempt at a Solution

I thought what I needed to do was to find the centripetal force and add it to the original force but I can't do that without a value for mass. I don't know what to do

 

[Orodruin]

What is the acceleration the head is lifted against just gravity? What is the acceleration lifted against in the slide?

 

[nate9519]

Against the head would be 9.8 m/s^2 . the centripetal acceleration would be 13.54 m/s^2

 

[Orodruin]

So, if a force of 55 N is required to lift against 9.8 m/s^2, what force is required to lift against 13.5 m/s^2 with the same geometry?

I should add a caveat here, it is not clear from the problem formulation if you also need to consider gravity. "Riding high on the outside" seems to indicate not, but you never know.

 

[HalfLostAndSearching]

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I would approach this problem by first understanding the physical principles at play. In this case, we know that the child is experiencing tension in her neck muscles, which is a result of the force needed to lift her head against the force of gravity. We also know that she is sliding down a water slide at a constant speed, which means that the forces acting on her must be balanced.

To find the tension in her neck muscles while sliding, we can use the equation F = ma, where F is the net force acting on the child and m is her mass. Since we are looking for the tension in her neck muscles specifically, we can assume that the only forces acting on her are the force of gravity and the tension in her neck muscles.

Therefore, we can set up the following equation:

F = mg + T

Where F is the net force, m is the mass of the child, g is the acceleration due to gravity (9.8 m/s^2), and T is the tension in her neck muscles.

We also know that the child is sliding at terminal speed, which means that her acceleration is zero. This means that the net force acting on her must also be zero. Therefore, we can set up a second equation:

F = 0

Combining these two equations, we can solve for the tension in her neck muscles:

mg + T = 0

T = -mg

Plugging in the known values, we get:

T = -(m)(9.8 m/s^2)

Since we do not know the mass of the child, we cannot calculate the exact value of T. However, we can still make some observations. We know that the tension in her neck muscles is equal to the force of gravity acting on her. This means that the tension will be the same regardless of whether she is sliding or lying down. However, the direction of the tension will change, since she is now sliding feet first down the water slide.

In conclusion, as a scientist, I would use my knowledge of physical principles and equations to approach this problem and make observations about the tension in the child's neck muscles. I would also note that more information, such as the mass of the child, would be needed to find a specific numerical value for the tension.