Child, Chair, and Spring Scale on Pulley: Forces

In summary, the problem involves a child sitting on a chair attached to a massless and frictionless rope that runs over a pulley. The tension in the rope is 250 N and the child's weight is 230 N. The correct approach is to draw a free body diagram and use Newton's second law of motion to find the acceleration of the child+chair combination. In part (b), a free body diagram of the forces acting only on the child can be used to find the remaining force from the chair.
  • #1
minimario
95
2

Homework Statement


4zJjMRV.png


Homework Equations



$F=ma$

The Attempt at a Solution



(a) Because the spring scale weighs 250 N, the effective weight on the child's side is 230 N. Therefore, $T-230 = \frac{230}{9.8} a$ and $T-250 = -\frac{250}{9.8} a$, so $a = 0.408$.

This is correct, but is the solution really legitimate? The "effective weight" argument seems a bit suspicious and nonrigorous.

(b) I have no idea where to even start. How would the "effective weights" work here? (Or would it even work?)

Thanks,
minimario
 
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  • #2
minimario said:

Homework Statement


4zJjMRV.png


Homework Equations



$F=ma$

The Attempt at a Solution



(a) Because the spring scale weighs 250 N, the effective weight on the child's side is 230 N. Therefore, $T-230 = \frac{230}{9.8} a$ and $T-250 = -\frac{250}{9.8} a$, so $a = 0.408$.

This is correct, but is the solution really legitimate? The "effective weight" argument seems a bit suspicious and nonrigorous.

(b) I have no idea where to even start. How would the "effective weights" work here? (Or would it even work?)

Thanks,
minimario

Hello minimario,

Welcome to Physics Forums! :)

First, here's a link to get you started with using [itex] \LaTeX [/itex] on Phyisics Forums.
https://www.physicsforums.com/threads/physics-forums-faq-and-howto.617567/#post-3977517

No, I don't think your approach is the correct way to go about this problem, even if it did coincidentally lead to the correct answer in this case.

The "250 N" is not the weight of the spring scale, rather it is the reading on the spring scale. You should consider the spring scale itself to be massless. That it means is that the tension in the rope is 250 N.

Whenever you work with a massless and frictionless rope and pulley, it means that the tension of the rope on one side of the pulley is equal to the tension on the other side (I think it is valid from this problem to assume that the rope is also massless and the pully is both massless and frictionless).

(i) Draw a free body diagram (FBD) of all the forces acting on the child+chair combination. Don't forget that the rope has two ends! (Hint: you already know the tension on the rope. Just don't forget both ends.)

(ii) What is the net force acting on the child+chair combination (i.e., sum together all the force vectors, to find the net force vector [and don't forget they are vectors, not scalars])?

(iii) What is the the mass of the child+chair combination. (i.e., not the weight, but the mass)?

(iv) Invoke Newton's second law of motion to find the acceleration.

[Edit: For part b, start by drawing a FBD of all the forces acting only on the child. Hint: you know the child's mass (or you can calculate it now) and the child's acceleration from previous calculations. You also know the child's weight (gravitational force) and the force from the rope that the child is holding onto. Invoke Newton's second law again, and solve for the remaining force on the child from the chair.]
 
Last edited:

What is a child, chair, and spring scale on pulley experiment?

The child, chair, and spring scale on pulley experiment is a simple demonstration of forces and how they interact with each other. It involves a child sitting on a chair with a spring scale attached to the back of the chair. The chair is then connected to a pulley system, and the child can pull on the scale to see the change in force as the chair is lifted.

What are the forces involved in this experiment?

There are three main forces involved in this experiment: the gravitational force acting on the child, the normal force from the chair supporting the child's weight, and the tension force from the spring scale as it is pulled by the child. These forces are all interacting with each other and can be measured using the spring scale.

What is the purpose of using a pulley system in this experiment?

The pulley system allows for a change in direction of the force being applied. In this experiment, the child can pull down on the scale, but the chair is lifted up. This allows for a better understanding of how forces can act in different directions and how they can be balanced.

How does the spring scale measure force?

Spring scales work based on Hooke's Law, which states that the force applied to a spring is directly proportional to the amount the spring stretches or compresses. The spring scale has a spring inside that is calibrated to measure force based on the amount it stretches or compresses.

What are some real-life applications of understanding forces through this experiment?

Understanding forces is essential in many fields, such as engineering, physics, and sports. This experiment can help in understanding how forces are balanced and how they affect the motion of objects. It can also be applied to the design of structures, machines, and even athletic movements.

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