What is the relationship between force, acceleration, and mass in a lift?

[TH02]

Homework Statement

A body hangs from a spring-balance which is suspended from the ceiling if a lift. What is the mass of the body if the balance registers a reading of 70N when the lift has an upward acceleration of 4.0ms^-2. (g = 10ms^-2)

Relevant Equations

F = ma
Weight = mg

Much like the previous question I've posted I was quite unsure of the the method I should take and resorted after many attempts to just trial and error which resulted in getting the correct answer of 5kg after dividing the weight of 70N by 14ms^-2 (sum of upward acceleration and gravitational field strength). Can someone please explain why this works, or the proper method to the question?

 

[PeroK]

Homework Statement:: A body hangs from a spring-balance which is suspended from the ceiling if a lift. What is the mass of the body if the balance registers a reading of 70N when the lift has an upward acceleration of 4.0ms^-2. (g = 10ms^-2)
Relevant Equations:: F = ma
Weight = mg

Much like the previous question I've posted I was quite unsure of the the method I should take and resorted after many attempts to just trial and error which resulted in getting the correct answer of 5kg after dividing the weight of 70N by 14ms^-2 (sum of upward acceleration and gravitational field strength). Can someone please explain why this works, or the proper method to the question?

Why do you think it doesn't work?

What is the $F$ in $F = ma$? And don't just say "force"!

 

[TH02]

Would it be the tension in the spring? Or the weight of the body?

 

[PeroK]

Would it be the tension in the spring? Or the weight of the body?

It's neither. It's the unbalanced or net force. See, for example:

https://www.khanacademy.org/science...ns-laws-of-motion/a/what-is-Newtons-first-law

 

[Chestermiller]

Let’s see your fbd.

 

[TH02]

Let’s see your fbd.

I am not sure if I've added all the forces I need

 

[PeroK]

View attachment 265762

I am not sure if I've added all the forces I need

Gravity? Isn't $T = 70N$?

 

[TH02]

Gravity? Isn't $T = 70N$?

I'm sorry, I'm getting quite confused

 

[PeroK]

I'm sorry, I'm getting quite confused

The question tells you that the spring balance reads $70N$. That means that $T = 70N$ in your diagram.

 

[TH02]

The question tells you that the spring balance reads $70N$. That means that $T = 70N$ in your diagram.

Is this more accurate?

 

[PeroK]

That looks better. What does $a = 4m/s^2$ tell you?

 

[TH02]

That looks better. What does $a = 4m/s^2$ tell you?

That I have a vertical acceleration of 4m/s^2?

 

[PeroK]

That I have a vertical acceleration of 4m/s^2?

Yes, okay, but more than that. Hint: Newton's 2nd Law.

 

[TH02]

Yes, okay, but more than that. Hint: Newton's 2nd Law.

I'm not following, is it that the force being applied to the body is directly proportional to the acceleration acting on the body?

 

[PeroK]

I'm not following, is it that the force being applied to the body is directly proportional to the acceleration acting on the body?

The $F$ in Newton's law is the unbalanced force, which is the vector sum of all forces on the body. In this case we have:
$$F = T - mg, \ \ \text{and} \ \ F = ma$$
Where, to be precise, I have taken upwards as the positive dircetion.

 

[TH02]

The F in Newton's law is the unbalanced force, which is the vector sum of all forces on the body. In this case we have:
F=T−mg, and F=ma
Where, to be precise, I have taken upwards as the positive dircetion.

Ahhh I see

Sorry for taking so long to get there! I appreciate the help

 

[Lnewqban]

I'm not following, is it that the force being applied to the body is directly proportional to the acceleration acting on the body?