# Why Is My Calculation Result for Acceleration Incorrect?

• nicky670
In summary, the conversation discusses the calculation of Fsp and Ffriction, with the correct answer being 1.11ms2. There is confusion about the direction of the spring force, with some believing it is opposite to T and others thinking it is in the same direction. It is clarified that when the spring extends, it exerts a force in the same direction as the tension force. It is also noted that an extended spring is under tension, while a compressed spring is under compression. The conversation ends with a confirmation that the correct answer is 1.11ms2.
nicky670
Homework Statement
In another set up where mass of block A is 𝑚𝐴 = 10.0 kg and the mass of block B is 𝑚𝐵 =12.0 𝑘𝑔. A spring with constant𝑘 = 90 𝑁 / 𝑚 is attached to block A as shown. The incline plane is 𝜃 = 37∘ and the coefficient of kinetic friction between the block A and theincline is 𝜇𝑘 = 0.30 as before. Block B is moving down and block A moving up the slope. (The magnitude of the spring force is
given by |𝐹𝑠𝑝| = 𝑘𝑥 where 𝑥 is the extension.)
Relevant Equations
For Ma(perpendicular) = FN - Magcos(titre) = 0
Ma (Parallel) = Fsp + T - Ffriction - Magsin(titre) = Ma(a)

For Mb: Mbg - T = Mb(a)
Fsp = 90 x 0.12 = 10.8
Ffriction = Magcos(titre) x 0.30
I got the answer 2.09ms2 when the correct answer is 1.11ms2. What am i doing wrong here?

Last edited by a moderator:
Isn't the spring force opposite to T?

Chestermiller said:
Isn't the spring force opposite to T?
But wouldn't the spring force push the block forward?

nicky670 said:
But wouldn't the spring force push the block forward?
It says the spring has an extension of 0.12m.

haruspex said:
It says the spring has an extension of 0.12m.
When the spring extends, wouldn't it exert a force in the same direction as the tension force?

nicky670 said:
When the spring extends, wouldn't it exert a force in the same direction as the tension force?
When you stretch a spring, doesn't it pull back on you in the opposite direction?

nicky670 said:
When the spring extends, wouldn't it exert a force in the same direction as the tension force?
Is an extended spring under tension or under compression?

Chestermiller said:
When you stretch a spring, doesn't it pull back on you in the opposite direction?
Oh, means to say when its extended it will have a tension pulling it back and if compressed there will be a force pushing the block forward?

haruspex said:
Is an extended spring under tension or under compression?
tension.

nicky670 said:
Oh, means to say when its extended it will have a tension pulling it back and if compressed there will be a force pushing the block forward?
Yes.

haruspex said:
Yes.
Thank you haruspex :)

## 1. How does a pulley with a spring work?

A pulley with a spring is a simple machine that uses the force of a spring to lift or lower objects. When the spring is pulled, it creates tension that can be used to lift objects attached to the pulley system. As the spring is released, the tension decreases and the object will lower.

## 2. What is the purpose of a pulley with a spring?

A pulley with a spring is used to make lifting heavy objects easier. The spring provides a mechanical advantage by reducing the amount of force needed to lift the object. It also helps to control the speed and direction of the object as it is being lifted or lowered.

## 3. How do you calculate the mechanical advantage of a pulley with a spring?

The mechanical advantage of a pulley with a spring can be calculated by dividing the load by the effort. The load is the weight of the object being lifted, and the effort is the force applied to the spring. The resulting ratio is the mechanical advantage, which tells you how many times easier it is to lift the load with the pulley and spring compared to lifting it without any assistance.

## 4. What are the different types of pulleys with springs?

There are two main types of pulleys with springs: fixed and movable. In a fixed pulley system, the pulley is attached to a stationary object and the spring is connected to the load. In a movable pulley system, the pulley is attached to the load and the spring is attached to a stationary object. Both types can also have multiple pulleys and springs for increased mechanical advantage.

## 5. How can a pulley with a spring be used in real life?

Pulleys with springs have many practical applications in daily life. They are commonly used in weightlifting and exercise equipment, as well as in elevators and cranes for lifting heavy objects. They can also be found in window blinds, garage doors, and other systems that require controlled movement and lifting of objects.

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