# Determine the acceleration of block m1 in this wedge-pulley system

• Kaushik
In summary, the conversation discusses solving equations to determine the rightward acceleration of block ##m_1##, with the conversation eventually leading to the conclusion that the book's given solution is incorrect. The conversation also mentions using relative acceleration and equations to find the acceleration of a horizontal string with respect to block ##m_1##. The final solution determined is ##a_0 = 3 \frac{m}{s^2}##.
Kaushik
Homework Statement
The acceleration of block m2 with respect to m1 is 2m/s^2 upward along the inclination. The block m3 accelerates downward with 5 m/s^2.
Relevant Equations
a( of m2 wrt m1) = 2m/s2
a(of m3) = 5m/s2
The equations i got are attached below. Is it right? If yes what should we do after this. I tried solving the equations, but i did not arrive at the solution.

What quantity are you trying to determine? If it is ##a_0## (the rightward acceleration of block ##m_1##) then you seem to be overthinking it.

Kaushik
jbriggs444 said:
What quantity are you trying to determine? If it is ##a_0## (the rightward acceleration of block ##m_1##) then you seem to be overthinking it.
Yes. I am trying to determine ##a_0##. So, do we have an easy way to solve this problem?

Last edited:
Kaushik said:
Yes. I am trying to determine ##a_0##. So, do we have an easy way to solve this problem?
Yes.

Let us start with a simpler version of the problem. If blocks ##m_1## and ##m_2## were glued together, how rapidly would the pair need to be accelerating rightward so that ##m_3## would be accelerating downward at 5 m/sec2?

Kaushik
jbriggs444 said:
Yes.

Let us start with a simpler version of the problem. If blocks ##m_1## and ##m_2## were glued together, how rapidly would the pair need to be accelerating rightward so that ##m_3## would be accelerating downward at 5 m/sec2?
## 5 \frac{m}{s^2} ##?

Kaushik said:
## 5 \frac{m}{s^2} ##?
Yes indeed.

If block ##m_1## were glued to the ground while block ##m_2## were once again free to slide, how rapidly would it need to be accelerating so that block ##m_3## would be accelerating downward at 5 m/sec2?

jbriggs444 said:
Yes indeed.

If block ##m_1## were glued to the ground while block ##m_2## were once again free to slide, how rapidly would it need to be accelerating so that block ##m_3## would be accelerating downward at 5 m/sec2?
## 5 \frac{m}{s^2} ##again? as the pulley attached to ## m_1 ## is not moving anymore?

Kaushik said:
## 5 \frac{m}{s^2} ##again? as the pulley attached to ## m_1 ## is not moving anymore?
Yes. Now unglue all blocks and return to the original problem. Can you write an equation for the downward acceleration of ##m_3## in terms of the rightward acceleration of ##m_1## and the diagonal acceleration of ##m_2##?

[If it were me, I would label the accelerations of ##m_1##, ##m_2## and ##m_3## as ##a_1##, ##a_2## and ##a_3##]

Kaushik
jbriggs444 said:
Yes. Now unglue all blocks and return to the original problem. Can you write an equation for the downward acceleration of ##m_3## in terms of the rightward acceleration of ##m_1## and the diagonal acceleration of ##m_2##?

[If it were me, I would label the accelerations of ##m_1##, ##m_2## and ##m_3## as ##a_1##, ##a_2## and ##a_3##]
Is ## a_0 = 3 \frac{m}{s^2}##?

jbriggs444
Kaushik said:
Is ## a_0 = 3 \frac{m}{s^2}##?
Yes

Kaushik
jbriggs444 said:
Yes
Oh, thanks. But in my book the solution given was 2. So is the solution given in my book wrong?

Kaushik said:
Oh, thanks. But in my book the solution given was 2. So is the solution given in my book wrong?
Yes, assuming the question is as stated then the book is wrong.

Kaushik
jbriggs444 said:
Yes
I used relative acceleration.

If the block ## m_3 ## is accelerating downwards with 5, then string that is horizontal should also accelerate right with 5. But the acceleration of that horizontal string with respect to the block ## m_1 ## should be 2.

Let the horizontal string be h.

## a_h = 5 \frac{m}{s^2} ##
## a_{h} ## ( with respect to ## m_1 ## ) ##= 5 - a_0##

But as ## a_h ##(with respect to ## m_1 ## ) ## = 2 \frac{m}{s^2} ##

we get ## a_0 = 3 \frac{m}{s^2} ##

jbriggs444 said:
Yes, assuming the question is as stated then the book is wrong.

## What is the wedge-pulley system?

The wedge-pulley system is a mechanical system that consists of a wedge-shaped object and one or more pulleys. It is commonly used to change the direction of a force or lift heavy objects.

## What is the role of block m1 in this system?

Block m1 is one of the objects that makes up the wedge-pulley system. It is the block that is attached to the pulley and is responsible for the movement of the system.

## How is the acceleration of block m1 determined in this system?

The acceleration of block m1 in this system is determined by the net force acting on the block. This force is a combination of the weight of the block, the tension in the rope, and the normal force exerted by the wedge.

## What factors affect the acceleration of block m1 in this system?

The acceleration of block m1 is affected by the mass of the block, the angle of the wedge, the coefficient of friction between the block and the wedge, and the tension in the rope. These factors can either increase or decrease the acceleration of the block.

## How can the acceleration of block m1 be calculated in this system?

The acceleration of block m1 can be calculated using Newton's second law of motion, which states that the net force on an object is equal to its mass times its acceleration. By considering all the forces acting on the block and using this equation, the acceleration of block m1 can be determined.

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