MHB Solving Mechanics Problem: Friction, 2 Boys, Toy Acceleration

AI Thread Summary
The discussion revolves around a mechanics problem involving two boys pulling a toy with different forces and angles on a rough surface. The toy has a mass of 3kg and a coefficient of friction of 0.3. Calculations show that the acceleration of the toy is 0.178 m/s², with the direction of acceleration favoring the younger boy's pull. The friction force acts opposite to the direction of motion, confirming that the younger boy's force overcomes the older boy's pull. The conclusion is that the toy moves in the direction of the younger boy’s pull.
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Two boys are arguing over who gets to play with a toy. The toy has mass 3kg and is at rest on rough horizontal ground with coefficient of friction 0.3. The older boy pulls with a force of 26N at an angle of 39 degree above the horizontal. The younger boy pulls in the opposite direction with a force of 24N at an angle of 9 degree above the horizontal. Determine whether the toy moves. If it accelerates find the size of the acceleration and direction.

Iam able to solve this.
I got a= 0.178m/s^2. What iam not able to reason is the direction of acceleration. Pls help
 
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in this case, friction acts opposite to the direction of motion … who wins?
 
skeeter said:
in this case, friction acts opposite to the direction of motion …
You mean the acceleration is positive so the friction acts in the opposite direction which is the young boy?
 
acceleration is in the direction of the young boy’s pull …

$24\cos(9) > 26\cos(39) + 0.3[3g - 24\sin(9) - 26\sin(39)]$
 
skeeter said:
acceleration is in the direction of the young boy’s pull …

$24\cos(9) > 26\cos(39) + 0.3[3g - 24\sin(9) - 26\sin(39)]$
Thank you so much!
 
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