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Physics Mechanics- friction

Shah 72

Member
Apr 14, 2021
193
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
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
935
in this case, friction acts opposite to the direction of motion … who wins?
 

Shah 72

Member
Apr 14, 2021
193
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?
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
935
acceleration is in the direction of the young boy’s pull …

$24\cos(9) > 26\cos(39) + 0.3[3g - 24\sin(9) - 26\sin(39)]$
 

Shah 72

Member
Apr 14, 2021
193
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!