Solving Mechanics Problem: Friction, 2 Boys, Toy Acceleration

In summary, two boys are arguing over a 3kg toy on rough ground with a coefficient of friction of 0.3. The older boy pulls with a force of 26N at an angle of 39 degrees above the horizontal, while the younger boy pulls in the opposite direction with a force of 24N at an angle of 9 degrees above the horizontal. It is determined that the toy will move and accelerate at 0.178m/s^2, but the direction of the acceleration is not specified. Friction acts in the opposite direction of motion, so it is unclear who ultimately wins the argument.
  • #1
Shah 72
MHB
274
0
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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  • #2
in this case, friction acts opposite to the direction of motion … who wins?
 
  • #3
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?
 
  • #4
acceleration is in the direction of the young boy’s pull …

$24\cos(9) > 26\cos(39) + 0.3[3g - 24\sin(9) - 26\sin(39)]$
 
  • #5
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!
 

1. What is friction and how does it affect the acceleration of a toy?

Friction is a force that resists the motion of an object when it is in contact with another surface. In the case of the two boys playing with a toy, friction can affect the acceleration by creating a force that opposes the motion of the toy, making it harder to accelerate.

2. How can I calculate the frictional force in this problem?

To calculate the frictional force, you will need to know the coefficient of friction between the toy and the surface it is moving on, as well as the weight of the toy. You can use the formula F = μmg, where F is the frictional force, μ is the coefficient of friction, m is the mass of the toy, and g is the acceleration due to gravity (9.8 m/s²).

3. What factors can affect the coefficient of friction in this problem?

The coefficient of friction can be affected by the type of surface the toy is moving on, the weight of the toy, and any external forces acting on the toy. Additionally, the smoothness or roughness of the surfaces in contact can also affect the coefficient of friction.

4. How can I determine the acceleration of the toy in this problem?

To determine the acceleration of the toy, you will need to use Newton's Second Law of Motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F=ma). By calculating the net force on the toy and dividing it by its mass, you can find the acceleration.

5. Can I ignore friction in this problem and still accurately solve it?

No, friction is an important factor to consider in this problem as it can greatly affect the acceleration of the toy. Ignoring friction would result in an inaccurate solution and may not reflect the real-world scenario of the two boys playing with the toy.

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