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BaLLatris [955]
2 years ago
5

9) A string exerts a force of 58 N on a box at an angle of 34 degrees from the horizontal. The box has a mass of 4 kg

Physics
1 answer:
Anna11 [10]2 years ago
8 0

The acceleration of the box that has a mass of 4 kg and a coefficient of kinetic friction of 0.2, when moved by an exerted force of 58 N, is 10.06 m/s².    

The acceleration of the box can be calculated with the sum of the forces acting on the x-direction:

\Sigma F_{x} = ma

We will not take into account the forces acting on the y-direction since we need to find the acceleration of the box when it is moving (x-direction).

T_{x} - F_{\mu} = ma    (1)

Where:

  • T_{x}: is the horizontal component of the tension force (T) exerted by the string on the box = T*cos(θ) 
  • θ: is the angle (from the horizontal) = 34°
  • F_{\mu}: is the force due to the kinetic friction = -μN (the minus sign is because it is in the opposite direction of motion)  
  • m: is the mass of the box = 4 kg
  • a: is the acceleration =?
  • μ: is the coefficient of kinetic friction = 0.2
  • N: is the normal force = mg
  • g: is the acceleation due to gravity = 9.81 m/s²

From equation (1) we have:

Tcos(34) - \mu N = ma  

Tcos(34) - \mu mg = ma  

Hence, the acceleration is:

58N*cos(34) - 0.2*4 kg*9.81 m/s^{2} = 4 kg*a  

a = \frac{58N*cos(34) - 0.2*4 kg*9.81 m/s^{2}}{4 kg} = 10.06 m/s^{2}

Therefore, the acceleration of the box when the box is moving is 10.06 m/s².

You can learn more about forces here:

  • brainly.com/question/2008782?referrer=searchResults
  • brainly.com/question/24611730?referrer=searchResults

 

I hope it helps you!

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