A box is being accelerated across a rough, level surface. A force is being applied to the box in an upward and a rightward direction (as shown below). This force makes an angle of 30 degrees with the horizontal. The force of friction experienced by box would be equal to______.
Fn = M*g-F*sin30 = Normal force.
Fk = uk * Fn = uk*(M*g-F*sin30).
To determine the force of friction experienced by the box, we can use the equation for friction:
\(f_{friction} = \mu \cdot N\)
where \(f_{friction}\) is the force of friction, \(\mu\) is the coefficient of friction, and N is the normal force.
In this case, since the box is on a rough, level surface, the normal force is equal to the weight of the box, which can be calculated as:
\(N = m \cdot g\)
where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Now, let's determine the components of the applied force. The upward component of the force is given by:
\(F_{up} = F \cdot \sin(\theta)\)
where F is the magnitude of the force and \(\theta\) is the angle between the force vector and the horizontal direction.
Similarly, the rightward component of the force is given by:
\(F_{right} = F \cdot \cos(\theta)\)
where F is the magnitude of the force and \(\theta\) is the angle between the force vector and the horizontal direction.
Since the force is being applied at an angle of 30 degrees with the horizontal, the components can be calculated as:
\(F_{up} = F \cdot \sin(30^\circ)\) and \(F_{right} = F \cdot \cos(30^\circ)\)
Lastly, the force of friction can be calculated as:
\(f_{friction} = \mu \cdot N\)
Now you have all the necessary equations to calculate the force of friction experienced by the box on the rough, level surface.