A 4.50 kg block is pressed against a vertical wall by a force (→F), as shown in the figure below. The coefficient of static friction between the block and the wall is 0.34 and the directional angle θ for the force is 48.0°. Determine the magnitude of the force (→F) when the block is about to slide down the wall.
Figure:
imgur. com/a/cFWYLRj
The two answers I got so far which are wrong are:
105.8921754
45.43350838
I will continue trying to do this question but I only have one submission attempt left
assuming the force is upward (the angle below the horizontal), I dont have the picture
forceup=sinTheta*F=F*sin48
force normal= F
force up due to friction= F*mu=F*.34
force down due to gravity=4.5*9.8=44.1
so if they are all balanced, then forcup=forcedown or
F*sin48+F*.34=44.1
F= 44.1/(.743 +.34)=40.7 or in sig digits 41N
Now if the force pressing is above the horizontal, that changes the equation.
delete the space in the imgur link to get the picture
Where did .743 come from?
To determine the magnitude of the force required for the block to start sliding down the wall, we can use the concept of static friction. The equation for static friction is given by:
fs = μs * N
Where fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force. In this case, the normal force is equal to the weight of the block, which can be calculated as:
N = m * g
Where m is the mass of the block and g is the acceleration due to gravity.
Next, we need to resolve the force (→F) into its horizontal and vertical components. The horizontal component of the force will contribute to overcoming the static friction, while the vertical component will be balanced by the normal force.
To determine the horizontal component of the force, we can use trigonometry. The equation is:
F_horizontal = F * cos(θ)
Where F is the magnitude of the force and θ is the directional angle.
Now we can calculate the force of static friction:
fs = μs * N = μs * m * g
Since the object is on the verge of sliding, the maximum static friction force is equal to the force of static friction:
fs = μs * m * g
Next, we can calculate the horizontal force required to overcome static friction:
F_horizontal = fs = μs * m * g
Substituting the given values:
F_horizontal = 0.34 * 4.50 kg * 9.8 m/s^2
Solving this equation gives:
F_horizontal ≈ 15.811 N
Therefore, the magnitude of the force (→F) required to start sliding the block down the wall is approximately 15.811 N.