A large 63.0kg board is propped at a 44 degree angle against the edge of a barn door that is 2.5 m wide.
How great a horizontal force must a person behind the door exert (at the edge) in order to open it? Assume that the coefficient of friction between the board and the door is 0.44, and that the board is firmly set against the ground.
Is the 44 degrees measured with respect to the ground or the door?
This is very similar to a problem asked yesterday, except that there is friction between board and door this time.
M1= m•g•L•cosα/2,
M2 = F•L•sinα,
M3 = F(fr) •L•cosα = μ•F•L• cosα,
M2 = M1 +M3,
F•L•sinα = m•g•L•cosα/2 + μ•F•L• cosα,
F•sinα - μ•F•cosα = m•g•cosα/2,
F = m•g•cosα/2•( sinα - μ•cosα) =
=63•9.8•cos44º/2•(sin44º - 0.44•cos44º) = 588 N.
If you have the answer for this problem write it.
To calculate the horizontal force needed to open the door, we need to consider the equilibrium of forces acting on the board. There are three forces involved: the weight of the board, the horizontal force exerted by the person, and the normal force exerted by the ground.
First, let's calculate the weight of the board using the formula: weight = mass × gravitational acceleration.
Given the mass of the board is 63.0 kg and the gravitational acceleration is approximately 9.8 m/s², the weight of the board is: weight = 63.0 kg × 9.8 m/s² = 617.4 N.
Now, let's break down the weight of the board into its vertical and horizontal components. The vertical component is given by: vertical component = weight × cos(θ), where θ is the angle the board makes with the ground. In this case, θ = 44 degrees.
Using this, we get: vertical component = 617.4 N × cos(44°) = 617.4 N × 0.7193 ≈ 444.8 N.
The normal force exerted by the ground is equal in magnitude but opposite in direction to the vertical component of the weight. Thus, the normal force is also 444.8 N.
Next, we need to calculate the maximum force of static friction between the board and the door. The maximum force of static friction is given by the equation: maximum friction force = coefficient of friction × normal force.
Given the coefficient of friction is 0.44 and the normal force is 444.8 N, we have: maximum friction force = 0.44 × 444.8 N ≈ 195.5 N.
Finally, the horizontal force needed to open the door is equal to the maximum force of static friction, as the person behind the door needs to overcome the friction. Therefore, the person must exert a horizontal force of approximately 195.5 N to open the door.