A 2.19 kg block is held in equilibrium on an incline of angle q = 55.0o by a horizontal force, F, applied in the direction shown in the figure below.
If the coefficient of static friction between block and incline is ms = 0.283, determine the minimum value of F.
Determine the normal force of the incline on the block.
Totally lost.
To find the minimum value of the applied force, we need to consider the forces acting on the block.
First, let's resolve the weight of the block into components. The weight of the block, given by the formula w = m * g (where m is the mass and g is the acceleration due to gravity), can be split into two components: one perpendicular to the incline (the normal force) and one parallel to the incline (the force of gravity pulling the block down the incline).
The perpendicular component of the weight is given by N = m * g * cos(q), where q is the angle of the incline and cos(q) represents the cosine function.
The parallel component of the weight can be calculated as F_parallel = m * g * sin(q), where sin(q) represents the sine function.
Next, we need to determine the maximum force of static friction (F_friction) that can act on the block without it sliding down the incline. The maximum force of static friction is given by F_friction_max = ms * N, where ms is the coefficient of static friction.
In equilibrium, F_applied must be equal to F_friction_max to prevent the block from sliding. Therefore, F_applied = F_friction_max.
To find the minimum value of F, we substitute the expression for F_friction_max:
F_applied = ms * N.
Now, to determine the normal force (N) acting on the block, we need to consider the equilibrium condition. In equilibrium, the sum of all vertical forces must be zero.
For the vertical forces, we have:
N - m * g * cos(q) = 0.
Rearranging this equation, we find:
N = m * g * cos(q).
Therefore, to find the normal force, substitute the known values of the mass (m = 2.19 kg), acceleration due to gravity (g = 9.8 m/s^2), and the angle of the incline (q = 55.0o) into the equation N = m * g * cos(q).
To find the minimum value of F, substitute the calculated value of N into the equation F_applied = ms * N, using the given value for the coefficient of static friction (ms = 0.283).
Without the diagram, we're as lost as you are!
Is the force F acting up the plane, or down the plane?
Is the force F acting horizontally or along the plane?