Assume a block on unknown weight rests on an incline of 25 degrees and is initially not moving. What push (P) is required to start moving the block if the coefficient of static friction is 0.7?
To determine the push (P) required to start moving the block, we need to consider the forces acting on the block. The main forces involved are the force of gravity, the normal force, and the force of static friction.
Let's break down the problem step by step:
Step 1: Identify the forces:
- The force of gravity (Fg): This is the force that acts vertically downward and depends on the weight of the block. It can be calculated using the formula Fg = m * g, where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2).
- The normal force (Fn): This is the force exerted by the inclined plane perpendicular to it. It counteracts the force of gravity and can be calculated using the formula Fn = m * g * cos(theta), where theta is the angle of the incline (in this case, 25 degrees).
- The force of static friction (Fs): This force opposes the motion of the block and can be calculated using the formula Fs = u * Fn, where u is the coefficient of static friction.
Step 2: Calculate the forces:
We know that the block is initially not moving, so the force of static friction must be equal to or greater than the component of the gravitational force pulling the block down the incline. Since the block is at the verge of sliding, the force of static friction can be written as Fs = m * g * sin(theta), where sin(theta) is the component of gravity along the incline.
Step 3: Equate the forces:
Setting the force of static friction equal to the component of gravity along the incline, we get:
m * g * sin(theta) = u * m * g * cos(theta)
Step 4: Cancel out the common terms:
Since mass (m) and acceleration due to gravity (g) are common to both sides of the equation, we can cancel them out:
sin(theta) = u * cos(theta)
Step 5: Calculate the push (P):
To find the required push (P) to overcome static friction and start moving the block, we multiply the normal force by the coefficient of static friction:
P = u * Fn = u * m * g * cos(theta)
Substituting the given values: theta = 25 degrees and u = 0.7, we can calculate P.