A uniform ladder of mass (m = 14.5 kg) and length (L) leans against a frictionless wall, see figure. Find the static friction force between the ladder and the floor if the angle θ = 64.0°?
consider the point where the ladder meets the wall. Sum moments about that point.
mg*1/2 *L*cos64-mu*mg*L sin64=0
solve for mu. Notice the weight of the ladder mg divides out, as does length L.
I did that work got .197 but its wrong
To find the static friction force between the ladder and the floor, we need to analyze the forces acting on the ladder and apply Newton's second law of motion.
Let's break down the problem step by step:
Step 1: Draw a free-body diagram of the ladder.
- Draw an upward force arrow representing the ladder's weight (mg) acting at the center of mass, which is halfway along the ladder's length.
- Draw a normal force arrow perpendicular to the floor, acting at the point where the ladder contacts the floor.
- Draw a static friction force arrow acting parallel to the floor and opposite to the direction of the ladder's attempted motion.
- Lastly, draw an arrow representing the static friction force between the ladder and the wall, which acts perpendicular to the wall.
Step 2: Resolve the forces parallel and perpendicular to the ladder.
- The normal force and the static friction force between the ladder and the floor cancel out any vertical or horizontal motion perpendicular to the ladder.
- The only remaining force parallel to the ladder is the static friction force, which prevents the ladder from sliding down the wall.
Step 3: Apply Newton's second law of motion.
- In the horizontal direction, the only force acting is the static friction force.
- Using Newton's second law (F = ma), we can write the equation: static friction force = (mass of the ladder) x (acceleration).
Step 4: Find the acceleration.
- Since the ladder is in static equilibrium (not moving), the acceleration is zero. Therefore, the static friction force equals zero.
In conclusion, the static friction force between the ladder and the floor is zero. This means that the ladder will not slide down the wall due to the static friction force's equal and opposite direction.