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°?
Ok, i misread my sketch.
summing vertical forces indicates the normal force at the ground is mg.
summing horizontal forces:
at the wall point, summing forces about the base point,
mg*L/2*cos64-Fwall*L*sin64=0
Fwall=.5mg*ctn64
Now, summing horizotal forces
.5mgctn64-Ffriction=
.5mg ctn64=mu*mg
mu=.5*cotan 64
check that.
No sir I have tried .243 did not work.
The ladder is against a wall/floor that makes the shape of a backwards L if that makes sense.
To find the static friction force between the ladder and the floor, we need to analyze the forces acting on the ladder. Let's break down the problem step by step:
1. Draw a free body diagram: Draw a diagram of the ladder leaning against the wall. Label the angle θ and the forces acting on the ladder - the weight (mg) acting at the center of mass, the normal force (N) exerted by the floor on the ladder base, and the static friction force (f) between the ladder and the floor.
2. Analyze the forces in the vertical direction (y-axis): Since the ladder is in equilibrium, the sum of the forces in the y-axis is equal to zero. The forces in the y-axis are the weight (mg) acting downward and the normal force (N) acting upward. We can express this as:
N - mgcos(θ) = 0
3. Calculate the normal force (N): From the equation in step 2, we can solve for the normal force N:
N = mgcos(θ)
4. Analyze the forces in the horizontal direction (x-axis): Again, since the ladder is in equilibrium, the sum of the forces in the x-axis is equal to zero. The only force acting in the x-axis is the static friction force (f), which prevents the ladder from sliding. We can express this as:
f - mgsin(θ) = 0
5. Solve for the static friction force (f): From the equation in step 4, we can solve for the static friction force f:
f = mgsin(θ)
6. Substitute the given values: Substitute the given values into the equation for the static friction force:
f = (14.5 kg)(9.8 m/s^2)sin(64.0°)
7. Calculate the static friction force: Plug in the values and calculate the static friction force using a calculator or by hand:
f ≈ 137.1 N
Therefore, the static friction force between the ladder and the floor is approximately 137.1 Newtons.