A ladder of weight 200 N and length 10 m leans against a smooth wall with no friction. A firefighter of weight 600 N climbs a distance x up the ladder (x goes from the bottom of the ladder to the firefighter’s feet). The coefficient of friction between the ladder and the floor is 0.5. What is the highest value of x if the ladder is not to slip?
tycho.physics.wisc.edu/courses/phys201/spring08/Lectures/Solids.pdf
see that solution. I can't help you without a diagrame presented there.
10m
To determine the highest value of x such that the ladder does not slip, we need to analyze the forces and conditions acting on the ladder.
1. Determine the weight and forces acting on the ladder:
The weight of the ladder is 200 N, which can be represented as a downward force acting at the center of gravity of the ladder.
The frictional force acting on the ladder due to the coefficient of friction between the ladder and the floor is given by the equation F_friction = coefficient_of_friction * Normal_force.
The normal force acting on the ladder is equal to the weight of the firefighter and the ladder combined, since they are both resting on the floor.
2. Analyze the forces in the vertical direction:
The sum of the vertical forces must be zero for the ladder to remain in equilibrium.
The vertical forces acting on the ladder are the normal force (equal to the combined weight of the ladder and the firefighter) and the component of the frictional force acting vertically, which can be calculated as F_friction_vertical = F_friction * sine(theta).
Theta denotes the angle between the ladder and the floor.
3. Analyze the forces in the horizontal direction:
There are no horizontal forces acting on the ladder since the wall is smooth and there is no friction between the ladder and the wall.
4. Determine the maximum value of x:
To find the maximum value of x, we need to consider the condition at which slipping is about to occur. This condition is achieved when the frictional force reaches its maximum value, which can be calculated as F_friction_maximum = coefficient_of_friction * Normal_force.
The maximum value of x can then be determined by setting the limit of the frictional force equal to its maximum value and solving for x.
Using the provided information and equations, you can calculate the highest value of x that satisfies the condition where the ladder does not slip.