Question

14.0 m uniform ladder weighing 480 N rests against a frictionless wall. The ladder makes a 57.0°-angle with the horizontal.

(a) Find the horizontal and vertical forces (in N) the ground exerts on the base of the ladder when an 850-N firefighter has climbed 3.70 m along the ladder from the bottom.
horizontal force
magnitude_________________
direction_______________
vertical force magnitude_________________
direction_______________

Answer 1

To find the horizontal and vertical forces exerted by the ground on the base of the ladder, you can use the principles of equilibrium and consider the forces acting on the ladder, including the weight of the ladder and the firefighter.

Step-by-step explanation:

To find the horizontal and vertical forces exerted by the ground on the base of the ladder, we need to consider the forces acting on the ladder. These forces are the weight of the ladder, the weight of the firefighter, and the normal forces from the ground and the wall.

The weight of the ladder is given by the formula w = mg, where m is the mass of the ladder (found by dividing its weight by the acceleration due to gravity) and g is the acceleration due to gravity (approximately 9.8 m/s^2). The weight of the firefighter is given by the formula w = mg, where m is the mass of the firefighter (found by dividing their weight by the acceleration due to gravity) and g is the acceleration due to gravity.

To find the horizontal and vertical forces exerted by the ground on the base of the ladder, we can use the principles of equilibrium. In the horizontal direction, the sum of the horizontal forces must be zero. In this case, the only horizontal force is the force exerted by the ground. In the vertical direction, the sum of the vertical forces must be zero. In this case, the vertical forces include the weight of the ladder, the weight of the firefighter, and the force exerted by the ground.

Answer 2

To find the horizontal and vertical forces at the base of a ladder when a firefighter is on it, principles of static equilibrium and torques must be considered. The wall provides a horizontal force opposite to friction at the base, while the vertical forces include the ladder's weight, the firefighter's weight, and the ground's normal force.

Step-by-step explanation:

To solve for the horizontal and vertical forces the ground exerts on the base of the ladder when an 850-N firefighter has climbed 3.70 m along the ladder from the bottom, we need to apply the principles of static equilibrium. The ladder and firefighter system must satisfy two conditions: the sum of all horizontal forces must be zero, and the sum of all vertical forces must be zero.

Let's call the horizontal force exerted by the wall on the ladder F, and the vertical and horizontal forces at the base N (normal force) and f (frictional force) respectively. Because the wall is frictionless, the only horizontal force is F which is equal in magnitude and opposite in direction to f. The vertical forces consist of the weight of the ladder, the weight of the firefighter, and the normal force N. The weight of the firefighter can be considered as acting at the point where he is on the ladder, and the weight of the ladder acts at its center of mass. To find these forces, we should also take into account the torque about a pivot point; in this case, the bottom of the ladder is a convenient pivot because it simplifies the calculations.