Torque, equilibrium and calculating angle of forces

In summary, the conversation discusses two equilibrium/torque problems and the confusion surrounding the angles of forces in each problem. In the first problem, the angle of the force of the ground on the ladder is different from the angle between the ladder and the ground. In the second problem, the angle of the force of the cable on the beam is assumed to be the same as the angle between the beam and the cable. The conversation also provides guidance on how to calculate the force on the window in the first problem.
  • #1
mm2424
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Homework Statement



I just did two equilibrium/torque problems and it seems like they contradict each other. I understand the basic steps here, but I'm baffled about what I perceive to be a contradiction. Here are the problems:

A 75 kg window cleaner uses a 10 kg ladder that is 5 m long. He places one end on the ground 2.5 m from a wall, rests the upper end against a cracked window and climbs the ladder. He is 3 m up along the ladder when the window breaks. Neglect friction between the ladder and window and assume that the base of the ladder does not slip. When the window is on the verge of breaking, what is the angle (relative to the horizontal) of the force of the ground on the ladder?

The second question entails a horizontal beam 3 m long, of weight 500 N, suspended horizontally. On the left end, it is hinged to a wall. The right end has a cable that runs to the wall, a distance of D above the hinge point. (The wall, cable and beam form three sides of a triangle). The least tension that will snap the cable is 1200 N. It asks what value of D corresponds to that tension.

Homework Equations



Horizontal forces are in equilibrium, as are vertical forces and torques.

The Attempt at a Solution



I'm confused here because in the first problem, the angle of the force of the ground on the ladder is NOT the same as the angle of the ladder and the ground. The angle between the ladder and ground is 60 degrees, whereas the answer to number 1 (and therefore the angle of the force relative to the ground) is 71 degrees.

HOWEVER, in the second problem, it seems like you find the answer by calculating the vertical component of the force of the cable on the beam (it ends up being 250 N), then using the sine trig relationship to find the angle of the force of the cable on the beam (it ends up being 12 degrees). You then assume that this angle is the same as the angle between the beam and the cable, and use the tangent trig relationship to relate 12 degrees, 3 meters (the length of the beam) and D. This yields a D of 0.64 m, which is the answer. My question is, why do we assume that the angle of the force and the angle between the ladder and ground is different whereas, in the second case, we assume that that the angle of force and the angle between the beam and the cable are the same.
 
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  • #2
The first thing you need to do is calculate the force of the ladder on the window at the instant it breaks.
You are told to ignore friction with the ladder and the window which means that the force on ladder/window is at right angles to the window (ie horizontal)
Take moments about the base of the ladder to find the force on the window... I got the force to be 284N
Hope this helps... get in touch if you need more guidance.
 

1. What is torque and how is it calculated?

Torque is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis to the point of application of the force.

2. How does equilibrium relate to torque?

In order for an object to be in equilibrium, the net torque acting on the object must be zero. This means that the sum of all the torques acting in one direction must be equal to the sum of all the torques acting in the opposite direction.

3. How do forces and angles affect torque?

The angle at which a force is applied to an object can greatly affect the amount of torque produced. A force applied perpendicular to an object's axis of rotation will create the maximum amount of torque, while a force applied parallel to the axis will create no torque. Additionally, the distance from the axis to the point of application of the force also affects the torque.

4. How do you calculate the angle of forces in a torque problem?

The angle of forces can be calculated using the trigonometric functions sine, cosine, and tangent. The angle can be determined by using the inverse trigonometric functions of these functions to find the ratio of the opposite and adjacent sides of the triangle formed by the force and the axis of rotation.

5. What are some real-world applications of torque and equilibrium?

Torque and equilibrium are important concepts in many fields such as engineering, physics, and biomechanics. Some real-world applications include designing structures that can withstand forces and maintain balance, creating efficient machinery and tools, and understanding the movement and stability of the human body during physical activities.

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