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Rigid Body Statics Exercise Collection

Are you ready to put your brain to the test in the exciting world of Rigid Body Statics? This section contains all the exercises you need to put your knowledge of central force systems to the test.

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  1. Choose your topic: Sorted by learning content, you will find the tasks that have been published so far.
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Central Force Systems

First Basic Task: Reduction to a Single Force

Practice Exercise S-1.1.1
Central Force System

Graphically and analytically determine the magnitude and direction of the resultant force from forces F1 to F6.

$$ \begin{alignat}{5} F_1 &= 1000~\mathrm{N} \quad && \alpha_1 &&=0° \\[7pt] F_2 &= 1280~\mathrm{N} \quad && \alpha_2 &&=30° \\[7pt] F_3 &= 1750~\mathrm{N} \quad && \alpha_3 &&=50° \\[7pt] F_4 &= 840~\mathrm{N} \quad && \alpha_4 &&=90° \\[7pt] F_5 &= 220~\mathrm{N} \quad && \alpha_5 &&=100° \\[7pt] F_6 &= 760~\mathrm{N} \quad && \alpha_6 &&=150° \end{alignat} $$
Practice Exercise S-1.1.2
Central Force System

Graphically and analytically determine the magnitude and direction of the resultant force from forces F1 to F5.

$$ \begin{alignat}{5} F_1 &= 120~\mathrm{N} \quad && \alpha_1 &&=80° \\[7pt] F_2 &= 200~\mathrm{N} \quad && \alpha_2 &&=123° \\[7pt] F_3 &= 220~\mathrm{N} \quad && \alpha_3 &&=165° \\[7pt] F_4 &= 90~\mathrm{N} \quad && \alpha_4 &&=290° \\[7pt] F_5 &= 150~\mathrm{N} \quad && \alpha_5 &&=317° \end{alignat} $$
Practice Exercise S-1.1.3
Central Force System

Graphically and analytically determine the magnitude and direction of the resultant force from forces F1 to F6.

$$ \begin{alignat}{5} F_1 &= 75~\mathrm{N} \quad && \alpha_1 &&=27° \\[7pt] F_2 &= 125~\mathrm{N} \quad && \alpha_2 &&=72° \\[7pt] F_3 &= 95~\mathrm{N} \quad && \alpha_3 &&=127° \\[7pt] F_4 &= 150~\mathrm{N} \quad && \alpha_4 &&=214° \\[7pt] F_5 &= 170~\mathrm{N} \quad && \alpha_5 &&=270° \\[7pt] F_6 &= 115~\mathrm{N} \quad && \alpha_6 &&=331° \end{alignat} $$
Practice Exercise S-1.1.4
Central Force System

Picture this: you've got two laundry lines, let's call them Line 1 and Line 2, that you need to attach to a wall. Imagine you're looking down at the setup from above. Something like this:

We know that the force acting on Line 1, which we'll call F1, is 100 Newtons (N).

Determine the force F2 acting on Line 2 in such a way that the combined force, or resultant force, is perpendicular to the wall.

Practice Exercise S-1.1.5
Central Force System

The traction rope of a conveyor system runs at an angle of \(\gamma = 40°\) to the vertical from the pulley. Due to the mass of the conveyor basket, a rope force F1 = 50 kN results.

  1. What is the magnitude of the resultant of the two rope forces that act as bearing loads in pulley bearings A?
  2. At what direction angle \(\alpha_R\) (measured from the positive x-axis) does the resultant act?
Practice Exercise S-1.1.6
Central Force System

Four people are pulling a cart with ropes that are hooked into the towing eye of the drawbar according to the sketch.

Given:

F1=400 N, F2=350 N, F3=300 N, F4=500 N

  1. Determine the magnitude of the resultant force R.
  2. Determine the direction angle \(\alpha_R\) of the resultant force relative to the horizontal line through the drawbar.

Second Basic Task: Equilibrium

Practice Exercise S-1.2.1
Central Force System

Determine graphically and analytically whether the depicted system of forces is in equilibrium.

$$ \begin{alignat}{5} F_1 &= 12~\mathrm{N} \\[7pt] F_2 &= 9~\mathrm{N} \\[7pt] F_3 &= 3~\mathrm{N} \\[7pt] F_4 &= 7~\mathrm{N} \\[7pt] F_5 &= 5~\mathrm{N} \\[7pt] F_6 &= 6~\mathrm{N} \end{alignat} $$

Third Basic Task: Decomposition of a Force

Practice Exercise S-1.3.1

A force F = 25 N is to be decomposed into two components F1 and F2 which are perpendicular to each other. The lines of action of F and F1 are to form an angle \(\alpha = 35°\).

Determine the magnitudes of F1 and F2 graphically and analytically.

Practice Exercise S-1.3.2
This illustration shows a weight force on two ropes. The ropes are attached to the ceiling.

A mass with the weight force FG is hanging on two ropes.

What are the components of the force FG = 10 kN in the direction of ropes 1 and 2?

Practice Exercise S-1.3.3
Central Force System.

A sphere is situated, as shown, in a recess.

What are the components of the weight force G = 40 kN in the direction of the walls?

Note:
Only forces normal (i.e., perpendicular) to the wall can be transmitted.