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Forces in action

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Question 10

A wheelie bin is tipped onto its wheels by applying two forces FFF and RRR.

A wheelie bin on flat ground. A downward weight vector W of mass 55 kg acts from the center of mass, which is 0.25 m to the left of the wheels. The wheels are at the bottom right of the base. The front left corner of the bin is labeled X and touches the ground. The handle is at the top right of the bin, at a height of 1.20 m directly above the wheels. A force F is applied to the handle, pointing downwards and to the right at an angle of 15 degrees below the horizontal. A horizontal force R points to the left at the wheels.

FFF is applied to the handle. FFF is to the right at an angle 15∘15^{\circ}15∘ below the horizontal. The height of the handle above the ground is 1.20 m1.20\text{ m}1.20 m. RRR is a horizontal force applied to the left to the wheels. The total weight of the wheelie bin and its contents is WWW. The perpendicular distance between the line of action of the weight and the bottom of the wheels is 0.25 m0.25\text{ m}0.25 m.

The wheelie bin and contents have a total mass of 55 kg55\text{ kg}55 kg.

a.

State the principle of moments.

[2]
b.

Show that the magnitude of the minimum force FFF which lifts the front end of the wheelie bin (point X) off the ground is approximately 116 N116\text{ N}116 N.

[5]
c.

Use your answer to (b)(i) to calculate the magnitude of the force RRR required to stop the wheelie bin from moving to the right.

[2]
d.

The wheelie bin is now placed on an adjustable slope. The wheels are now fixed so they cannot move.

The same wheelie bin on an adjustable slope tilted at an angle \alpha to the horizontal. The wheels on the right are fixed on the slope, and the front corner is lifted off the slope. The weight vector W acts vertically downwards from the center of mass.

The angle α\alphaα made by the slope with the horizontal is steadily increased from zero.

Explain, without calculation, at what angle α\alphaα the wheelie bin starts to topple clockwise.

[2]

Forces in action Questions

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  3. /Forces in action