Resolving Forces in Horizontal and Vertical Directions in Equilibrium Problems

Find the components of the forces in the diagrams:vertically, specifying whether it is upwards or downwards.

Find the components of the forces in the diagrams:vertically, specifying whether it is upwards or downwards.

Find the components of the forces in the diagrams:vertically, specifying whether it is upwards or downwards.

Find the components of the forces in the diagrams:vertically, specifying whether it is upwards or downwards.

Find the components of the forces in the diagrams:Horizontally and vertically, specifying whether it is upwards or downwards.

Find the components of the forces in the diagrams: vertically, specifying whether it is upwards or downwards.

Find the components of the forces in the diagrams:

vertically, specifying whether it is upwards or downwards.

Find the components of the forces in the diagrams:vertically, specifying whether it is upwards or downwards.

A box of mass $20 \mathrm{kg}$ is on a horizontal surface. There are three rods attached on one side, at $10°, 25°$ and $35°$ above the horizontal, for people to drag it. Three people are available to pull on these rods and they are capable of providing forces of $150 \mathrm{N}, 200 \mathrm{N}$ and $250 \mathrm{N}.$

The box is being pulled in the opposite direction by a horizontal force of $425 \mathrm{N}.$ Show that only two of the people are required to keep the box in equilibrium. State which of the rods each person holds.

A book of mass $3 \mathrm{kg}$ is prevented from sliding down a slope at $15°$ to the horizontal by friction acting up the slope and parallel to it. Find the force of friction and the normal contact force. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Find the component of the following force perpendicular to the direction of the dashed arrow. Make it clear whether the component is in the perpendicular direction clockwise or anticlockwise from the direction given.

Find the component of the following force in the direction of the dashed arrow. Although it might seem clear from the diagram, make sure you specify whether the component is in the given direction or in the opposite direction.

Find the component of the following force in the direction of the dashed arrow. Although it might seem clear from the diagram, make sure you specify whether the component is in the given direction or in the opposite direction.

A particle has three horizontal forces acting on it, as shown in the diagram. Show that $\cos \alpha =\frac{14-13\cos \beta }{15}$ and find an expression for $\sin \alpha$. Use ${\cos }^2\alpha +{\sin }^2\alpha =1$ to get an equation in $\beta$. Hence, find $\alpha$ and $\beta$.

A particle has three forces acting on it, as shown in the diagram, where $\sin \theta =\frac{3}{5}.$ Show that $\sin \theta =\frac{3}{5}$ by resolving horizontally, and write down another equation by resolving vertically. Hence, show that $G=75\sqrt{3}+100$ and find $F.$

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A box with weight $400 \mathrm{N}$ is at rest on a horizontal surface. A man is pulling on a rope to try to get the box to move. The force he can exert depends on the angle at which he holds the rope, so that when the rope is at an angle $1600\sin \theta \mathrm{N}$ above the horizontal, the force he exerts is $1600\sin \theta \mathrm{N}.$ He starts by holding the rope horizontally and gradually increases the angle, thereby increasing the force. Another man tries to prevent this motion of the box, by pulling horizontally. He can exert a maximum force of $700 \mathrm{N}.$ Find the angle at which the box can no longer remain on the ground. Hence, determine whether the box lifts off the ground first or slides along the ground first.

A block with weight $44 \mathrm{N}$ is held in equilibrium by two ropes, one with tension, $T_1,$ acting at angle ${\sin }^{-1}\frac{15}{17}$ to the upwards vertical and the other with tension, $T_2,$ acting at angle ${\sin }^{-1}\frac{5}{13}$ to the upwards vertical. Find $T_1$ and $T_2.$

A wooden block is held in position by three horizontal forces, as shown in the diagram. One acts to the left with force $56 \mathrm{N}.$ One acts with force $F$ at an angle $\theta .$ where $\sin \theta =\frac{3}{5},$, above the rightwards horizontal. One acts with force $G$ at an angle $\phi ,$ where $\sin \phi =\frac{15}{17},$, below the rightwards horizontal. Find $F$ and $G$.

A small aeroplane of mass $5000 \mathrm{kg}$ is towed along a runway at constant speed by a rope acting at $20°$ below the horizontal. There is friction and air resistance horizontally with total force $4000 \mathrm{N}.$ Find the tension in the rope and the normal contact force.

A box of weight $50 \mathrm{N}$ is being dragged at constant velocity along a horizontal road by a force, $F,$, acting at $15°$ above the horizontal. It experiences friction of $10 \mathrm{N}.$

Find $F$ and the normal contact force.