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Three forces act on a point: 3 N at 0°, 4 N at 90°, and 5 N at 217°. What is the net force?

A cyclist heads due west on a straight road. The wind is blowing from 248° at 10 m/s.

Is this wind more like a headwind or a tailwind?

What is the headwind/tailwind speed?

What is the crosswind speed?

One unfortunate winter day I happened to slip on an icy ramp inclined 37° to the horizontal. Find my acceleration down the ramp given that the acceleration due to gravity points straight down and has a value of 9.8 m/s^{2}. (Assume the ice is perfectly frictionless.)

conceptual

Prove that the angle between the surface of an inclined plane and a the horizontal (the angle of inclination) is equal to the angle between the normal of the plane and the vertical.

numerical

A utility pole is held upright with a single guy wire under 3,500 N of tension. The guy wire meets the ground at a 60° angle. What is the magnitude of the component of this force that…

prevents the pole from tipping over?

keeps the pole in contact with the Earth?

A force of 90 N is applied to a push lawn mower along a handle that makes a 30° angle with the vertical. What is the magnitude of the component of this force that…

propels the lawnmower?

keeps the lawnmower in contact with the ground?

A boy pulls a sled along level ground by means of a rope under 78 N of tension. The rope makes an angle of 37° with the horizontal. What is the magnitude of the component of the tension that…

actually moves the sled?

is essentially wasted?

A cyclist heads out on a straight road with a bearing of 60° east of north. A north wind is blowing at 10 m/s.

Is this wind more like a headwind or a tailwind?

What is the effective speed of this headwind/tailwind?

A cyclist heads out on a straight road with a bearing of 60° east of north. A southwest wind is blowing at 10 m/s.

Is this wind more like a headwind or a tailwind?

What is the effective speed of this headwind/tailwind?

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worksheet-components.pdf Calculate the magnitude (in centimeters) and direction (in standard form) of the resultant vector for each diagram using the method of components. Use the 1 cm grid lines towards this end. A ruler and protractor are not needed for this exercise.