What is the y-component of the force due to gravity? (This would be the componen

Question

What is the y-component of the force due to gravity? (This would be the component of the weight which is trying to hold the box onto the incline) In this case include a positive or negative sign which is consistent with the axes chosen in the picture.

In this situation the x-axis is defined to be parallel to the incline and positive up and to the right. The y-axis is perpendicular to the surface. The challenge is that the force due to gravity is still straight down, so you have to break the force to due gravity down into a component that is parallel to the surface and a component that is perpendicular to the surface. These components are shown in red on the diagram above (the x-component is shown twice, once on the axis, and once moved over to helpcomplete the triangle

Explanation / Answer

follow thisIf the skier is on the slope, gravity acts on the skier (Vertically downwards), however the direction the skier travels is down the slope, hence you need to find the component of the force due to gravity that acts upon the skier down the slope. If you imagine a set of axis, the x axis parallel to the slope and the y axis normal (perpendicular) to the slope then draw a vector representing the force due to gravity on this axis. You can then find the x and y components. It is the x component you are interested in acting down the slope. To do this you form a triangle from which the force due to gravity (the weight, mg) is the hypotenuse of the triangle. Using trigonometry** you find the x-component which comes out to be: F_x = m*g*sin(35). taking g = 9.81, this returns an answer of 450N. This is the component force that acts parallel to the slope. The y-component force is balanced because of the normal force of the slope (the slope pushing back on the skier, perpendicular), and hence does not contribute to the skier's motion. ** = The trigonometry is done whereby you know the the angles in the triangle and you know one side - the hypotenuse, in the case of the 35 degree angle the x-component is opposite, and trigonometry tells us that the opposite side = hypotenuse*sin(angle)

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