A box sits on a ramp that is inclined at 42 degrees. The force of gravity on the box is 200N.
If the x-axis is in the direction down the ramp and the y-axis is perpendicular to the ramp, find the x and y components of the force of gravity.
Notice that the vector of gravitational force is orthogonal to x axis and it is parallel to y axis.
The x axis component of gravitational force acts parallel to the ramp direction and y axis component is orthogonal to the ramp.
The angle between x axis component and vector of gravitational force is of `42^o.` Notice that vector of gravitational force represents the hypotenuse of a right angle triangle and the x axis component represents the leg, hence you may use cosine function to find the x axis component.
`cos 42^o = x/G =gt x = G*cos 42^o`
Substsituting 200N for G and `0.743` for cos `42^o` yields:
`x = 200*0.743 =gtx = 148.6 N`
`sin 42^o = y/G =gty = G*sin 42^o`
`y = 200*0.669 =gt y = 133.8 N`
Hence, evaluating x and y components of gravitational force yields x = 148.6 N and y = 133.8 N.
Gravitational force on box = 200 N
Angle of incline of ramp = 42 degrees
x-component of force of gravity (along the ramp) = 200.sin(42)
= 133.8 N
y-component of force of gravity (perpendicular to ramp) = 200.cos(42)
= 148.6 N
The x component of force of gravity is 133.8 N and
The y component of force of gravity is 148.6 N