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...

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.

Asked on by boblee12456

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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.

najm1947's profile pic

najm1947 | Elementary School Teacher | (Level 1) Valedictorian

Posted on

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

=

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