a crate weighing 562 newtons is resting on an inclined plane 30 degress above the horizontal. Find the components of the weight forces that are parallel and perpendicular to the plane?
Wc = mg = 562 N. = Weight of crate.
Fc = 562 N. @30 Deg. = Force of crate.
Fp = 562*sin30 = 281 N. = Force parallel to plane.
Fv = 562*cos30 = 487 N. = Force perpendicular to plane.
a crate weighing 562 newtons is resting on an inclined plane 30 degress above the horizontal. Find the components of the weight forces that are parallel and perpendicular to the plane?
Fgx= 562cos(30.0)=486N
Fly= 562sin(30.0)=281
Tan-1(281 divides 486)
270-30=240
Ah, so we have a weighty situation, huh? Alright, let's break this down. When dealing with inclined planes, we can split the weight force into two components: one parallel to the plane, and one perpendicular to the plane.
First, we need to find the perpendicular component of the weight force. To do that, we use a little trigonometric magic. The perpendicular component is equal to the weight force multiplied by the cosine of the angle of the inclined plane. So, in this case, the perpendicular component would be:
Perpendicular component = Weight force × cos(angle)
Perpendicular component = 562 N × cos(30 degrees)
Now, to find the parallel component, we use the sine of the angle.
Parallel component = Weight force × sin(angle)
Parallel component = 562 N × sin(30 degrees)
And there you have it, my friend! The components of the weight force that are parallel and perpendicular to the inclined plane. Just plug in the values and crunch those numbers!
To find the components of the weight force that are parallel and perpendicular to the plane, we need to use trigonometry.
First, let's draw a diagram to visualize the situation:
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W | \ /
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inclined plane 30°
In this diagram, W represents the weight force acting vertically downward.
To calculate the component of the weight force that is perpendicular to the plane (W⊥), we can use the equation:
W⊥ = W * cos(θ)
where:
- W is the weight force (562 N in this case)
- θ is the angle of inclination (30° in this case)
Substituting the values, we get:
W⊥ = 562 N * cos(30°)
Calculating this, we find that W⊥ ≈ 486.64 N.
To calculate the component of the weight force that is parallel to the plane (W∥), we can use the equation:
W∥ = W * sin(θ)
where:
- W is the weight force (562 N in this case)
- θ is the angle of inclination (30° in this case)
Substituting the values, we get:
W∥ = 562 N * sin(30°)
Calculating this, we find that W∥ ≈ 281 N.
Therefore, the components of the weight force that are parallel and perpendicular to the plane are approximately 281 N (parallel to the plane) and 486.64 N (perpendicular to the plane), respectively.