crate weighs 823 N rests on plank that makes a 25 degree angle with the ground. Find components of crate's weight parallel and perpendicular to the plank
Well, if you've got a crate resting on a plank at a 25-degree angle with the ground, it seems like that crate is really enjoying its relaxing slant. However, let's get down to the serious business of finding the components of the crate's weight.
To start, we need to remember the forces involved here. The weight of the crate can be broken down into two components - one parallel to the plank, and the other perpendicular to the plank.
To find the parallel component, we'll use a little bit of trigonometry magic. We take the weight of the crate (823 N) and multiply it by the cosine of the angle (25 degrees). That should give us the amount of weight that's parallel to the plank.
Now, for the perpendicular component, we multiply the weight of the crate by the sine of the angle (25 degrees). This should give us the amount of weight that's perpendicular to the plank.
So, when we crunch the numbers, we find that the parallel component of the crate's weight is approximately 746 N, and the perpendicular component is about 367 N.
Now, I must say, those numbers are pretty weighty. But hey, at least the crate gets to relax at an angle, right?
To find the components of the crate's weight parallel and perpendicular to the plank, we need to consider the forces acting on the crate.
First, let's draw a diagram representing the situation:
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/ |
/ o |
/ / |
/ / |
/ / |
/ / |
/ /θ |
/------------------------
In this diagram, the line represents the plank, and the angle θ is 25 degrees.
Now, let's break down the crate's weight into components. The weight of the crate can be represented by a vector pointing straight down.
The vertical component of the weight (perpendicular to the plank) can be found by multiplying the weight magnitude by the cosine of the angle θ. This component acts against the normal force exerted by the plank to keep the crate from sinking into it.
The horizontal component of the weight (parallel to the plank) can be found by multiplying the weight magnitude by the sine of the angle θ. This component is responsible for causing any motion along the plank.
Let's calculate these components:
Weight = 823 N
Vertical component = Weight × cos(θ)
= 823 N × cos(25°)
Horizontal component = Weight × sin(θ)
= 823 N × sin(25°)
By evaluating these calculations, you will get the numerical values for the vertical and horizontal components of the crate's weight.