A trunk weighing 562 N is resting on a plane inclined at 30.0o from the horizontal. Find the components of the trunk's weight parallel and perpendicular to the plane
a = g x sin θ
Well, well, well, looks like this trunk has decided to go on a slanted adventure! Now, let's break it down, shall we?
First things first, we need to determine the angle at which the plane is inclined. You mentioned it's inclined at 30.0 degrees from the horizontal. Excellent!
Now, since we're dealing with an inclined plane, it's handy to break down the trunk's weight into two components: one parallel and one perpendicular to the plane. Sounds fancy, doesn't it?
To find the components, we need to use trigonometry. Specifically, we'll be using sine and cosine like true math magicians.
Let's start with the component parallel to the plane. We'll call it "W_parallel" because, why not?
W_parallel = Weight * sin(angle)
So, if the weight of the trunk is 562 N, using a little trigonometric magic:
W_parallel = 562 N * sin(30.0 degrees)
Calculating time! Drumroll, please...
W_parallel = 281 N
Voilà! The parallel component of the trunk's weight is 281 N. Now, on to the next component!
The component perpendicular to the plane is a funny one. Let's name it "W_perpendicular" because we like fancy names.
W_perpendicular = Weight * cos(angle)
Now, back to calculations. We take the weight of the trunk (562 N) and multiply it by the cosine of the angle (30.0 degrees) to find the perpendicular component:
W_perpendicular = 562 N * cos(30.0 degrees)
And the calculation gods reveal...
W_perpendicular = 486.5 N
Ta-da! The perpendicular component of the trunk's weight is 486.5 N.
So, to sum it up, we have the parallel component (W_parallel) of 281 N and the perpendicular component (W_perpendicular) of 486.5 N.
Now, remember to thank me the next time you need a little math clowning around!
To find the components of the trunk's weight parallel and perpendicular to the plane, we need to resolve the weight vector into its components.
Step 1: Draw a diagram representing the situation.
Label the weight vector as W, the angle of inclination as θ = 30.0°, the parallel component as W_parallel, and the perpendicular component as W_perpendicular.
Step 2: Determine the weight vector magnitude.
Given the weight of the trunk is 562 N, the magnitude of the weight vector is equal to the weight. Thus, |W| = 562 N.
Step 3: Split the weight vector into its components.
The weight vector can be split into two components: one parallel to the inclined plane and one perpendicular to the inclined plane.
W_parallel = |W| * cos(θ)
W_perpendicular = |W| * sin(θ)
Step 4: Substitute values and calculate.
Plugging in the given values, we have:
W_parallel = 562 N * cos(30.0°)
W_perpendicular = 562 N * sin(30.0°)
Using a calculator, we can evaluate these expressions:
W_parallel ≈ 486 N
W_perpendicular ≈ 281 N
Therefore, the trunk's weight has a parallel component of approximately 486 N and a perpendicular component of approximately 281 N to the inclined plane.
To find the components of the trunk's weight parallel and perpendicular to the inclined plane, we can use trigonometry.
First, let's resolve the weight of the trunk into its components. The weight of the trunk acts vertically downward, so we need to find the parallel and perpendicular components relative to the inclined plane.
The component of the trunk's weight parallel to the inclined plane is given by:
Parallel component = Weight of the trunk * sin(angle of inclination)
Parallel component = 562 N * sin(30.0o)
Now, let's calculate this value:
Parallel component = 562 N * 0.5
Parallel component = 281 N
Therefore, the component of the trunk's weight parallel to the inclined plane is 281 N.
The component of the trunk's weight perpendicular to the inclined plane is given by:
Perpendicular component = Weight of the trunk * cos(angle of inclination)
Perpendicular component = 562 N * cos(30.0o)
Now, let's calculate this value:
Perpendicular component = 562 N * 0.866
Perpendicular component = 487.492 N
Therefore, the component of the trunk's weight perpendicular to the inclined plane is 487.492 N.
To summarize:
Component parallel to the inclined plane = 281 N
Component perpendicular to the inclined plane = 487.492 N