Good night .....................
2 answers:
You might be interested in
Answer:
- <u>See the picture attached with the drawing of the forces.</u>
Explanation:
Find the figures with the question and the answer attached.
The answer shows the free body diagram with four arrows starting on, and pointing way from, the dot.
The red vertical upward arrow, labeled , represents the normal force, which is the force exerted by the ground on the cart.
The red vertical downward arrow, labeled , represents the gravity force (weight), which is the pull that the Earth exerts of the cart.
Both vertical arrows are of the same side because the normal force and the weight are balanced (since there is not vertical acceleration).
The blue horizontal arrow pointing to the right, labeled , represents the horizontal pulling force exerted by the hand.
The blue horizontal arrow pointing to the left, labeled , represents the frictional force which is not neglicible.
Since the cart is accelerating in the positive direction, toward the right,
and the arrow to the right is larger than the arrow to the left.
Answer:
The sum of the area of the shaded regions = 0.248685
Explanation:
The sum of the area of the shaded region is given as follows;
The point of intersection of the graphs are;
y = x/2
y = sin²x
∴ At the intersection, x/2 = sin²x
sinx = √(x/2)
Using Microsoft Excel, or Wolfram Alpha, we have that the possible solutions to the above equation are;
x = 0, x ≈ 0.55 or x ≈ 1.85
The area under the line y = x/2, between the points x = 0 and x ≈ 0.55, A₁, is given as follows
1/2 × (0.55)×0.55/2 ≈ 0.075625
The area under the line y = sin²x, between the points x = 0 and x ≈ 0.55, A₂, is given using as follows;
Therefore;
∴ A₂ =1/2 × ((0.55 - sin(0.55)×cos(0.55)) - (0 - sin(0)×cos(0)) ≈ 0.0522
The shaded area, = A₁ - A₂ = 0.075625 - 0.0522 ≈ 0.023425
Similarly, we have, between points 0.55 and 1.85
A₃ = 1/2 × (1.85 - 0.55) × 1/2 × (1.85 - 0.55) + (1.85 - 0.55) × 0.55/2 = 0.78
For y = sin²x, we have;
The shaded area, = A₄ - A₃ = 1.00526 - 0.78 ≈ 0.22526
The sum of the area of the shaded regions, ∑A = +
∴ A = 0.023425 + 0.22526 = 0.248685
The sum of the area of the shaded regions, ∑A = 0.248685