Which of the following is a chemical property of matter?
2 answers:
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An advertisement for an all-terrain vehicle (ATV) claims that the ATV can climb inclined slopes of 35°. The minimum coefficient of static friction needed for this claim to be possible is 0.7
In an inclined plane, the coefficient of static friction is the angle at which an object slide over another.
As the angle rises, the gravitational force component surpasses the static friction force, as such, the object begins to slide.
Using the Newton second law;
- So; On the L.H.S
- On the R.H.S
N = mg cos θ
Equating both force component together, we have:
From trigonometry rule:
∴
Therefore, we can conclude that the minimum coefficient of static friction needed for this claim to be possible is 0.7
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The two ladybugs have same rotational (angular) speed
Explanation:
The rotational (angular) speed of an object in circular motion is defined as:
where
is the angular displacement
t is the time interval considered
Here we have two ladybugs, which are located at two different distances from the axis. In particular, ladybug 1 is halfway between ladybug 2 and the axis of rotation. However, since they rotate together with the disk, and the disk is a rigid body, every point of the disk cover the same angle in the same time
: this means that every point along the disk has the same angular speed, and therefore the two ladybugs also have the same angular speed.
On the other hand, the linear speed of the two ladybugs is different, because it follows the equation:
where r is the distance from the axis: and since the two ladybugs are located at different , they have different linear speed.
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Refer to the diagram shown below.
We want to find y in terms of d, φ and θ.
By definition,
Therefore
y = x tan(θ) (1)
y = (x - d) tan(φ) (2)
Equate (1) and (2).
![(x - d) \, tan(\phi) = x \, tan(\theta) \\ x[tan(\phi) - tan(\theta)] = d \, tan(\phi) \\ x= \frac{d tan(\phi)}{tan(\phi)-tan(\theta)}](https://tex.z-dn.net/?f=%28x%20-%20d%29%20%5C%2C%20tan%28%5Cphi%29%20%3D%20x%20%5C%2C%20tan%28%5Ctheta%29%20%5C%5C%20x%5Btan%28%5Cphi%29%20-%20tan%28%5Ctheta%29%5D%20%3D%20d%20%5C%2C%20tan%28%5Cphi%29%20%5C%5C%20x%3D%20%5Cfrac%7Bd%20tan%28%5Cphi%29%7D%7Btan%28%5Cphi%29-tan%28%5Ctheta%29%7D%20)
From (1), obtain the required expression for y.
Answer:
We want to find y in terms of d, φ and θ.
By definition,
Therefore
y = x tan(θ) (1)
y = (x - d) tan(φ) (2)
Equate (1) and (2).
From (1), obtain the required expression for y.
Answer: