when car moves along a circular path then centripetal force for taking turn will be provided by the component of normal force
Let the road is tilted by some angle
so force equations are given as
![F_n cos\theta = mg](https://tex.z-dn.net/?f=F_n%20cos%5Ctheta%20%3D%20mg)
![F_n sin\theta = \frac{mv^2}{R}](https://tex.z-dn.net/?f=F_n%20sin%5Ctheta%20%3D%20%5Cfrac%7Bmv%5E2%7D%7BR%7D)
now divide two equations
![tan\theta = \frac{v^2}{Rg}](https://tex.z-dn.net/?f=tan%5Ctheta%20%3D%20%5Cfrac%7Bv%5E2%7D%7BRg%7D)
now as it is given to us that
![v = 80 km/h](https://tex.z-dn.net/?f=v%20%3D%2080%20km%2Fh)
![v = 80* \frac{5}{18} = 22.2 m/s](https://tex.z-dn.net/?f=v%20%3D%2080%2A%20%5Cfrac%7B5%7D%7B18%7D%20%3D%2022.2%20m%2Fs)
![R = 50 m](https://tex.z-dn.net/?f=R%20%3D%2050%20m)
now we have
![tan\theta = \frac{22.2^2}{50*9.8}](https://tex.z-dn.net/?f=tan%5Ctheta%20%3D%20%5Cfrac%7B22.2%5E2%7D%7B50%2A9.8%7D)
![tan\theta = 1](https://tex.z-dn.net/?f=tan%5Ctheta%20%3D%201)
![\theta = tan^{-1}1](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%5E%7B-1%7D1)
![\theta = 45^0](https://tex.z-dn.net/?f=%5Ctheta%20%3D%2045%5E0)
so it is inclined at an angle of 45 degree
Hello there.
<span>Natalie accelerates her skateboard along a straight path from 4 m/s to 0 m/s in 25.0 s. Find the acceleration.
</span><span>6.25 m/s2
</span>
Answer:
The first two statements are false
The third statement is true
Explanation:
<u>The dot product assures that the integrand is always nonnegative.</u>
The dot product may be negative, this could ocurr when the vectors are directed oposite each other, for example take the unitary vector i and -i its doct product will give -1.
Another way to consider this is to take the definition of the dot product in terms of teh angle between the vetcors:
![\vec{A} \cdot \vec{B} = |\vec{A}| \times |\vec{B}| cos(\theta)](https://tex.z-dn.net/?f=%5Cvec%7BA%7D%20%5Ccdot%20%5Cvec%7BB%7D%20%3D%20%7C%5Cvec%7BA%7D%7C%20%5Ctimes%20%7C%5Cvec%7BB%7D%7C%20cos%28%5Ctheta%29)
When θ>π :
cos(θ)<0
<u>The dot product indicates that only the component of the force perpendicular to the path contributes to the integral</u>
In fact the dot product is a projection of the vectors, the perpendicular component may be obtained using the cross product
<u>The dot product indicates that only the component of the force parallel to the path contributes to the integral.</u>
This one is true, since the dot product gives the projection of one vector to another, that is, the parallel component of the vector among the other one
The answer to the question above is letter "D. sound pitch". This is a perceptual quantity that allows to order the frequency-related values. More commonly, it allows people to classify music as "higher" or "lower" in the sense of musical melodies.
Answer:
0.686 m/s
Explanation:
The principle of conservation says the sum of momenta before collision is equal to the sum of momenta after collision in an isolated system. Here, we assume the system is not acted upon by any external force.
The initial momentum = momentum of 1 st cart + momentum of 2nd cart
= 0.400 × 1.2 + 0.300 × 0 = 0.48 kg m/s
The final momentum = (0.400 + 0.300) × v (since they stick together)
0.700 v = 0.48
v = 0.686 m/s