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;
![\sum F_x = \sum F_y = 0](https://tex.z-dn.net/?f=%5Csum%20F_x%20%3D%20%5Csum%20F_y%20%3D%200)
![\mathbf{mg sin \theta -f_s= N-mgcos \theta = 0 }](https://tex.z-dn.net/?f=%5Cmathbf%7Bmg%20sin%20%5Ctheta%20-f_s%3D%20N-mgcos%20%5Ctheta%20%3D%200%20%7D)
![\mathbf{mg sin \theta =f_s}](https://tex.z-dn.net/?f=%5Cmathbf%7Bmg%20sin%20%5Ctheta%20%3Df_s%7D)
![\mathbf{mg sin \theta =\mu_s N}](https://tex.z-dn.net/?f=%5Cmathbf%7Bmg%20sin%20%5Ctheta%20%3D%5Cmu_s%20N%7D)
N = mg cos θ
Equating both force component together, we have:
![\mathbf{mg sin \theta =\mu_s \ mg \ cos \theta}](https://tex.z-dn.net/?f=%5Cmathbf%7Bmg%20sin%20%5Ctheta%20%3D%5Cmu_s%20%5C%20mg%20%5C%20cos%20%5Ctheta%7D)
![\mathbf{sin \theta =\mu_s \ \ cos \theta}](https://tex.z-dn.net/?f=%5Cmathbf%7Bsin%20%5Ctheta%20%3D%5Cmu_s%20%5C%20%5C%20cos%20%5Ctheta%7D)
![\mathbf{\mu_s = \dfrac{sin \theta }{ cos \theta}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cmu_s%20%3D%20%5Cdfrac%7Bsin%20%5Ctheta%20%7D%7B%20cos%20%5Ctheta%7D%7D)
From trigonometry rule:
![\mathbf{tan \theta= \dfrac{sin \theta }{ cos \theta}}](https://tex.z-dn.net/?f=%5Cmathbf%7Btan%20%5Ctheta%3D%20%5Cdfrac%7Bsin%20%5Ctheta%20%7D%7B%20cos%20%5Ctheta%7D%7D)
∴
![\mathbf{\mu_s =\tan \theta}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cmu_s%20%3D%5Ctan%20%5Ctheta%7D%7D)
![\mathbf{\mu_s =\tan 35^0}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cmu_s%20%3D%5Ctan%2035%5E0%7D%7D)
![\mathbf{\mu_s = 0.700}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cmu_s%20%3D%200.700%7D%7D)
Therefore, we can conclude that the minimum coefficient of static friction needed for this claim to be possible is 0.7
Learn more about static friction here:
brainly.com/question/24882156?referrer=searchResults
Answer:
Speed =0.283m/ s
Direction = 47.86°
Explanation:
Since it is a two dimensional momentum question with pucks having the same mass, we derive the momentum in xy plane
MU1 =MU2cos38 + MV2cos y ...x plane
0 = MU2sin38 - MV2sin y .....y plane
Where M= mass of puck, U1 = initial velocity of puck 1=0.46, U2 = final velocity of puck 1 =0.34, V2 = final velocity of puck 2, y= angular direction of puck2
Substitute into equation above
.46 = .34cos38 + V2cos y ...equ1
.34sin38 = V2sin y...equ2
.19=V2cos Y...x
.21=V2sin Y ...y
From x
V2 =0.19/cost
Sub V2 into y
0.21 = 0.19(Sin y/cos y)
1.1052 = tan y
y = 47.86°
Sub Y in to x plane equ
.19 = V2 cos 47.86°
V2=0.283m/s
Answer:
cellular respiration.
explanation: cellular respiration, the process by which organisms combine oxygen with foodstuff molecules, diverting the chemical energy in these substances into life-sustaining activities and discarding, as waste products, carbon dioxide and water.
Answer:
, it will sink
Explanation:
The density of an object is given by
![d=\frac{m}{V}](https://tex.z-dn.net/?f=d%3D%5Cfrac%7Bm%7D%7BV%7D)
where
m is the mass of the object
V is its volume
For the body in the problem, we have
m = 4 kg = 4000 g
![V=2000 cm^3](https://tex.z-dn.net/?f=V%3D2000%20cm%5E3)
Therefore, its density is
![d=\frac{4000}{2000}=2 g/cm^3](https://tex.z-dn.net/?f=d%3D%5Cfrac%7B4000%7D%7B2000%7D%3D2%20g%2Fcm%5E3)
And the object will sink in water, because its density is larger than that of water, which is
. (an object sinks when its density is larger than that of water, otherwise it floats).