F=mgsinα –F(fr)=
= mgsinα - μmgcosα
a=F/m =g(sinα – μcosα)
=9.8(sin14-0.57•cos14)= -3.04 m/s²
v²=v₀²+2ad
v=sqrt{ v₀²+2ad} =
=sqrt{18²+2• (-3.04) •25}=13.1 m/
Newton's second law and kinematics allow us to find the speed with which the car collided are:
a) Coefficient of friction 0.60, the speed is: v = 11.8 m / s.
b) Coefficient of friction 0.10, the speed is: v = 16.4 m / s.
Newton's second law says that force is proportional to the product of mass and acceleration.
Σ F = m a
Where bold indicates vectors, F is force, m is mass, and acceleration.
A reference system is a coordinate system against which to measure and decompose forces. In the attached we can see a free body diagram of the car that is going down, we take the x axis parallel to the plane and with a positive direction in the direction of movement, the y axis is perpendicular to the plane.
Let's use trigonometry to descompose the weight.
sin θ = [tex]\frac{W_x}{W}[/tex]
cos θ = [tex]\frac{W_y}{W}[/tex]
Wₓ = W sin θ
W_y = W cos θ
We write Newton's second law for each axis.
y-axis
N - W_y = 0
N = mg cos θ
x axis
Wₓ -fr = ma
The friction force is a macroscopic force that opposes the movement of bodies and its expression is:
fr = μ N
Let's substitute
m a = m g sin θ - μ m g cos θ
a = g (sin θ - μ cos θ)
a) They indicate that the coefficient of kinetic friction is μ = 0.60
We calculate
a = 9.8 (sin 12- 0.6 cos 12)
a = 3.71 m / s²
Now we can use kinematics to find the velocity after traveling the distance of x = 25 m.
v² = v₀² - 2 a x
v² = 18.0² - 2 3.71 25
v = [tex]\sqrt{138.5}[/tex]
v = 11.8 m / s
b) They indicate that the coefficient of kinetic friction is μ = 0.10
We calculate
a = 9.8 (sin 12 - 0.1 cos 12)
a = 1.08 m / s²
speed is
v² = 18² - 2 1.08 25
v = [tex]\sqrt{270}[/tex]
v = 16.4 m / s
In conclusion using Newton's second law and kinematics we can find the speed with which the car collided are:
a) Friction coefficient of 0.60, the speed is: v = 11.8 m / s
b) Friction coefficient of 0.10, the speed is: v = 16.4 m / s
Learn more here: brainly.com/question/10535515
