A girl is sledding down a slope that is inclined at 30º with respect to the horizontal. The wind is aiding the motion by providi
ng a steady force of 148 N that is parallel to the motion of the sled. The combined mass of the girl and the sled is 75.7 kg, and the coefficient of kinetic friction between the snow and the runners of the sled is 0.299. How much time is required for the sled to travel down a 124-m slope, starting from rest?
1 answer:
Answer:
travel time is 7.58 s
Explanation:
We must know the acceleration of the sled and the girl, for this we must use Newton's second law
F = m a
Since this is a vector equation, let's separate it into its xy components, the best selection of the coordinate system is the X axis parallel to the plane and the Y axis perpendicular to it.
In the attached you can see a free body diagram of this situation, let's write Newton's equations on each axis
X axis
Wx + F - fr = m a (1)
Axis y
N- Wy = 0
N = Wy
Let's use trigonometry to find the weight components
Wx = W sin θ
Wy = W cos θ
In addition, the formula for friction force is
fr = n N
Let's clear the acceleration of equation 1
a = (W sin θ + F - m N) / m
a = (mg sin θ + F - m mg cos θ) / m
a = g (sin θ -m cos θ) + F / m
Let's replace and calculate
a = 9.8 (sin 30 - 0.299 cos 30) + 148 / 75.7
a = 2.36 + 1.96
a = 4,317 m / s²
We already have the acceleration, the speed is zero to leave the rest (Vo = 0) and give the length that runs 124 m, let's use the kinematic equations
x = v₀ t + ½ a t²
x = ½ a t²
t² = 2x / a
t = √ 2x / a
Let's calculate
t = √( 2 124 / 4,317) = √ 57.45
t = 7.58 s
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A) 2.64t
B) 2.64h
C) 2.64D
Explanation:
A)
The motion of the athlete is equivalent to the motion of a projectile, which consists of two independent motions:
- A uniform motion (constant velocity) along the horizontal direction
- A uniformly accelerated motion (constant acceleration) along the vertical direction
The time of flight of a projectile can be found from the equations of motion, and it is found to be
where
u is the initial speed
is the angle of projection
g is the acceleration due to gravity
In this problem, when the athlete is on the Earth, the time of flight is .
When she is on Mars, the acceleration due to gravity is:
where g is the acceleration due to gravity on Earth. Therefore, the time of flight on Mars will be:
B)
The maximum height reached by a projectile can be also found using the equations of motion, and it is given by
where
u is the initial speed
is the angle of projection
g is the acceleration due to gravity
In this problem, when the athlete is on the Earth, the maximum height is .
When she is on Mars, the acceleration due to gravity is:
where g is the acceleration due to gravity on Earth. So, the maximum height reached on Mars will be:
C)
The horizontal distance covered by a projectile is also found from the equations of motion, and it is given by
where:
u is the initial speed
is the angle of projection
g is the acceleration due to gravity
In this problem, when the athlete is on the Earth, the horizontal distance covered is D.
When she is on Mars, the acceleration due to gravity is:
where g is the acceleration due to gravity on Earth. Therefore, the horizontal distance reached on Mars will be:
The ball drops about 1 m.
Answer:
Explanation:
When an electromagnetic wave passes through the interface between two mediums, it undergoes refraction, which means that it bents and its speed and its wavelength change.
In particular, the wavelength of an electromagnetic wave in a certain medium is related to the index of refraction of the medium by:
where
is the wavelength in a vacuum (air is a good approximation of vacuum)
n is the refractive index of the medium
In this problem:
is the original wavelength of the wave
n = 1.47 is the index of refraction of corn oil
Therefore, the wavelength of the electromagnetic wave in corn oil is: