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Fittoniya [83]
2 years ago
12

On a planet where g = 10.0 m/s2 and air resistance is negligible, a sled is at rest on a rough inclined hill rising at 30°. The

initial position is 8.0 m up the hill along the slope from the bottom. The object is allowed to move and it stops on a rough horizontal surface, at a distance of 4.0 m from the bottom of the hill. The coefficient of kinetic friction on the hill is 0.40. What is the coefficient of kinetic friction between the horizontal surface and the sled?

Physics
2 answers:
Cloud [144]2 years ago
8 0

Answer:

Explanation:

a is the acceleration

μ is the coefficient of friction

Acceleration of the object is given by

a = g (\sin  \theta -\mu \cos \theta)\\\\=10( \sin 30 - 0.4 \cos 30)\\\\=10(0.5-0.3464)\\\\=1.54m/s^2

Velocity at the bottom

v^2=u^2+2as\\\\u=0\\\\v^2=2as\\\\=2*1.54*8\\\\=24.576\\\\v=4.96m/s

after travelling 4m , its velocity becomes 0

a=\frac{v^2-u^2}{2s}

a=\frac{0-u^2}{2s}

a=\frac{-(-4.96)^2}{2*4} \\\\=-3.075m/s^2

Coefficient of kinetic friction

μ = F/N

=\frac{ma}{mg} \\\\=\frac{3.075}{10} \\\\=0.31

Therefore, the Coefficient of kinetic friction is 0.31

Romashka-Z-Leto [24]2 years ago
5 0

Answer:

Coefficient of kinetic friction = 0.31

Explanation:

g = 10 m/s²

distance covered up the hill, S = 8 m

Horizontal distance covered, d = 4 m

From the free body diagram attached:

ma =  mgsin \theta - \mu_{k} N\\N = mgcos \theta\\ma = mgsin \theta - \mu_{k} mgcos \theta\\a = gsin \theta - \mu_{k} gcos \theta\\a = 10sin 30 - (0.4*10cos30)\\a = 1.4 m/s^2

The velocity at the bottom can be calculated by:

v^{2} = u^{2} + 2aS\\u = 0 m/s\\v^{2} = 2aS\\v^{2} = 2*1.54*8\\v^{2} = 24.64\\v = 4.96 m/s

Work done through to frictional force = change in kinetic energy:

f_{k} d = 0.5 mv^{2} \\\mu_{k} mgd = 0.5mv^{2} \\\mu_{k} = \frac{0.5v^{2} }{gd} \\\mu_{k} = \frac{0.5*4.96^{2} }{10*4} \\\mu_{k} = 0.31

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The wavelength of a certain portion of an electromagnetic wave is 314 nm. what is its frequency and classification?
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5 0
1 year ago
After flying for 15 min in a wind blowing 42 km/h at an angle of 19° south of east, an airplane pilot is over a town that is 48
masha68 [24]

Answer:

The speed of the airplane relative to the air is 209.47km/hr

Explanation:

Whenever we are solving a physics problem, it's really useful to start by drawing a diagram of the problem (See picture attached). It will help us visualize the problem better.

Now, we know that the plane flew for an amount of time of 15 minutes. For our dimensions to be the same, we need to turn those 15min to hours, like this:

15min*\frac{1hr}{60min}=0.25hr

Once our time is rewritten as hours, we can now calculate the velocity towards north of the plane.

V=\frac{distance}{time}

the plane traveled a distance to the north of 48km so the velocity is:

V=\frac{48km}{0.25hr}

so

V=192km/hr j

Now, we can calculate the x and y-components of the velocity of the wind. The problem states that the wind is blowing at 42km/hr at an angle of 19° south of east, so the x and y-components of the velocity of the wind are:

V_{x}=42km/hr*cos(-19^{o} )=39.71 i

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V_{y}=42km/hr*sin(-19^{o} )=-13.67 j

So the velocity of the wind can be expressed as a vector as:

V_{wind}=(39.71i - 13.67j)km/hr

Once we know this, we can find the velocity of the plane with respect of the wind on x and on y:

V_{plane x}=V_{plane/wind x}+V_{wind x}

V_{plane/wind x}=V_{plane x}-V_{wind x}

V_{plane/wind x}=(0-39.71 i)km/hr

V_{plane/wind x}= -39.71 i km/hr

and

V_{plane y}=V_{plane/wind y}+V_{wind y}

V_{plane/wind y}=V_{plane y}-V_{wind y}

V_{plane/wind y}=192km/hr j - (- 13.67j)km/hr

V_{plane/wind x}= 205.67 j km/hr

So the velocity of the plane with respect to the wind can be rewritten as:

V_{plane/wind x}= (-39.71i + 205.67 j) km/hr

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speed=\sqrt{(-39.71)^{2}+(205.67)^{2}  }

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