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The height of a typical playground slide is about 1.8 m and it rises at an angle of 30 ∘ above the horizontal.

Salsk061 [2.6K]

Answer:

$5.94\ \text{m/s}$

$1.7$

$0.577$

Explanation:

g = Acceleration due to gravity = $9.81\ \text{m/s}^2$

$\theta$ = Angle of slope = $30^{\circ}$

v = Velocity of child at the bottom of the slide

$\mu_k$ = Coefficient of kinetic friction

$\mu_s$ = Coefficient of static friction

h = Height of slope = 1.8 m

The energy balance of the system is given by

$mgh=\dfrac{1}{2}mv^2\\\Rightarrow v=\sqrt{2gh}\\\Rightarrow v=\sqrt{2\times 9.81\times 1.8}\\\Rightarrow v=5.94\ \text{m/s}$

The speed of the child at the bottom of the slide is $5.94\ \text{m/s}$

Length of the slide is given by

$l=h\sin\theta\\\Rightarrow l=1.8\sin30^{\circ}\\\Rightarrow l=0.9\ \text{m}$

$v=\dfrac{1}{2}\times5.94\\\Rightarrow v=2.97\ \text{m/s}$

The force energy balance of the system is given by

$mgh=\dfrac{1}{2}mv^2+\mu_kmg\cos\theta l\\\Rightarrow \mu_k=\dfrac{gh-\dfrac{1}{2}v^2}{gl\cos\theta}\\\Rightarrow \mu_k=\dfrac{9.81\times 1.8-\dfrac{1}{2}\times 2.97^2}{9.81\times 0.9\cos30^{\circ}}\\\Rightarrow \mu_k=1.73$

The coefficient of kinetic friction is $1.7$ .

For static friction

$\mu_s\geq\tan30^{\circ}\\\Rightarrow \mu_s\geq0.577$

So, the minimum possible value for the coefficient of static friction is $0.577$ .

8 0

3 years ago

In simple harmonic motion, the acceleration is proportional to In simple harmonic motion, the acceleration is proportional to:__

erik [133]

Answer:

e. all of the above

Explanation:

In simple harmonic motion, the acceleration is given as;

a = -ω²x = -(2πf)²x

$a_{max} = -\omega ^2A$

where;

ω is the angular velocity

f is the frequency

x is the displacement

A is the amplitude

Thus, In simple harmonic motion, the acceleration is proportional to the amplitude, velocity, frequency, and displacement.

The correct option is E.

"all of the above"

5 0

3 years ago

Explain how the extension of a spring is determined

fgiga [73]

Answer:

For a given spring the extension is directly proportional to the force applied For example if the force is doubled, the extension doubles When an elastic object is stretched beyond its limit of proportionality the object does not return to its original length when the force is removed

Explanation:

6 0

3 years ago

Four students measured the same line with a ruler like the one shown below. The results were as follows: 5.52 cm, 6.63 cm, 5.5,

hammer [34]

Answer:

1) 5.52 cm , C) 5.5 cm

Explanation:

When a measurement is carried out, in addition to the value of the magnitude, the error or uncertainty of the measurement must occur, in a direct measurement with an instrument the uncertainty is equal to the appreciation of the instrument.

Uniform see the errors by the number of significant figures days, in this cases they are two decimals for which the appreciation of the instrument ± - 0.01

now we can analyze the measurements made

1) 5.52 cm. Validate. It is a valid measurement is within the uncertainty range

2) 6.63 cm. It does not validate. It is out of the error range

3) 5.5 cm Valid. It is within the given error range,

4) 5.93 cm Not Valid. It is out of the error range.

7 0

3 years ago

Two wires, each of length 1.3 m, are stretched between two fixed supports. On wire A there is a second-harmonic standing wave wh

UNO [17]

Answer:

Explanation:

Given