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Pani-rosa [81]
2 years ago
11

A crate is placed on an adjustable, incline board. the coefficient of static friction between the crate and the board is 0.29.

Physics
1 answer:
sasho [114]2 years ago
7 0

Let the angle be Θ (theta)

Let the mass of the crate be m.

a) When the crate just begins to slip. At that moment the net force will be equal to zero and the static friction will be at the maximum vale.

Normal force (N) = mg CosΘ

μ (coefficient of static friction) = 0.29

Static friction = μN = μmg CosΘ

Now, along the ramp, the equation of net force will be:

mg SinΘ - μmg CosΘ = 0

mg SinΘ = μmg CosΘ

tan Θ = μ

tan Θ = 0.29

Θ = 16.17°

b) Let the acceleration be a.

Coefficient of kinetic friction = μ = 0.26

Now, the equation of net force will be:

mg sinΘ - μ mg CosΘ = ma

a = g SinΘ - μg CosΘ

Plugging the values

a = 9.8 × 0.278 - 0.26 × 9.8 × 0.96

a = 2.7244 - 2.44608

a = 0.278 m/s^2

Hence, the acceleration is 0.278 m/s^2

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Let \theta be the direction the swimmer must swim relative to east. Then her velocity relative to the water is

\vec v_{S/W}=\left(4.0\dfrac{\rm km}{\rm h}\right)(\cos\theta\,\vec\imath+\sin\theta\,\vec\jmath)

The current has velocity vector (relative to the Earth)

\vec v_{W/E}=\left(3.0\dfrac{\rm km}{\rm h}\right)\,\vec\imath

The swimmer's resultant velocity (her velocity relative to the Earth) is then

\vec v_{S/E}=\vec v_{S/W}+\vec v_{W/E}

\vec v_{S/E}=\left(\left(4.0\dfrac{\rm km}{\rm h}\right)\cos\theta+3.0\dfrac{\rm km}{\rm h}\right)\,\vec\imath+\left(4.0\dfrac{\rm km}{\rm h}\right)\sin\theta\,\vec\jmath

We want the resultant vector to be pointing straight north, which means its horizontal component must be 0:

\left(4.0\dfrac{\rm km}{\rm h}\right)\cos\theta+3.0\dfrac{\rm km}{\rm h}=0\implies\cos\theta=-\dfrac{3.0}{4.0}\implies\theta\approx138.59^\circ

which is approximately 41º west of north.

6 0
2 years ago
A farm hand does 972 J of work pulling an empty hay wagon along level ground with a force of 310 N [23° below the horizontal]. T
irina1246 [14]

Answer:

Option d)

Solution:

As per the question:

Work done by farm hand, W_{FH} = 972J

Force exerted, F' = 310 N

Angle, \theta = 23^{\circ}

Now,

The component of force acting horizontally is F'cos\theta

Also, we know that the work done is the dot or scalar product of force and the displacement in the direction of the force acting on an object.

Thus

W_{FH} = \vec{F'}.\vec{d}

972 = 310\times dcos23^{\circ}

d = 3.406 m = 3.4 m

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7. A local sign company needs to install a new billboard. The signpost is 30 m tall, and the ladder truck is parked 24 m away fr
wolverine [178]
<h2>Solution :</h2>

Here ,

• Height of sign post = 30 m

• Distance between signpost and truck = 24 m

Let the

• Top of signpost = A

• Bottom of signpost = B

• The end of truck facing sign post be = C

Now as we can clearly imagine that the ladder will act as an hypotenuse to the Triangle ABC .

Where

• AB = Height of signpost = 30 m

• BC = distance between both = 24 m

• AC = Minimum length of ladder

→ AC² = AB² + BC² ( As we can see AB is perpendicular to BC )

→ AC² = (30)² + (24)²

→ AC² = 900 + 576

→ AC² = 1476

→ AC = 38.41875

or AC apx = 38.42

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Brian and Jack decided to investigate which water fountain at school has the coldest water. The two boys take measurements using
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Answer:

b

Explanation:

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Calculate the average speed and average velocity of a complete round-trip in which the outgoing 250 km is covered at 95 km/h fol
ser-zykov [4K]

To solve this problem we will apply the concepts related to the kinematic equations of linear motion. From them we will consider speed as the distance traveled per unit of time. Said unit of time will be cleared to find the total time taken to travel the given distance. Later with the calculated average times and distances, we will obtain the average speed.

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The time taken to travel a distance of 250km with a speed of 95km/h is

t = \frac{d}{v}

t = \frac{250km}{95km/h}

t = 2.63h

Time taken for the lunch is

t = 1h

The time taken travel a distance of 250km with a speed of 55km/h

t = \frac{d}{v}

t = \frac{250}{55}

t = 4.54h

The total time taken is

t = t_{outgoing}+t_{lunch}}t_{return}

t = 2.63+1+4.54

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v = \frac{250+250}{8.17}

v = 61.15km/h

PART B)

As the displacement is zero the average velocity is zero.

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