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Nataliya [291]
2 years ago
15

A popular ride at some playgrounds consists of two circular disks joined by rungs . The center of the unit is attached to a hori

zontal axle around which the unit rotates. The rotational inertia of the unit is 550 kg⋅m2 , and its radius is 1.00 m. A 30-kg child runs and grabs the bottom rung of the ride when it is initially at rest. Because the child can pull herself up to meet the rung at waist height, treat her as a particle located on the rung. The friction between unit and axle is minimal and can be ignored. What is the minimum speed v the child must have when she grabs the bottom rung in order to make the unit rotate about its axle and carry her over the top of the unit? Express your answer with the appropriate units.
Physics
1 answer:
weeeeeb [17]2 years ago
7 0

Answer:

v = 36.667 m/s

Explanation:

Knowing the rotational inertia as

Lₙ = 550 kg * m²

r = 1.0 m

m = 30.0 kg

To determine the minimum speed v must have when she grabs the bottom

Lₙ =  I * ω

I = ¹/₂ * m * r²

I = ¹/₂ * 30.0 kg * 1.0² m

I = 15 kg * m²

Lₙ =  I * ω  ⇒ ω =  Lₙ / I

ω = [ 550 kg * m² /s  ] / ( 15 kg * m² )

ω = 36.667 rad /s

v = ω * r

v = 36.667 m/s

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a_sh-v [17]

Answer:

The minimum speed of the box bottom of the incline so that it will reach the skier is 8.19 m/s.

Explanation:

It is given that,

Mass of the box, m = 2.2 kg

The box is inclined at an angle of 30 degrees

Vertical distance, d = 3.1 m

The coefficient of friction, \mu=6\times 10^{-2}

Using the work energy theorem, the loss of kinetic energy is equal to the sum of gain in potential energy and the work done against friction.

KE=PE+W

\dfrac{1}{2}mv^2=mgh+W

W is the work done by the friction.

W=f\times d

f=\mu mg\ cos\theta

W=\mu mg\ cos\theta\times \dfrac{d}{sin\theta}

W=\dfrac{\mu mgh}{tan\theta}

\dfrac{1}{2}mv^2=mgh+\dfrac{\mu mgh}{tan\theta}

\dfrac{1}{2}v^2=gh+\dfrac{\mu gh}{tan\theta}

\dfrac{1}{2}v^2=9.8\times 3.1+\dfrac{6\times 10^{-2}\times 9.8\times 3.1}{tan(30)}

v = 8.19 m/s

So, the speed of the box is 8.19 m/s. Hence, this is the required solution.

8 0
2 years ago
A 38 kg crate rests on a floor. A horizontal pulling force of 170 N is needed to start the crate
Mandarinka [93]

Answer:

0.456033049

Explanation:

F=\mu N where N=mg hence

F=\mu mg where m is mass of object, g is acceleration due to gravity whose value is taken as 9.81 m/s^{2}, \mu is the coefficient of static friction and F is the applied force.

Making \mu the subject we obtain

\mu=\frac {mg}{N} and substituting m for 38 Kg, g for 9.81 m/s^{2} and 170 N for  F we obtain

\mu=\frac{170} {38*9.81}=0.456033049

Therefore, the coefficient of static friction is 0.456033049

5 0
2 years ago
Two forces F1 and F2 act on a 5.00 kg object. Taking F1=20.0N and F2=15.00N, find the acceleration of the object for the configu
Anit [1.1K]
A) mass m with F1 acting in the positive x direction and F2 acting perpendicular in the positive y direction<span>

m = 5.00 kg
F1=20.0N  ... x direction
F2=15.00N</span><span>  ... y direction

Net force ^2 = F1^2 + F2^2 = (20N)^2 + (15n)^2 =  625N^2 =>

Net force = √625 = 25N

F = m*a => a = F/m = 25.0 N /5.00 kg = 5 m/s^2

Answer: 5.00 m/s^2

b) mass m with F1 acting in the positive x direction and F2 acting on the object at 60 degrees above the horizontal. </span>

<span>m = 5.00 kg
F1=20.0N  ... x direction
F2=15.00N</span><span>  ... 60 degress above x direction

Components of F2

F2,x = F2*cos(60) = 15N / 2 = 7.5N

F2, y = F2*sin(60) = 15N* 0.866 = 12.99 N ≈ 13 N


Total force in x = F1 + F2,x = 20.0 N + 7.5 N = 27.5 N

Total force in y = F2,y = 13.0 N

Net force^2 = (27.5N)^2 + (13.0N)^2 = 925.25 N^2 = Net force = √(925.25N^2) =

= 30.42N

a = F /m = 30.42 N / 5.00 kg = 6.08 m/s^2

Answer: 6.08 m/s^2


</span>
8 0
2 years ago
Read 2 more answers
A rock of mass m is thrown horizontally off a building from a height h. the speed of the rock as it leaves the thrower's hand at
Stells [14]
The correct answer is <span>3) K_f =  \frac{1}{2}mv_0^2 + mgh.
</span>
In fact, the total energy of the rock when it <span>leaves the thrower's hand is the sum of the gravitational potential energy U and of the initial kinetic energy K:
</span>E=U_i+K_i=mgh +  \frac{1}{2}mv_0^2
<span>As the rock falls down, its height h from the ground decreases, eventually reaching zero just before hitting the ground. This means that U, the potential energy just before hitting the ground, is zero, and the total final energy is just kinetic energy: 
</span>E=K_f<span>
But for the law of conservation of energy, the total final energy must be equal to the tinitial energy, so E is always the same. Therefore, the final kinetic energy must be
</span>K_f = mgh +  \frac{1}{2}mv_0^2<span>
</span>

7 0
2 years ago
1. A 930-kg car traveling 56 km/h comes to a complete stop in 2.0 s. What is the
Juli2301 [7.4K]

The force exerted on the car during this stop is 6975N

<u>Explanation:</u>

Given-

Mass, m = 930kg

Speed, s = 56km/hr = 56 X 5/18 m/s = 15m/s

Time, t = 2s

Force, F = ?

F = m X a

F = m X s/t

F = 930 X 15/2

F = 6975N

Therefore, the force exerted on the car during this stop is 6975N

6 0
2 years ago
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