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LenKa [72]
2 years ago
7

A 235-kg merry-go-round at the Great Escape in Lake George is in the shape of a uniform, solid, horizontal disk of radius 1.50 m

. It is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.400 rev/s in 2.00 s?
Physics
1 answer:
Kruka [31]2 years ago
4 0

Answer:

The constant force to be exerted on the rope is 221.55 N

Explanation:

Given;

mass of the merry, m = 235 kg

radius, r = 1.5 m

number of revolution per second, = 0.4 rev/s

time of motion, t= 2.00 s

The angular acceleration is given by;

\alpha = \frac{0.4 \ rev}{s} *\frac{2\pi \ rad}{rev} *\frac{1}{2.0\ s} = 1.257 \ rad/s^2

Torque is given by;

τ = F.r

Also torque in uniform solid disk is given by;

τ = ¹/₂mr²α

Thus, equating the two;

F.r = ¹/₂mr²α

F =  ¹/₂mrα

F = ¹/₂(235)(1.5)(1.257)

F = 221.55 N

Therefore, the constant force to be exerted on the rope is 221.55 N

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Answer:

Only the perpendicular component of gravity is responsible for the rotation because wind points toward the pivot.

Explanation:

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3 years ago
The magnitude of each force is 208 N the force on the right is applied at an angle 36° and the mass of the block is 17 kg the co
djyliett [7]

Answer:

<em>11.06m/s²</em>

Explanation:

According to Newtons second law of motion

\sm F_x = ma_x\\F_m - F_f = ma_x\\mgsin \theta - \mu R mgcos \theta = ma_x\\

Given

Mass m = 17kg

Fm = 208N

theta = 36 degrees

g = 9.8m/s²

a is the acceleration

Substitute

208 - 0.148(17)(9.8)cos 36 = 17a

208 - 24.6568cos36 = 17a

208 - 19.9478 = 17a

188.05 = 17a

a = 188.05/17

a = 11.06m/s²

<em>Hence the  the magnitude of the resulting acceleration is 11.06m/s²</em>

6 0
2 years ago
After driving a portion of the route, the taptap is fully loaded with a total of 27 people including the driver, with an average
belka [17]

We will define the Total mass to calculate the force, so our values are:M_p = 69*27=1823Kg\\M_g=15*3=45Kg\\M_c=3*5=15Kg\\M_B=25Kg

Total Mass = 1863+45+15+25=1948Kg

The Weight is,

F=mg=1948*98=19090.4N

Through the hook's Law we calculate X.

F_s=Kx, where x is the lenght of compression and K the Spring constant.

We don't have a K-Spring, but we can assume a random value (or simply let the equation in function of K)

X = \frac{F_s}{x} \\X = \frac{1909.4}{k}

I assume a value of K=4*10^4N/m

X= \frac{1909.4}{4*10^4} = 0.48m

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3 years ago
To analyze the motion of a body that is traveling along a curved path, to determine the body's acceleration, velocity, and posit
DiKsa [7]

To solve this problem we will apply the kinematic equations of linear motion and centripetal motion. For this purpose we will be guided by the definitions of centripetal acceleration to relate it to the tangential velocity. With these equations we will also relate the linear velocity for which we will find the points determined by the statement. Our values are given as

R = 350ft

a_t = 1.1ft/s^2

PART A )

a_c = \frac{V^2}{R}

a_c = \frac{V^2}{350}

Calculate the velocity of the motorcycle when the net acceleration of the motorcycle is 5.25ft/s^2

a = \sqrt{a_t^2+a_r^2}

5.25 = \sqrt{(1.1)^2+(\frac{v^2}{350})^2}

27.5625 = 1.21 + \frac{v^4}{122500}

v=42.3877ft/s

Now calculate the angular velocity of the motorcycle

v = r\omega

42.3877 = 350\omega

\omega = 0.1211rad/s

Calculate the angular acceleration of the motorcycle

a_t = r\alpha

1.1 = 350\alpha

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Calculate the time needed by the motorcycle to reach an acceleration of

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\omega = \alpha t

0.1211 = 3.1428*10^{-3}t

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PART B) Calculate the velocity of the motorcycle when the net acceleration of the motorcycle is 6.75ft/s^2

a = \sqrt{a_t^2+a_r^2}

6.75 = \sqrt{(1.1)^2+(\frac{v^2}{350})^2}

45.5625 = 1.21 + \frac{v^4}{122500}

v=48.2796ft/s

PART C)

Calculate the radial acceleration of the motorcycle when the velocity of the motorcycle is 21.5ft/s

a_r = \frac{v^2}{R}

a_r = \frac{21.5^2}{350}

a_r =1.3207ft/s^2

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a = \sqrt{a_t^2+a_r^2}

a = \sqrt{(1.1)^2+(1.3207)^2}

a = 1.7187ft/s^2

PART D) Calculate the maximum constant speed of the motorcycle when the maximum acceleration of the motorcycle is 6.75ft/s^2

a = \sqrt{a_t^2+a_r^2}

6.75 = \sqrt{(1.1)^2+(\frac{v^2}{350})^2}

45.5625 = 1.21 + \frac{v^4}{122500}

v=48.2796ft/s

3 0
3 years ago
Without friction, what force is needed to maintain a 1,000 kg car in uniform motion for 30 minutes?
VARVARA [1.3K]
<span>The answer is none. According to the first law of Newton, an object stays at the same speed in the same direction if there are not forces unbalancing the object. Without friction, the car would be moving forever, unless there is another force accelerating or stopping the car.</span>
6 0
3 years ago
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