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krok68 [10]
3 years ago
6

What is the moment of inertia of an object that rolls without slipping down a 3.5-m- high incline starting from rest, and has a

final velocity of 7.3 m/s? Express the moment of inertia as a multiple of MR2, where M is the mass of the object and R is its radius. (Hint: Use total conservation of mechanical energy)
Physics
1 answer:
Daniel [21]3 years ago
3 0

Answer:

I = 0.287 MR²

Explanation:

given,

height of the object = 3.5 m

initial velocity = 0 m/s

final velocity  = 7.3 m/s

moment of inertia = ?

Using total conservation of mechanical energy

change in potential energy will be equal to change in KE (rotational) and KE(transnational)

PE = KE(transnational) + KE (rotational)

mgh = \dfrac{1}{2}mv^2 + \dfrac{1}{2}I\omega^2

v = r ω

mgh = \dfrac{1}{2}mv^2 + \dfrac{1}{2}\dfrac{Iv^2}{r^2}

I = \dfrac{m(2gh - v^2)r^2}{v^2}

I = \dfrac{mr^2(2\times 9.8 \times 3.5 - 7.3^2)}{7.3^2}

I =mr^2(0.287)

I = 0.287 MR²

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A tightrope walker is walking between two buildings holding a pole with length L=14.0 m, and mass mp=17.5 kg. The daredevil grip
Artemon [7]

Answer:

F = 32.28 N

Explanation:

For this exercise we must use the rotational equilibrium relation

          Σ τ = 0

In the initial configuration it is in equilibrium, for which all the torque and forces are compensated. By the time the payment lands on the bar, we assume that the counter-clockwise turns are positive.

          W_bird  L / 2 - F_left 0.595 - F_right 0.595 = 0

we assume that the magnitude of the forces applied by the hands is the same

          F_left = F_right = F

          W_bird L / 2 - 2 F 0.595 = 0

          F = \frac{m_{bird} \ g L} { 4 \ 0.595}

   

we calculate

         F = 0.560 9.8 14.0 /2.38

         F = 32.28 N

7 0
3 years ago
THE WINNER WILL BE AWARDED THE BRAINLIEST PLEASE HELPP
Ivenika [448]

Answer:Correct answer: 15.85 kg·m/s

Explanation:

A 30 kg gun is standing on a frictionless sur-face. The gun fires a 50 g bullet with a muzzlevelocity of 317 m/s.The positive direction is that of the bullet.Calculate the momentum of the bullet im-mediately after the gun was fired.

7 0
3 years ago
A light rope is attached to a block with mass 4.10 kg that rests on a frictionless, horizontal surface. The horizontal rope pass
musickatia [10]

Answer:

a)  please find the attachment

(b) 3.65 m/s^2

c) 2.5 kg

d) 0.617 W

T<weight of the hanging block

Explanation:

a) please find the attachment

(b) Let +x be to the right and +y be upward.

The magnitude of acceleration is the same for the two blocks.  

In order to calculate the acceleration for the block that is resting on the horizontal surface, we will use Newton's second law:  

∑Fx=ma_x

   T=m1a_x

  14.7=4.10a_x

 a_x= 3.65 m/s^2

c) <em>in order to calculate m we will apply newton second law on the hanging   </em>

<em>    block</em>

<em> </em>∑F=ma_y

T-W= -ma_y

T-mg= -ma_y

T=mg-ma_y

T=m(g-a_y)

a_x=a_y

14.7=m(9.8-3.65)

 m = 2.5 kg

<em>the sign of ay is -ve cause ay is in the -ve y direction and it has the same magnitude of ax</em>

d) calculate the weight of the hanging block :

W=mg

W=2.5*9.8

  =25 N

T=14.7/25

 =0.617 W

T<weight of the hanging block

6 0
3 years ago
A girl travels along the circumference of a circle of radius 14 m. What is her total distance travelled and displacement when sh
AysviL [449]

Answer:

87.976meters, 43.988 meters, 65.982 meters

Explanation:

Given data

Radius= 14m

Let us find the circumference of the circle

This is equivalent to the total distance covered

C= 2πr

C= 2*3.142*14

C= 87.976 meters

Hence the total distance is

87.976meters

The displacement when she has covered 1/2 the circle is

=87.976/2

=43.988 meters

The displacement when she has covered 3/4 the circle is

=87.976* 3/4

=65.982 meters

6 0
3 years ago
A vector makes an angle, theta, with the horizontal. The horizontal and vertical components of the vector will be equal in magni
nika2105 [10]

Answer:

The correct option is;

c. 45°

Explanation:

The given information is that the angle the vector makes with the horizontal = θ

Let the magnitude of the resultant vector = R

The horizontal component of the vector are given as follows;

Rₓ = R × cos(θ)

The vertical component of the vector are given as follows;

R_y = R × sin(θ)

The resultant vector, R, in vector form, R, is the sum of the horizontal and vertical components as follows;

R = R × cos(θ)·i + R × sin(θ)·j

Therefore;

The horizontal and vertical component will be equal when cos(θ) = sin(θ)

Given that tan(θ) = sin(θ)/cos(θ), we have that when cos(θ) = sin(θ), tan(θ) = sin(θ)/cos(θ) = sin(θ)/sin(θ) = 1

tan(θ) = 1,

∴ θ = tan⁻¹(1) = 45°

θ = 45°.

8 0
3 years ago
Read 2 more answers
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