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Brrunno [24]
3 years ago
14

A 1.80-kg monkey wrench is pivoted 0.250 m from its center of mass and allowed to swing as a physical pendulum. The period for s

mall- angle oscillations is 0.940 s. (a) What is the moment of inertia of the wrench about an axis through the pivot? (b) If the wrench is initially displaced 0.400 rad from its equilibrium position, what is the angular speed of the wrench as it passes through the equilibrium position?
Physics
1 answer:
Evgen [1.6K]3 years ago
5 0

Answer:

(a) I (Moment of inertia)=0.0987 kgm^{2}

(b) W(Angular Speed)=2.66 \frac{rad}{s}

Explanation:

Given data

m (Monkey mass)= 1.80 kg

d=2.50 m

T (Time Period)=0.940 s

Angle= 0.400 rad

(a) I (Moment of Inertia)=?

(b) W (Angular Speed)=?

For part (a) I (Moment of Inertia)=?

Time Period Formula is given as

T=2(3.14)\sqrt{\frac{I}{mgd} }

After Simplifying we get

I=\frac{mgdT^{2} }{4*(3.14)^{2}}

I=\frac{1.8*9.8*0.25*(0.94)^{2} }{4(3.14)^{2} }

I=0.0987 kgm^{2}

For Part (b) Angular Speed

From Kinetic Energy we get

KE=\frac{1}{2}IW^{2}

Pontential Energy

PE=mgd(1-Cosa)

KE=PE

\frac{1}{2}IW^{2}=mgd(1-Cosa)

W^{2}=\frac{2mgd(1-Cosa)}{I}

W=\sqrt{\frac{2*1.8*9.8*0.25*(1-Cos(0.4)rad)}{0.0987} }

W=2.66\frac{rad}{s}

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asambeis [7]

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3 0
3 years ago
Mike is cutting the grass using a human-powered lawn mower. He pushes the mower with a force of 45 n directed at an angle of 41Â
Andrej [43]

Answer:

work done will be equal to 305.05 J

Explanation:

We have given force exerted F = 45 N

Angle with the horizontal \Theta =41^{\circ}

Distance moved due to exerted force d = 9.1 m

Work done is equal to W=Fcos\Theta \times d , here F is force \Theta is angle with horizontal and d is distance moved due to force

So work done W=45\times cos41^{\circ}\times 9.1=309.05J

So work done will be equal to 305.05 J

7 0
3 years ago
Snorkeling by humans and elephants. When a person snorkels, the lungs are connected directly to the atmosphere through the snork
fgiga [73]

Answer:

2354.4 Pa

40221 Pa

Explanation:

\rho = Density = 1000 kg/m³

g = Acceleration due to gravity = 9.81 m/s²

h = Depth

The pressure difference would be

\Delta P=\rho gh\\\Rightarrow \Delta P=1000\times 0.24\times 9.81\\\Rightarrow \Delta P=2354.4\ Pa

The pressure difference in the first case is 2354.4 Pa

\Delta P=\rho gh\\\Rightarrow \Delta P=1000\times 4.1\times 9.81\\\Rightarrow \Delta P=40221\ Pa

The pressure difference in the second case is 40221 Pa

7 0
3 years ago
On a bet, you try to remove water from a glass by blowing across the top of a vertical straw immersed in the water. What is the
MArishka [77]

Answer:

       v₂ = 0.56 m / s

Explanation:

This exercise can be done using Bernoulli's equation

        P₁ + ½ ρ v₁² + ρ g y₁ = P₂ + ½ ρ v₂² + ρ g y₂

Where points 1 and 2 are on the surface of the glass and the top of the straw

The pressure at the two points is the same because they are open to the atmosphere, if we assume that the surface of the vessel is much sea that the area of ​​the straw the velocity of the surface of the vessel is almost zero v₁ = 0

The difference in height between the level of the glass and the straw is constant and equal to 1.6 cm = 1.6 10⁻² m

We substitute in the equation

         P_{atm} + ρ g y₁ = P_{atm} + ½ ρ v₂² + ρ g y₂

         ½ v₂² = g (y₂-y₁)

        v₂ = √ 2 g (y₂-y₁)

Let's calculate

        v₂ = √ (2 9.8 1.6 10⁻²)

       v₂ = 0.56 m / s

5 0
3 years ago
Determine the linear velocity of an object with an angular velocity of 5.9 radians per second at a distance of 12 centimeters fr
Andre45 [30]
The linear velocity of a rotating object is the product of the angular velocity and the radius of the circular motion. Angular velocity is the rate of the change of angular displacement of a body that is in a circular motion. It is a vector quantity so it consists of a magnitude and direction. From the problem, the angular velocity is 5.9 rad per second and the radius is given as 12 centimeters. We calculate as follows:

Linear velocity = angular velocity (radius)
Linear velocity = 5.9 (12 ) = 70.8 cm / s

The linear velocity of the body in motion is 70.8 centimeters per second or 0.708 meters per second.
7 0
3 years ago
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