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Umnica [9.8K]
3 years ago
10

A rotating object starts from rest at t = 0 s and has a constant angular acceleration. At a time of t = 2.5 s the object has an

angular displacement of 13 rad. What is its displacement θ at a time of t = 5.0 s?
Physics
2 answers:
Anarel [89]3 years ago
8 0

Answer:

\theta = 52 rads

Explanation:

The rotational kinetic equation is given by the formula:

\theta = w_{0} t + 0.5 \alpha t^{2}..............(1)

The object is starting from rest, angular speed, w = 0 rad/s

At t = 2.5 sec, angular displacement, θ = 13 rad

Inserting these parameters into equation (1)

13 = (0 *  2.5) + 0.5 \alpha 2.5^{2}\\\alpha = \frac{13}{3.125} \\\alpha = 4.16 rad/s^{2}

At time, t = 5.0 sec, we substitute the value of \alpha into the kinematic equation in (1)

\theta = (0*5) + 0.5 *4.16* 5^{2}\\\theta = 52 rad

Evgesh-ka [11]3 years ago
6 0

Answer:

52 rad

Explanation:

Using

Ф = ω't +1/2αt²................... Equation 1

Where Ф = angular displacement of the object, t = time, ω' = initial angular velocity, α = angular acceleration.

Since the object states from rest, ω' = 0 rad/s.

Therefore,

Ф = 1/2αt²................ Equation 2

make α the subject of the equation

α = 2Ф/t².................. Equation 3

Given: Ф = 13 rad, t = 2.5 s

Substitute into equation 3

α = 2(13)/2.5²

α = 26/2.5

α = 4.16 rad/s².

using equation 2,

Ф = 1/2αt²

Given: t = 5 s, α = 4.16 rad/s²

Substitute into equation 2

Ф = 1/2(4.16)(5²)

Ф = 52 rad.

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A 12.0 g bullet was fired horizontally into a 1 kg block of wood. The bullet initially had a speed of 250 m/s. The block of wood
LuckyWell [14K]

Answer:

The rise in height of combined block/bullet from its original position is 0.45m

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initial speed of block of wood, u₂ = 0

From the principle of conservation of linear momentum, calculate the final speed of the combined block/bullet system.

m₁u₁ + m₂u₂ = v(m₁+m₂)

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v is the final speed of the combined block/bullet system.

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¹/₂v² = gh

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4.3808 = 9.8h

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The vacuum pressure of a condenser is given to be 80 kpa. if the atmospheric pressure is 98 kpa, what is the gage pressure and a
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The absolute pressure is given by the equation,

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Here, P_{abs} is absolute pressure,P_{atm} is atmospheric pressure and P_{vac} is vacuum pressure.

Therefore,

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The gage pressure is given by the equation,

P_{gage}=P_{abs}-P_{atm}.

Thus,

P_{gage}=18kPa-98 kPa=-80 kPa.

In kn/m^2,

The absolute pressure,

P_{abs}=18kPa(\frac{1kN/m^2}{kPa}) =18\ kN/m^2

The gage pressure,

P_{gage}=-80kPa(\frac{1kN/m^2}{kPa}) =-80\ kN/m^2.

In lbf/in2

The absolute pressure,

P_{abs}=18\ kPa(\frac{1.45\times 10^{-1}\ lbf/in^2 }{1kPa} )=2.6\ lbf/in^2

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In psi,

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The gage pressure,

P_{gage}=-80kPa(\frac{1.45037738\times 10^{-1}\ psi }{1kPa} )=-11.6030\ psi

In  mm Hg

The absolute pressure,

P_{abs}=18kPa(\frac{7.5\ mm\ of\ Hg }{1\ kPa})= 135\ mm\ of\ Hg

The gage pressure,

P_{gage}=-80kPa(\frac{7.5\ mm\ of\ Hg }{1\ kPa})=-600\ mm\ of\ Hg



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