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zalisa [80]
3 years ago
9

A 4.76 kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force F(t) is applied to the en

d of the rope, and the height of the crate above its initial position is given by y(t)=(2.80m/s)t +(0.61 m/s3 )t3
What is the magnitude of the force F when 3.71 s ?
Physics
1 answer:
Romashka-Z-Leto [24]3 years ago
6 0

Answer:

The magnitude of the force is 64.634 newtons.

Explanation:

According to the statement, the crate is a constant mass system, whose upward force is described by the following expression:

F(t) = m\cdot \ddot{y} (t) (1)

Where:

F(t) - Force, in newtons.

m - Mass, in kilograms.

\ddot {y}(t) - Acceleration, in meters per square second.

The function acceleration is obtained by deriving the function position twice in time:

\dot y (t) = 2.80 + 1.83\cdot t^{2} (2)

\ddot y(t) = 3.66\cdot t (3)

And we expand (1) by applying (3):

F(t) = 3.66\cdot m \cdot t

Where t is the time, in seconds.

If we know that m = 4.76\,kg and t = 3.71\,s, then the magnitude of the force is:

F = 3.66\cdot (4.76)\cdot (3.71)

F = 64.634\,N

The magnitude of the force is 64.634 newtons.

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  Approximate volume of head =\frac{4}{3} \pi r^3=\frac{4}{3} *\pi* 10^3=4188cm^3

 In the given options the closest value to the approximate volume is 1000 cm^3.

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How can groundwater flow, elevation can transport contaminates
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3 years ago
A 50-g cube of ice, initially at 0.0°C, is dropped into 200 g of water in an 80-g aluminum container, both initially at 30°C.
MakcuM [25]

Answer:

b. 9.5°C

Explanation:

m_i = Mass of ice = 50 g

T_i = Initial temperature of water and Aluminum = 30°C

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m_w = Mass of water = 200 g

c_w = Specific heat of water = 4186 J/kg⋅°C

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c_{Al} = Specific heat of Aluminum = 900 J/kg⋅°C

The equation of the system's heat exchange is given by

m_i(L_f+c_wT)+m_wc_w(T-T_i)+m_{Al}c_{Al}=0\\\Rightarrow 0.05\times (3.33\times 10^5+4186\times T)+0.2\times 4186(T-30)+0.08\times 900(T-30)=0\\\Rightarrow 1118.5T-10626=0\\\Rightarrow T=\dfrac{10626}{1118.5}\\\Rightarrow T=9.50022\ ^{\circ}C

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