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3 years ago

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(a) At a certain instant, a particle-like object is acted on by a force F = (5.0 N) i hat - (2.0 N) j + (8.0 N) k while the obje

ct's velocity is v = - (2.0 m/s) i hat + (4.0 m/s) k. What is the instantaneous rate at which the force does work on the object?

1 answer:

Ksenya-84 [330]3 years ago

7 0

Answer:

Power, P = 22 W

Explanation:

It is given that,

Force acting on the object, $F=5i-2j+8k$

Velocity of the object, $v=-2i+4k$

To Find,

The rate at which the force does work on the object

Solve,

The rate at which the force does work on the object is called its power. Its formula is given by :

$P=\dfrac{W}{t}$

$P=\dfrac{F.d}{t}$

$P=F\times v$

$P=(5i-2j+8k)\times (-2i+4k)$

$P=-10+0+32=22\ W$

So, the force work on the object at the rate of 22 watts

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The amount of energy needed is 2093 J

Explanation:

The amount of energy needed to increase the temperature of a substance by $\Delta T$ is given by the equation

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where

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For the water in this problem, we have

m = 50.0 g = 0.050 kg

$C=4186 J/g^{\circ}C$ (specific heat capacity of water)

$\Delta T=10.0^{\circ}C$

Therefore, the amount of energy needed is

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3 years ago

A red train travelling at 72 km/h and a green train travelling at 144 km/h are headed toward each

abruzzese [7]

Answer:

Collision will occur.

Speed of red train when they collide = 0 m/s.

Speed of green train when they collide = 10 m/s.

Explanation:

Speed of red train = 72 km/h = 20 m/s

Speed of green train = 144 km/h = 40 m/s.

Deceleration of trains = 1 m/s²

For red train:-

Equation of motion v = u + at

u = 20 m/s

v = 0 m/s

a = -1 m/s²

Substituting

0 = 20 - 1 x t

t = 20 s.

Equation of motion s = ut + 0.5at²

u = 20 m/s

t = 20 s

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Substituting

s = 20 x 20 - 0.5 x 1 x 20² = 200 m

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For green train:-

Equation of motion v = u + at

u = 40 m/s

v = 0 m/s

a = -1 m/s²

Substituting

0 = 40 - 1 x t

t = 40 s.

Equation of motion s = ut + 0.5at²

u = 40 m/s

t = 40 s

a = -1 m/s²

Substituting

s = 40 x 40 - 0.5 x 1 x 40² = 800 m

So green train travel 800 m before coming to stop.

Total distance traveled = 800 + 200 = 1000 m>950 m.

So both trains collide.

Distance traveled by green train when red train stops(t=20s)

Equation of motion s = ut + 0.5at²

u = 40 m/s

t = 20 s

a = -1 m/s²

Substituting

s = 40 x 20 - 0.5 x 1 x 20² = 600 m

Total distance after 20 s = 600 + 200 = 800 m< 950m . So they collide after red train stops.

Speed of red train when they collide = 0 m/s.

Distance traveled by green train when they collide = 950 - 200 = 750 m

Equation of motion v² = u² + 2as

u = 40 m/s

s= 750 m

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Substituting

v² = 40² - 2 x 1 x 750 = 100

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kondaur [170]

Answer:

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x=8.4 m

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Given that

$v=A+Bt^{-1}$

$v=2+0.25t^{-1}$

To find acceleration :

we know that

$a=\dfrac{dv}{dt}$

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$a=-0.5t^{-2}$

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$v=\dfrac{dx}{dt}$

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Position at t= 5 s:

$\int_{0}^{x}dx=\int_{1}^{5} \left(2+0.25\dfrac{1}{t}\right)dt$

$x=\left [2t+0.25\ lnt \right ]_{1}^{5}$

x=8+0.25 ln5

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