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scZoUnD [109]
3 years ago
15

Describe the circumstances for which the output work would equal the input work in a machine

Physics
1 answer:
tiny-mole [99]3 years ago
3 0
That's only possible if there is absolutely zero friction in the machine.

In the real world, we can come close, with lubricants (oil, grease) and
streamlining, but we can never build anything with totally zero loss of
energy inside.
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1. What net force is required to accelerate a car at a rate of 2 m/s2 if the car has a mass of 3,000 kg?
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Answer:

Net force required to accelerate the car is 6000 N

Explanation:

Force is calculated by the equation, F = Mass × Acceleration

This is based on Newton's Second Law of Motion which states that the force acting on an object is its mass times the acceleration of the object.

Here, mass = 3000 kg and acceleration = 2 m/s²

⇒ Force = Mass × Acceleration

             = 3000 × 2 = 6000 N

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⇒ M = 3000 kg

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. A block of mass 4.0 kg on a spring has displacement as a function of time given by, x (t) = (1.0 cm) cos [(2.0 rad/s) t + 0.25
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Answer and Explanation:

1. Evaluate the function x(t) at t=0.5

x(t)=1cos(2t+0.25)\\x(0.5)=cos(2*0.5+0.25)=cos(1+0.25)=cos(1.25)=0.3153223624\approx0.31cm

2. The period of motion T can be calculated as:

T=\frac{2\pi}{\omega}

Where:

\omega=2rad/s

So:

T=\frac{2\pi}{2}=\pi\approx3.14s

3. The angular frequency can be expressed as:

\omega=\sqrt{\frac{k}{m} }

Solving for k:

k=(\omega)^2*m=(2)^2*4=4*4=16\frac{N}{m}

4. Find the derivate of x(t):

\frac{dx}{dt} =v(t)=-2sin(2t+0.25)

Now, the sine function reach its maximum value at π/2 so:

2t+025=\frac{\pi}{2}

Solving for t:

t=\frac{\frac{\pi}{2} -0.25}{2} =0.6603981634s

Evaluating v(t) for 0.6603981634:

v(0.6603981634)=-2sin(2*0.6603981634+0.25)=-2sin(\frac{\pi}{2} )=-2*1=2

So the maximum speed of the block is:

v(0.6603981634)=2cm/s=0.02m/s

In the negative direction of x-axis

5. The force is given by:

F=kx

The cosine function reach its maximum value at 2π so:

2t+0.25=2\pi

Solving for t:

t=\frac{2\pi-0.25}{2} =3.016592654s

Evaluating x(t) for 3.016592654:

x(3.016592654)=cos(2*3.016592654+0.25)=cos(2\pi)=1cm=0.01m

Therefore the the maximum force on the block is:

F=16*0.01=0.16N

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