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prisoha [69]
3 years ago
10

A machine uses 1000 J of electric energy to raise a heavy mass, increasing its potential energy by 300 J. What is the efficiency

of this process?
Physics
2 answers:
-Dominant- [34]3 years ago
7 0

Answer:

Efficiency of this process is 30 %.

Explanation:

It is given that,

Electric energy used by the machine, W_{in}=1000\ J

The potential energy of the machine is increased, W_{out}=300\ J  

The efficiency of this machine is given by :

\eta=\dfrac{W_{out}}{W_{in}}\times 100

\eta=\dfrac{300}{1000}\times 100    

eta=30\%

So, the efficiency of this process is 30 %. Hence, this is the required solution.                

Slav-nsk [51]3 years ago
6 0

Answer

30 %

Explanation:

Here machine uses 1000 J means input of machine is 1000 J

And its increases the potential energy by 300 J so output of the machine is 300 J

The efficiency of any system is defined as the ratio of output and input

So efficiency will be \eta =\frac{output}{input}=\frac{300}{1000}=0.3 = 30% so the efficiency of the machine will be 30%

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c) V_i =\sqrt{2 \frac{W_g + W_{spring}}{0.21 kg}}}=\sqrt{2 \frac{(1-0.2058)}{0.21 kg}}}=2.75m/s

d)  d_1 =0.183m or 18.3 cm

Explanation:

For this case we have the following system with the forces on the figure attached.

We know that the spring compresses a total distance of x=0.10 m

Part a

The gravitational force is defined as mg so on this case the work donde by the gravity is:

W_{g}=mdx = 0.21 kg *9.8\frac{m}{s^2} 0.10m=0.2058 J

Part b

For this case first we can convert the spring constant to N/m like this:

2 \frac{N}{cm} \frac{100cm}{1m}=200 \frac{N}{m}

And the work donde by the spring on this case is given by:

W_{spring}= -\frac{1}{2} Kx^2 =-\frac{1}{2} 200 N/m (0.1m)^2=-1 J

Part c

We can assume that the initial velocity for the block is Vi and is at rest from the end of the movement. If we use balance of energy we got:

W_{g} +W_{spring} = K_{f} -K_{i}=0- \frac{1}{2} m v^2_i

And if we solve for the initial velocity we got:

V_i =\sqrt{2 \frac{W_g + W_{spring}}{0.21 kg}}}=\sqrt{2 \frac{(1-0.2058)}{0.21 kg}}}=2.75m/s

Part d

Let d1 represent the new maximum distance, in order to find it we know that :

-1/2mV^2_i = W_g + W_{spring}

And replacing we got:

-1/2mV^2_i =mg d_1 -1/2 k d^2_1

And we can put the terms like this:

\frac{1}{2} k d^2_1 -mg d_1 -1/2 m V^2_i =0

If we multiply all the equation by 2 we got:

k d^2_1 -2 mg d_1 -m V^2_i =0

Now we can replace the values and we got:

200N/m d^2_1 -0.21kg(9.8m/s^2)d_1 -0.21 kg(5.50 m/s)^2) =0

200 d^2_1 -2.058 d_1 -6.3525=0

And solving the quadratic equation we got that the solution for d_1 =0.183m or 18.3 cm because the negative solution not make sense.

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Explanation:

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