Answer:
6 m/s
Explanation:
Given that :
mass of the block m = 200.0 g = 200 × 10⁻³ kg
the horizontal spring constant k = 4500.0 N/m
position of the block (distance x) = 4.00 cm = 0.04 m
To determine the speed the block will be traveling when it leaves the spring; we applying the work done on the spring as it is stretched (or compressed) with the kinetic energy.
i.e ![\frac{1}{2} kx^2 = \frac{1}{2} mv^2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20kx%5E2%20%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E2)
![kx^2 = mv^2](https://tex.z-dn.net/?f=kx%5E2%20%3D%20mv%5E2)
![4500* 0.04^2 = 200*10^{-3} *v^2](https://tex.z-dn.net/?f=4500%2A%200.04%5E2%20%3D%20200%2A10%5E%7B-3%7D%20%2Av%5E2)
![7.2 =200*10^{-3}*v^{2}](https://tex.z-dn.net/?f=7.2%20%3D200%2A10%5E%7B-3%7D%2Av%5E%7B2%7D)
![v^{2} =\frac{7.2}{200*10^{-3}}](https://tex.z-dn.net/?f=v%5E%7B2%7D%20%20%20%3D%5Cfrac%7B7.2%7D%7B200%2A10%5E%7B-3%7D%7D)
![v =\sqrt{\frac{7.2}{200*10^{-3}}}](https://tex.z-dn.net/?f=v%20%20%20%3D%5Csqrt%7B%5Cfrac%7B7.2%7D%7B200%2A10%5E%7B-3%7D%7D%7D)
v = 6 m/s
Hence,the speed the block will be traveling when it leaves the spring is 6 m/s
Answer:
(a) Initial volume will be 7.62 L
(b) Final temperature will be 303.85 K
Explanation:
We have given one mole of ideal gas done 3000 J
So work done W = 3000 J
Let initial volume is
and initial pressure
( As pressure is constant )
Final volume
= 0.025 ![m^3](https://tex.z-dn.net/?f=m%5E3)
Number of moles n = 1
(B) From ideal gas of equation we know that ![PV=nRT](https://tex.z-dn.net/?f=PV%3DnRT)
So ![1.01\times 10^5\times0.025=1\times 8.31\times T](https://tex.z-dn.net/?f=1.01%5Ctimes%2010%5E5%5Ctimes0.025%3D1%5Ctimes%208.31%5Ctimes%20T)
T = 303.85 Kelvin
(B) For isothermal process work done is equal to
![W=nRTln\frac{V_2}{V_1}](https://tex.z-dn.net/?f=W%3DnRTln%5Cfrac%7BV_2%7D%7BV_1%7D)
![3000=1\times 8.314\times 303.85\times ln\frac{0.025}{V_1}](https://tex.z-dn.net/?f=3000%3D1%5Ctimes%208.314%5Ctimes%20303.85%5Ctimes%20ln%5Cfrac%7B0.025%7D%7BV_1%7D)
![ln\frac{0.025}{V_1}=1.1881](https://tex.z-dn.net/?f=ln%5Cfrac%7B0.025%7D%7BV_1%7D%3D1.1881)
![\frac{0.025}{V_1}=3.2808](https://tex.z-dn.net/?f=%5Cfrac%7B0.025%7D%7BV_1%7D%3D3.2808)
![V_2=0.00846m^3=7.62L](https://tex.z-dn.net/?f=V_2%3D0.00846m%5E3%3D7.62L)
So initial volume will be 7.62 L
The answer for the following question is explained below.
- <u><em>Therefore the work done is 130 kilo Joules.</em></u>
Explanation:
Work:
A force causing the movement or displacement of an object.
Given:
mass of the person (m) = 65 kg
height of the cliff (h) = 2000 m
To calculate:
work done (W)
We know;
According to the formula:
<u>W = m × g × h</u>
Where;
m represents mass of the person
g represents the acceleration due to gravity
where the value of g is;
<u> g = 10 m/ s²</u>
h represents the height of the cliff
From the above formula;
W = 65 × 10 × 2000
W = 130,000 J
W = 130 Kilo Joules
<u><em>Therefore the work done is 130 kilo Joules.</em></u>
Answer:
![Q = 4.40 \times 10^5 Cal](https://tex.z-dn.net/?f=Q%20%3D%204.40%20%5Ctimes%2010%5E5%20Cal)
Explanation:
Here we know that initial temperature of ice is given as
![T = 0^o C](https://tex.z-dn.net/?f=T%20%3D%200%5Eo%20C)
now the latent heat of ice is given as
![L = 80 Cal/g](https://tex.z-dn.net/?f=L%20%3D%2080%20Cal%2Fg)
now we also know that the mass of ice is
![m = 5.50 kg](https://tex.z-dn.net/?f=m%20%3D%205.50%20kg)
so here we know that heat required to change the phase of the ice is given as
![Q = mL](https://tex.z-dn.net/?f=Q%20%3D%20mL)
![Q = (5.50 \times 10^3)(80)](https://tex.z-dn.net/?f=Q%20%3D%20%285.50%20%5Ctimes%2010%5E3%29%2880%29)
![Q = 4.40 \times 10^5 Cal](https://tex.z-dn.net/?f=Q%20%3D%204.40%20%5Ctimes%2010%5E5%20Cal)