String the·o·ry
noun
a cosmological theory based on the existence of cosmic strings.
Answer:
the magnitude of the work done by the two blocks is the same.
Explanation:
The work done by block a on block b is given by:
![W_a = F_a d](https://tex.z-dn.net/?f=W_a%20%3D%20F_a%20d)
where Fa is the force exerted by block a on block b, and d is the distance they cover.
The work done by block b on block a is given by:
![W_b = F_b d](https://tex.z-dn.net/?f=W_b%20%3D%20F_b%20d)
where Fb is the force exerted by block b on block a, and d is still the distance they cover.
For Newton's third law, the force exerted by block a on block b is equal to the force exerted by block b on block a, therefore
![F_a = F_b](https://tex.z-dn.net/?f=F_a%20%3D%20F_b)
and so
![W_a=W_b](https://tex.z-dn.net/?f=W_a%3DW_b)
Answer:
5.4 J.
Explanation:
Given,
mass of the object, m = 2 Kg
initial speed, u = 5 m/s
mass of another object,m' = 3 kg
initial speed of another orbit,u' = 2 m/s
KE lost after collusion = ?
Final velocity of the system
Using conservation of momentum
m u + m'u' = (m + m') V
2 x 5 + 3 x 2 = ( 2 + 3 )V
16 = 5 V
V = 3.2 m/s
Initial KE = ![\dfrac{1}{2}mu^2 + \dfrac{1}{2}m'u'^2](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7Dmu%5E2%20%2B%20%5Cdfrac%7B1%7D%7B2%7Dm%27u%27%5E2)
= ![\dfrac{1}{2}\times 2\times 5^2 + \dfrac{1}{2}\times 3 \times 2^2](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%202%5Ctimes%205%5E2%20%2B%20%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%203%20%5Ctimes%202%5E2)
= 31 J
Final KE = ![\dfrac{1}{2} (m+m')V^2 = \dfrac{1}{2}\times 5 \times 3.2^2 = 25.6 J](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%20%28m%2Bm%27%29V%5E2%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%205%20%5Ctimes%203.2%5E2%20%3D%2025.6%20J)
Loss in KE = 31 J - 25.6 J = 5.4 J.
Answer:
The compression in the spring is 5.88 meters.
Explanation:
Given that,
Mass of the car, m = 39000 kg
Height of the car, h = 19 m
Spring constant of the spring, ![k=4.2\times 10^5\ N/m](https://tex.z-dn.net/?f=k%3D4.2%5Ctimes%2010%5E5%5C%20N%2Fm)
We need to find the compression in the spring in stopping the ore car. It can be done by balancing loss in gravitational potential energy and the increase in elastic energy. So,
![mgh=\dfrac{1}{2}kx^2](https://tex.z-dn.net/?f=mgh%3D%5Cdfrac%7B1%7D%7B2%7Dkx%5E2)
x is the compression in spring
![x=\sqrt{\dfrac{2mgh}{k}} \\\\x=\sqrt{\dfrac{2\times 39000\times 19\times 9.8}{4.2\times 10^5}} \\\\x=5.88\ m](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B%5Cdfrac%7B2mgh%7D%7Bk%7D%7D%20%5C%5C%5C%5Cx%3D%5Csqrt%7B%5Cdfrac%7B2%5Ctimes%2039000%5Ctimes%2019%5Ctimes%209.8%7D%7B4.2%5Ctimes%2010%5E5%7D%7D%20%5C%5C%5C%5Cx%3D5.88%5C%20m)
So, the compression in the spring is 5.88 meters.
Only the tiny command module survives to return to Earth. The Saturn V rocket's first stage carries 203,400 gallons (770,000 liters) of kerosene fuel and 318,000 gallons (1.2 million liters) of liquid oxygen needed for combustion