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Hi pupil Here's Your answer :::
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Student's justification is not correct. Two equal and opposite force cancel each other if the act on the same body. According to the third law of motion action and reaction forces are equal and opposite but they both act on different bodies. Hence, they cannot cancel each other.
When we push a message track, then the applied force on the truck is not sufficient to overcome the force of friction between the tyres of truck and ground, hence, truck does not move.
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Hope this helps .
Answer:
1000 kgm²/s, 400 J
1000 kgm²/s, 1000 J
600 J
Explanation:
m = Mass of astronauts = 100 kg
d = Diameter
r = Radius = ![\frac{d}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7B2%7D)
v = Velocity of astronauts = 2 m/s
Angular momentum of the system is given by
![L=mvr+mvr\\\Rightarrow L=2mvr\\\Rightarrow L=2\times 100\times 2\times 2.5\\\Rightarrow L=1000\ kgm^2/s](https://tex.z-dn.net/?f=L%3Dmvr%2Bmvr%5C%5C%5CRightarrow%20L%3D2mvr%5C%5C%5CRightarrow%20L%3D2%5Ctimes%20100%5Ctimes%202%5Ctimes%202.5%5C%5C%5CRightarrow%20L%3D1000%5C%20kgm%5E2%2Fs)
The angular momentum of the system is 1000 kgm²/s
Rotational energy is given by
![K=I\omega^2\\\Rightarrow K=\frac{1}{2}(mr^2)\left(\frac{v}{r}\right)^2\\\Rightarrow K=mv^2\\\Rightarrow K=100\times 2^2\\\Rightarrow K=400\ J](https://tex.z-dn.net/?f=K%3DI%5Comega%5E2%5C%5C%5CRightarrow%20K%3D%5Cfrac%7B1%7D%7B2%7D%28mr%5E2%29%5Cleft%28%5Cfrac%7Bv%7D%7Br%7D%5Cright%29%5E2%5C%5C%5CRightarrow%20K%3Dmv%5E2%5C%5C%5CRightarrow%20K%3D100%5Ctimes%202%5E2%5C%5C%5CRightarrow%20K%3D400%5C%20J)
The rotational energy of the system is 400 J
There no external toque present so the initial and final angular momentum will be equal to the initial angular momentum 1000 kgm²/s
![L_i=L_f\\\Rightarrow 2mv_ir_i=2mv_fr_f\\\Rightarrow v_f=\frac{v_ir_i}{r_f}\\\Rightarrow v_f=\frac{2\times 2.5}{0.5}\\\Rightarrow v_f=10\ m/s](https://tex.z-dn.net/?f=L_i%3DL_f%5C%5C%5CRightarrow%202mv_ir_i%3D2mv_fr_f%5C%5C%5CRightarrow%20v_f%3D%5Cfrac%7Bv_ir_i%7D%7Br_f%7D%5C%5C%5CRightarrow%20v_f%3D%5Cfrac%7B2%5Ctimes%202.5%7D%7B0.5%7D%5C%5C%5CRightarrow%20v_f%3D10%5C%20m%2Fs)
Energy
![E_2=mv_f^2\\\Rightarrow E_2=100\times 10\\\Rightarrow E_2=1000\ J](https://tex.z-dn.net/?f=E_2%3Dmv_f%5E2%5C%5C%5CRightarrow%20E_2%3D100%5Ctimes%2010%5C%5C%5CRightarrow%20E_2%3D1000%5C%20J)
The new energy will be 1000 J
Work done will be the change in the kinetic energy
![W=E_2-E\\\Rightarrow W=1000-400\\\Rightarrow W=600\ J](https://tex.z-dn.net/?f=W%3DE_2-E%5C%5C%5CRightarrow%20W%3D1000-400%5C%5C%5CRightarrow%20W%3D600%5C%20J)
The work done is 600 J
The forces of gravity between two objects are smaller when the objects are farther apart.