Answer:
(a). The speed of the ball after collision is 2.01 m/s.
(b). The speed of the block after collision 1.11 m/s.
Explanation:
Suppose, A steel ball of mass 0.500 kg is fastened to a cord that is 50.0 cm long and fixed at the far end. The ball is then released when the cord is horizontal.
Given that,
Mass of steel block = 2.30 kg
Mass of ball = 0.500 kg
Length of cord = 50.0 cm
We need to calculate the initial speed of the ball
Using conservation of energy
![\dfrac{1}{2}mv^2=mgl](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7Dmv%5E2%3Dmgl)
![v=\sqrt{2gl}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B2gl%7D)
Put the value into the formula
![u=\sqrt{2\times9.8\times50.0\times10^{-2}}](https://tex.z-dn.net/?f=u%3D%5Csqrt%7B2%5Ctimes9.8%5Ctimes50.0%5Ctimes10%5E%7B-2%7D%7D)
![u=3.13\ m/s](https://tex.z-dn.net/?f=u%3D3.13%5C%20m%2Fs)
The initial speed of the ball ![u_{1}=3.13\ m/s](https://tex.z-dn.net/?f=u_%7B1%7D%3D3.13%5C%20m%2Fs)
The initial speed of the block ![u_{2}=0](https://tex.z-dn.net/?f=u_%7B2%7D%3D0)
(a). We need to calculate the speed of the ball after collision
Using formula of collision
![v_{1}=(\dfrac{m_{1}-m_{2}}{m_{1}+m_{2}})u_{1}+(\dfrac{2m_{2}}{m_{1}+m_{2}})u_{2}](https://tex.z-dn.net/?f=v_%7B1%7D%3D%28%5Cdfrac%7Bm_%7B1%7D-m_%7B2%7D%7D%7Bm_%7B1%7D%2Bm_%7B2%7D%7D%29u_%7B1%7D%2B%28%5Cdfrac%7B2m_%7B2%7D%7D%7Bm_%7B1%7D%2Bm_%7B2%7D%7D%29u_%7B2%7D)
Put the value into the formula
![v_{1}=(\dfrac{0.5-2.30}{0.5+2.30})\times3.13](https://tex.z-dn.net/?f=v_%7B1%7D%3D%28%5Cdfrac%7B0.5-2.30%7D%7B0.5%2B2.30%7D%29%5Ctimes3.13)
![v_{1}=-2.01\ m/s](https://tex.z-dn.net/?f=v_%7B1%7D%3D-2.01%5C%20m%2Fs)
Negative sign shows the opposite direction of initial direction.
(b). We need to calculate the speed of the block after collision
Using formula of collision
![v_{2}=(\dfrac{2m_{1}}{m_{1}+m_{2}})u_{1}+(\dfrac{m_{1}-m_{2}}{m_{1}+m_{2}})u_{2}](https://tex.z-dn.net/?f=v_%7B2%7D%3D%28%5Cdfrac%7B2m_%7B1%7D%7D%7Bm_%7B1%7D%2Bm_%7B2%7D%7D%29u_%7B1%7D%2B%28%5Cdfrac%7Bm_%7B1%7D-m_%7B2%7D%7D%7Bm_%7B1%7D%2Bm_%7B2%7D%7D%29u_%7B2%7D)
Put the value into the formula
![v_{2}=(\dfrac{2\times0.5}{0.5+2.30})\times3.13+0](https://tex.z-dn.net/?f=v_%7B2%7D%3D%28%5Cdfrac%7B2%5Ctimes0.5%7D%7B0.5%2B2.30%7D%29%5Ctimes3.13%2B0)
![v_{2}=1.11\ m/s](https://tex.z-dn.net/?f=v_%7B2%7D%3D1.11%5C%20m%2Fs)
Hence, (a). The speed of the ball after collision is 2.01 m/s.
(b). The speed of the block after collision 1.11 m/s.