Answer is miles sir your welcome it was simple
Answer:
book speed is 3.99 m/s
Explanation:
given data
mass m = 490 g = 0.490 kg
compressing x = 7.10 cm = 0.0710 m
spring constant k = 1550 N/m
to find out
book speed
solution
we know energy is conserve so
we can say
loss in spring energy is equal to gain in kinetic energy
so
..................1
put here value
v = 3.99 m/s
so book speed is 3.99 m/s
(a) The plastic rod has a length of L=1.3m. If we divide by 8, we get the length of each piece:
![L/8=1.3m/8=0.1625 m](https://tex.z-dn.net/?f=L%2F8%3D1.3m%2F8%3D0.1625%20m)
(b) The center of the rod is located at x=0. This means we have 4 pieces of the rod on the negative side of x-axis, and 4 pieces on the positive side. So, starting from x=0 and going towards positive direction, we have: piece 5, piece 6, piece 7 and piece 8. Each piece is 0.1625 m long. Therefore, the center of piece 5 is at 0.1625m/2=0.0812 m. And the center of piece 6 will be shifted by 0.1625m with respect to this:
![c_6 = 0.0812m+0.1625m=0.2437 m](https://tex.z-dn.net/?f=c_6%20%3D%200.0812m%2B0.1625m%3D0.2437%20m)
(c) The total charge is
![Q=-3 \cdot 10^{-8}C](https://tex.z-dn.net/?f=Q%3D-3%20%5Ccdot%2010%5E%7B-8%7DC)
. To get the charge on each piece, we should divide this value by 8, the number of pieces:
![Q/8=-3\cdot 10^{-8}C/8=-3.75\cdot 10^{-9}C](https://tex.z-dn.net/?f=Q%2F8%3D-3%5Ccdot%2010%5E%7B-8%7DC%2F8%3D-3.75%5Ccdot%2010%5E%7B-9%7DC)
(d) We have to calculate the electric field at x=0.7 generated by piece 6. The charge on piece 6 is the value calculated at point (c):
![q= -3.75\cdot 10^{-9}C](https://tex.z-dn.net/?f=q%3D%20-3.75%5Ccdot%2010%5E%7B-9%7DC)
If we approximate piece 6 as a single charge, the electric field is given by
![E=k_e \frac{q}{d^2}](https://tex.z-dn.net/?f=E%3Dk_e%20%20%5Cfrac%7Bq%7D%7Bd%5E2%7D%20)
where
![k_e=8.99\cdot 10^9Nm^2C^{-2}](https://tex.z-dn.net/?f=k_e%3D8.99%5Ccdot%2010%5E9Nm%5E2C%5E%7B-2%7D)
and d is the distance between the charge (center of piece 6, located at 0.2437m) and point a (located at x=0.7m). Therefore we have
![E= 8.99\cdot 10^9 Nm^2C^{-2} \frac{-3.75\cdot 10^9 C}{(0.2437m-0.7m)^2} =-161.9 V/m](https://tex.z-dn.net/?f=E%3D%208.99%5Ccdot%2010%5E9%20Nm%5E2C%5E%7B-2%7D%20%5Cfrac%7B-3.75%5Ccdot%2010%5E9%20C%7D%7B%280.2437m-0.7m%29%5E2%7D%20%3D-161.9%20V%2Fm)
poiting towards the center of piece 6, since the charge is negative.
(e) missing details on this question.