Chứng tỏ rằng các trường véc tơ sau là trường thế và tính Z C
F · dR theo
đường cong trơn từng khúc nào đó nối A(10, −1), B(0, −1, 1).
a. F(x, y, z) = hsin z, −z sin yx cos z + cos yi
b. F(x, y, z) = h3x
2
y
2
z, 2x
3
yz, x3
y
2 − e
−z
i

You have been hired to design a spring-launched roller coaster thatwill carry two passengers per car. the car goes up a 10-m highhill, then descends 15m to the track's lowest point. you'vedetermined that the spring can be compressed a maximum o 2.0m andthat a loaded car will have a maximum mass of 400kg. for safetyreasons, the spring constant should be 10% larger than the minimumneeded for the car to just make it over the top. a) what spring constant (k) should you specify ? b) what is the maximum speed of a 350 kg car if the spring iscompressed the full amount.