Aspring required a force of 5.0 n to compress it 0.1 m. how much work is required to stretch the spring 0.4 m

20N

Explanation:

The force (Hooke's Law) is proportional to the deformation. To extend the spring 4 times longer, you will need 4 times the force. In total, 20 N

4Joules

F=-kx

E=1/2kx^2

5N=-k(.01m)

k=50N/m

E=1/2kx^2

E=1/2(50N/m)(0.4m)^2

E=4Joules

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west