As we know that force F makes an angle of 60 degree with X axis
so the X component is given as

now we have


Similarly we know that force F makes an angle of 45 degree with Y axis
so the X component is given as

now we have


Now for the component along z axis we know that

now plug in all components





there were different outcomes each time.
Answer: D
Height of marble from ground
Explanation:
From the formula of kinetic energy and potential energy,
K.E = 1/2mv^2
While
P.E = mgh
From all the parameters given from the question. You can see that mass is constant, acceleration due to gravity is also constant.
Independent variable must be a value that can varies.
Since Jack rolled a marble down a ramp and recorded the potential energy and kinetic energy of the marble at different positions on the ramp to see the effects on both energies.
This different position must be the height which will produce an effect on the potential and kinetic energy of the marble.
Independent variable always provides an effect for dependent variable. Which are kinetic energy and potential energy in this case.
Height of marble from ground is the right answer.
Answer
given,
D = 50 mm = 0.05 m
d = 10 mm = 0.01 m
Force to compress the spring




F = 3160 N
stress correction factor from stress correction curve is equal to 1.1
now, calculation of corrected stress


= 442.6 Mpa
The tensile strength of the steel material of ASTM A229 is equal to 1300 Mpa
now,



since corrected stress is less than the
hence, spring will return to its original shape.