Hi guys, could anyone please help me with this points? Please 8) It requires 178

Question

Hi guys, could anyone please help me with this points? Please

8) It requires 178 J of work to stretch an ideal very light spring from a length of 1.4 m to a length of 2.9 m. What is the value of the spring constant of this spring?
A) 158 N/m B) 79 N/m C) 107 N/m D) 55 N/m
9) A force F = bx3 acts in the x direction, where the value of b is 3.7 N/m3. How much work is done by this force in moving an object from x = 0.00 m to x =3.1 m?
A) 102 J B) 85 J C) 115 J D) 18 J

11) A 1000.0 kg car is moving at 15 km/h. If a 2000.0 kg truck has 72 times the kinetic energy of the car, how fast is the truck moving?

A) 127 km/h B) 72 km/h C) 108 km/h D) 90 km/h

12) How much energy is needed to change the speed of a 1600 kg sport utility vehicle from 15.0 m/s to 40.0 m/s?
A) 40.0 kJ B) 10.0 kJ C) 20.0 kJ D) 0.960 MJ E) 1.10 MJ
13) The coefficient of the restitution of an object is defined as the ratio of its outgoing to incoming speed when the object collides with a rigid surface. For an object with a coefficient of 0.84, what fraction of the object's kinetic energy is lost during a single collision?
A) 35% B) 12% C) 71% D) 29%

I need step by step, I will appreciate a lot your help!

Explanation / Answer

As we know that

(8)

work, or energy.
equation wise
178 J = ½kx²
178 = ½k(2.9 - 1.4)²
178 = ½k(1.5)²
356 = k(2.25)
k = 158.222222 N/m

(9)As we know that

Work done
= Fd
= [b*3*(3.1-0)]J
= (3.7*3*3.1)J
= 34.41J

(11)As we know that

K1 = 1/2m1v1^2 = 1/2(1000)(15)^2 = 112500

K2 = 1/2m2v2^2 = 1/2(2000)v2^2 = 72*112500

v2^2 = 72*112.5
v2 = sqrt(8100) = 90 km/h

(12)

Minimum energy needed = 0.5*1600*[40^2 - 15^2] = 1100000 J = 1.10 MJ

1.10 MJ" is correct

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