Answer:
0.6983 m/s
Explanation:
k = spring constant of the spring = 0.4 N/m
L₀ = Initial length = 11 cm = 0.11 m
L = Final length = 27 cm = 0.27 m
x = stretch in the spring = L - L₀ = 0.27 - 0.11 = 0.16 m
m = mass of the mass attached = 0.021 kg
v = speed of the mass
Using conservation of energy
Kinetic energy of mass = Spring potential energy
(0.5) m v² = (0.5) k x²
m v² = k x²
(0.021) v² = (0.4) (0.16)²
v = 0.6983 m/s
<h2>Answer</h2>
option D)
2.4 seconds
<h2>Explanation</h2>
Given in the question,
mass of car = 1200kg
speed of car = 19m/s
Force due to direction of travel
F = ma
= 12000(a)
Force to due frictional force in reverse direction
-F = mg(friction coefficient)
= -12000(9.81)(0.8)
<h2>
-mg(friction coefficient) = ma </h2>
(cancelling mass from both side of equation)
g(0.8) = a
(9.81)(0.8) = a
a = 7.848 m/s²
<h2>Use Newton Law of motion</h2><h3>vf - vo = a • t</h3>
where vf = final velocity
vo = initial velocity
a = acceleration
t = time
0 - 19 = 7.8(t)
t = 19/7.8
= 2.436 s
≈ 2.4s
The formula for the rotational kinetic energy is

where I is the moment of inertia. This is just mass times the square of the perpendicular distance to the axis of rotation. In other words, the radius of the propeller or this is equivalent to the length of the rod. ω is the angular velocity. We determine I and ω first.

ω = 573 rev/min * (2π rad/rev) * (1 min/60 s) = 60 rad/s
Then,
