Answer:
The maximum mass that can fall on the mattress without exceeding the maximum compression distance is 16.6 kg
Explanation:
Hi there!
Due to conservation of energy, the potential energy (PE) of the mass at a height of 3.32 m will be transformed into elastic potential energy (EPE) when it falls on the mattress:
PE = EPE
m · g · h = 1/2 k · x²
Where:
m = mass.
g = acceleration due to gravity.
h = height.
k = spring constant.
x = compression distance
The maximum compression distance is 0.1289 m, then, the maximum elastic potential energy will be the following:
EPE =1/2 k · x²
EPE = 1/2 · 65144 N/m · (0.1289 m)² = 541.2 J
Then, using the equation of gravitational potential energy:
PE = m · g · h = 541.2 J
m = 541.2 J/ g · h
m = 541.2 kg · m²/s² / (9.8 m/s² · 3.32 m)
m = 16.6 kg
The maximum mass that can fall on the mattress without exceeding the maximum compression distance is 16.6 kg.
For every force in nature that there is an equal and opposite reaction
Answer:
a) 45 s , b) vₐ = 90 m / s, v_b = 162 m / s, c) x_b = 3.328 10⁴ m
Explanation:
We can solve this exercise using the kinematic relations
Vehicle A
xₐ = v₀ₐ t + ½ aₐ t²
vehicle B
starts two seconds later
x_b = v_{ob} (t-2) + ½ a_b (t-2) ²
as cars start from rest their initial velocities are zero
at the point where they meet, the position must be the same for both vehicles
xa = 0 + ½ aₐ t²
xb = 0 + ½ a_b (t-2) ²
½ aₐ t² = ½ a_b (t-2) ²
t = (t-2)
t (1 - \sqrt{ \frac{a_a}{a_b} }) = 2
t (1 - ⅔, ) = 2
t = 2 / 0.4444
t = 45 s
b)
the speed of each car
vₐ = voa + aa t
vₐ = 0 + 2 45
vₐ = 90 m / s
v_b = 3.6 45
v_b = 162 m / s
c) xb = 0 + ½ ab (t-2) ²
x_b = ½ 3.6 (45-2) ²
x_b = 3.328 10⁴ m
Well, they both start chain reactions and they are also both used in certain nuclear bombs. Also they are both natural processes that occur in the sun, where hydrogen fuses with helium atoms and then they split by the process of fission.