Answer:
Explanation:
Using Boyles law
Boyle's law states that, the volume of a given gas is inversely proportional to it's pressure, provided that temperature is constant
V ∝ 1 / P
V = k / P
VP = k
Then,
V_1 • P_1 = V_2 • P_2
So, if we want an increase in pressure that will decrease volume of mercury by 0.001%
Then, let initial volume be V_1 = V
New volume is V_2 = 0.001% of V
V_2 = 0.00001•V
Let initial pressure be P_1 = P
So,
Using the equation above
V_1•P_1 = V_2•P_2
V × P = 0.00001•V × P_2
Make P_2 subject of formula by dividing be 0.00001•V
P_2 = V × P / 0.00001 × V
Then,
P_2 = 100000 P
So, the new pressure has to be 10^5 times of the old pressure
Now, using bulk modulus
Bulk modulus of mercury=2.8x10¹⁰N/m²
bulk modulus = P/(-∆V/V)
-∆V = 0.001% of V
-∆V = 0.00001•V
-∆V = 10^-5•V
-∆V/V = 10^-5
Them,
Bulk modulus = P / (-∆V/V)
2.8 × 10^10 = P / 10^-5
P = 2.8 × 10^10 × 10^-5
P = 2.8 × 10^5 N/m²
Gravity acts to accelerate the ball downward, and air resistance acts in a way to slow the ball along it's instantaneous velocity (no matter which way it's moving air applies a force in the opposite direction)
Answer:
θ = 12.95º
Explanation:
For this exercise it is best to separate the process into two parts, one where they collide and another where the system moves altar the maximum height
Let's start by finding the speed of the bar plus clay ball system, using amount of momentum
The mass of the bar (M = 0.080 kg) and the mass of the clay ball (m = 0.015 kg) with speed (v₀ = 2.0 m / s)
Initial before the crash
p₀ = m v₀
Final after the crash before starting the movement
= (m + M) v
p₀ =
m v₀ = (m + M) v
v = v₀ m / (m + M)
v = 2.0 0.015 / (0.015 +0.080)
v = 0.316 m / s
With this speed the clay plus bar system comes out, let's use the concept of conservation of mechanical energy
Lower
Em₀ = K = ½ (m + M) v²
Higher
= U = (m + M) g y
Em₀ =
½ (m + M) v² = (m + M) g y
y = ½ v² / g
y = ½ 0.316² / 9.8
y = 0.00509 m
Let's look for the angle the height from the pivot point is
L = 0.40 / 2 = 0.20 cm
The distance that went up is
y = L - L cos θ
cos θ = (L-y) / L
θ = cos⁻¹ (L-y) / L
θ = cos⁻¹-1 ((0.20 - 0.00509) /0.20)
θ = 12.95º
Stars don't have moons and planets do
The unmagnetized pieces of iron would be randomly pointing to directions, this is true because although influenced with the magnetic domain, the direction of the unmagnetized iron field of attraction is not uniform or does not have preferred direction.
