Answer:
Approximately 
(approximately 
) assuming that the magnetic field and the wire are both horizontal.
Explanation:
Let 
denote the angle between the wire and the magnetic field.
Let 
denote the magnitude of the magnetic field.
Let 
denote the length of the wire.
Let 
denote the current in this wire.
The magnetic force on the wire would be:
.
Because of the 
term, the magnetic force on the wire is maximized when the wire is perpendicular to the magnetic field (such that the angle between them is 
.)
In this question:
(or, equivalently, 
radians, if the calculator is in radian mode.)
.
.
.
Rearrange the equation 
to find an expression for , the current in this wire.
.
Given:
I₁ = 0.70 kg-m², the moment of inertia with arms and legs in
I₂ = 3.5 kg-m², the moment of inertia with arms and a leg out.
ω₁ = 4.8 rev/s, the angular speed with arms and legs in.
That is,
ω₁ = (4.8 rev/s)*(2π rad/rev) = 30.159 rad/s
Let ω₂ = the angular speed with arms and a leg out.
Because momentum is conserved, therefore
I₂ω₂ = I₁ω₁
ω₂ = (I₁/I₂)ω₁
= (0.7/3.5)*(30.159)
= 6.032 rad/s
ω₂ = (6.032 rad/s)*(1/(2π) rev/rad) = 0.96 rev/s
Answer: 0.96 rev/s
Answer:
A 0.17 kg baseball is launched from the roof of a building 14 m above the ground. Its initial velocity is 29 m/s at 40° above the horizontal. Assume any effects of air resistance are negligible.
(a) What is the maximum height above the ground that the ball reaches?
m
(b) What is the speed of the ball as it strikes the ground?
m/s
The potential energy is defined as the energy is contained in the body due to the height over the surface of the earth and it is calculated from the equation
<em>where:</em>
- PE: the potential energy in Joules.
- m: the mass of the body in kg.
- g: the acceleration due to the gravity in m/
- h: the height of the body over the earth in meters.
<em>in our problem:</em>
Answer:
The pH of the mixture is 0.7926
Explanation:
Hi there!
The acetylsalicylic acid was completely neutralized by the sodium hydroxide so that the only protons present in the solution come from the HCl. The volume of the solution can be calculated as the addition of the volume of sodium hydroxide and the volume of HCl (assuming that the mixture is an ideal solution).
The number of moles of HCl added can be calculated as follows:
13.46 ml (0.4472 mol/1000 ml) = 6.019 × 10⁻³ mol
The volume of the solution is 13.46 ml + 23.88 ml = 37.34 ml
Then, we can calculate the concetration of protons in the solution:
[H] = 6.019 × 10⁻³ mol /0.03734 l = 0.1612 M
The pH of the mixture:
pH = -log[H]
pH = -log[0.1612] = 0.7926
