Answer:
t=37 mins -> 2220sec
We want "T" which is the pendulum time constant
Using this equation
.5A=Ae^(-t/T)
The .5A is half the amplitude
Take ln of both sides to get ride of Ae
=ln(.5)=-2220/T
Now rearrange to = T
T=-2220/ln(.5) = 3202.78sec / 60 secs = 53.38 mins -> first part of the answer.
The second part is really easy. It took 37 mins to decay half way. meaning to decay another half of 50% which equals 25% it will take an additional 37 mins!
Answer:
10.4 m/s
Explanation:
The problem can be solved by using the following SUVAT equation:

where
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time
For the diver in the problem, we have:
is the initial velocity (positive because it is upward)
is the acceleration of gravity (negative because it is downward)
By substituting t = 1.7 s, we find the velocity when the diver reaches the water:

And the negative sign means that the direction is downward: so, the speed is 10.4 m/s.
Answer:
The charge to mass ratio is 
Explanation:

We need to find how much charge is contained in the electron per unit of mass, to do this we divide the charge in an electron and the mass of an electron:

The charges are the same in absolute value, so the change of potential energy is the same. That means that the change in kinetic energy is also the same. Then:
1 = Ke/Kp = m_e *v_e^2 / m_p * v_p^2, or
v_e/v_p = sqrt( m_p/m_e),
So the speed of the electron will be sqrt( m_p/m_e) times greater than the speed of the proton
Answer:
Tension in the string at this position: 3.1 N.
Explanation:
Convert the radius of the circle to meters:
.
What's the net force on the object?
The object is in a circular motion. As a result,
,
where
is the net force on the object,
is the mass of the object,
is the velocity of the object, and
is the radius of the circular motion.
For this object,
.
The output unit of net force should be standard if the unit for mass, velocity, and radius are all standard. The net force shall always point towards the center. In this case the net force points downwards.
What are the forces on this object?
There are two forces on the object at this moment:
- Weight,
, which points downwards.
. - Tension,
, which also points downwards. The size of the tension force needs to be found.
What's the size of the tension force?
Gravity and tension points in the same direction. The size of their resultant force is the sum of the two forces. In other words,
.
.
All three values in this question are given with two sig. fig. Round the value of
to the same number of significant figures.