A person pulls a bucket of water up from a well with a rope. Assume the initial and final speeds of the bucket are zero (Vi-Vf-0
), and that the person lifted the bucket a vertical distance h. By looking at energy changes in the bucket-Earth physical system, we can make sense of the force the person must exert to pull the bucket up and the amount of work the person does. a) Think about whether this is an open or closed system. What energy systems undergo a change in energy during the process? Construct a particular Energy-System Diagram for this process and include the algebraic expression of energy conservation (in terms of AE's and if open, any Heat or Work). b) Substitute the algebraic expression we use for the change in gravitational potential energy and solve algebraically for the work done by the person on the rope/bucket. c) Use the definition of work in terms of force and distance (see p.39-40 of Chapter 2 in the Course Notes) to find the average force exerted by the person on the rope and bucket while they are lifting it up.
1 answer:
Answer:
a
This a closed system because the mass of the system is conserved
The energy system that undergoes change is the Potential energy system
The energy system diagram is shown on the first uploaded image
b
Work done = Change in gravitational potential energy
So solving algebraically for work done would be
Work done =
where m is mass
g is acceleration due to gravity
and h is the height
c
Work done in terms of force and distance is = mg
where m is mass of bucket and
g is acceleration due to gravity
Explanation:
a) At the start, potential and kinetic energy were zero. so, energy is zero.
As the person pulls the bucket up, the potential energy becomes mgh.
so,final energy will be consisting of only potential energy.
B) Here work done is equal to change in gravitational potential energy.
W =
W = m*g*h
where g = 9.9 m/
C) Work = force * distance
mgh = force * h
force = mg
force = weight of bucket
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Complete Question
The complete question is shown on the first uploaded image
Answer:
The acceleration would be
Explanation:
The objective of this solution is to obtain the acceleration of the particle
Now looking at Newton law which is mathematically represented as
Where F is the force experience by a particle
m is the mass of the particle
a is the acceleration of the particle
And also this force is equivalent to magnetic force in a magnetic field which is mathematically represented as
Where q is the charge of the particle
v is the velocity of the charge
B is the magnetic field the charge is under it influence
Now equating this two formulas
Making a the subject we have
In the question the direction of the is in the positive x-axis which is hence the direction would be in the
direction
So substituting for B
Substituting for v and
for q
According to vector multiplication
So
Answer:
Velocity of the two balls after collision: .
of kinetic energy would be lost.
Explanation:
<h3>Velocity</h3>Because the question asked about energy, convert all units to standard units to keep the calculation simple:
- Mass of the first ball:
.
- Mass of the second ball:
.
The two balls stick to each other after the collision. In other words, this collision is a perfectly inelastic collision. Kinetic energy will not be conserved. The velocity of the two balls after the collision can only be found using the conservation of momentum.
Assume that the system of the two balls is isolated. Thus, the sum of the momentum of the two balls will stay the same before and after the collision.
The momentum of an object of mass and velocity
is:
.
Momentum of the two balls before collision:
- First ball:
.
- Second ball:
.
- Sum:
given that the two balls are moving in the same direction.
Based on the assumptions, the sum of the momentum of the two balls after collision should also be . The mass of the two balls, combined, is
. Let the velocity of the two balls after the collision
. (There's only one velocity because the collision had sticked the two balls to each other.)
- Momentum after the collision from
:
.
- Momentum after the collision from the conservation of momentum:
.
These two values are supposed to describe the same quantity: the sum of the momentum of the two balls after the collision. They should be equal to each other. That gives the equation about :
.
.
In other words, the velocity of the two balls right after the collision should be .
The kinetic energy of an object of mass and velocity
is
.
Kinetic energy before the collision:
- First ball:
.
- Second ball:
.
- Sum:
.
The two balls stick to each other after the collision. Therefore, consider them as a single object when calculating the sum of their kinetic energies.
- Mass of the two balls, combined:
.
- Velocity of the two balls right after the collision:
.
Sum of the kinetic energies of the two balls right after the collision:
.
Therefore, of kinetic energy would be lost during this collision.
To solve this problem we will apply the concepts related to the double slit experiment. Here we test a relationship between the sine of the deviation angle and the distance between slit versus wavelength and the bright fringe order. Mathematically it can be described as,
Here,
d = Distance between slits
m = Any integer which represent the order number or the number of repetition of the spectrum
= Wavelength
= Angular deviation
Replacing with our values we have,
Part A)
PART B)