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VashaNatasha [74]

2 years ago

12

A balloon of mass M is floating motionless in the air. A person of mass less than M is on a rope ladder hanging from the balloon

. The person begins to climb the ladder at a uniform speed v relative to the ground. How does the balloon move relative to the ground?

1 answer:

Alex73 [517]2 years ago

4 0

Answer:

Down with a speed less than v

Explanation:

Let the person's mass be represented by m

The mass of the balloon = M

Total momentum is conserved thus F = external force = 0

when the person starts to climb the ladder, external force is still equal to zero.

We know that change is p = F * change in t

in this equation, F is the external force = 0

Hence change in p = 0

This means that total momentum is conserved thus F = external force = 0

(owing to the fact that exterior forces on the system are balanced)

Since all external force was zero before they began to climb the ladder, as they climb all external forces will still = 0

Thus, As the person starts moving

mv + MV = 0

or mv = MV

V = mv/M

Since M > m, m/M will definitely be a number that is less than 1,

Hence, V = (a number less than 1)v.

This means that V < v, or the balloon moves down a speed V which is less than v.

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5.16 An insulated container, filled with 10 kg of liquid water at 20 C, is fitted with a stirrer. The stirrer is made to turn by

Anna007 [38]

Answer:

a) W=2.425kJ

b) $\Delta E=2.425kJ$

c) $T_f=20.06^{o}C$

d) Q=-2.425kJ

Explanation:

a)

First of all, we need to do a drawing of what the system looks like, this will help us visualize the problem better and take the best possible approach. (see attached picture)

The problem states that this will be an ideal system. This is, there will be no friction loss and all the work done by the object is transferred to the water. Therefore, we need to calculate the work done by the object when falling those 10m. Work done is calculated by using the following formula:

$W=Fd$

Where:

W=work done [J]

F= force applied [N]

d= distance [m]

In this case since it will be a vertical movement, the force is calculated like this:

F=mg

and the distance will be the height

d=h

so the formula gets the following shape:

$W=mgh$

so now e can substitute:

$W=(25kg)(9.7 m/s^{2})(10m)$

which yields:

W=2.425kJ

b) Since all the work is tansferred to the water, then the increase in internal energy will be the same as the work done by the object, so:

$\Delta E=2.425kJ$

c) In order to find the final temperature of the water after all the energy has been transferred we can make use of the following formula:

$\Delta Q=mC_{p}(T_{f}-T_{0})$

Where:

Q= heat transferred

m=mass

$C_{p}$ =specific heat

$T_{f}$ = Final temperature.

$T_{0}$ = initial temperature.

So we can solve the forula for the final temperature so we get:

$T_{f}=\frac{\Delta Q}{mC_{p}}+T_{0}$

So now we can substitute the data we know:

$T_{f}=\frac{2 425J}{(10000g)(4.1813\frac{J}{g-C})}+20^{o}C$

Which yields:

$T_{f}=20.06^{o}C$

d)

For part d, we know that the amount of heat to be removed for the water to reach its original temperature is the same amount of energy you inputed with the difference that since the energy is being removed this means that it will be negative.

$\Delta Q=-2.425kJ$

3 0

1 year ago

How much heat Q2Q2 is transferred to the skin by 25.0 gg of steam onto the skin? The heat of vaporization for steam is L=2.256×1

astraxan [27]

Answer:

56400Joules

Explanation:

The quantity of heat required is expressed as;

Q = mL

m is the mass = 25g = 0.025kg

L is the latent heat of vaporization for steam = 2.256×10^6J/kg

Substitute into the formula as shown;

Q = 0.025×2.256×10^6

Q = 56400Joules

Hence the quantity of hear required is 56400Joules

3 0

1 year ago

Two hockey players skating on essentially frictionless ice collide head-on. Madeleine, of mass 65.0 kg, is moving at 6.00 m/s to

xeze [42]

Explanation:

It is given that,

Mass of Madeleine, $m_1=65\ kg$

Initial speed of Madeleine, $u_1=6\ m/s$ (due east)

Final speed of Madeleine, $v_1=-3\ m/s$ (due west)

Mass of Buffy, $m_2=55\ kg$

Final speed of Buffy, $v_2=3.5\ m/s$ (due east)

Let $u_1$ is the Buffy's velocity just before the collision. Using the conservation of linear momentum as :

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

$65\times 6+55\times u_2=65\times (-3)+55\times 3.5$

$u_2=-7.13\ m/s$

So, the initial speed of the Buffy just before the collision is 7.13 m/s and it is moving due west. Hence, this is the required solution.

5 0

1 year ago

Consider a long, closely wound solenoid with 10,000 turns per meter. What current, in amperes, is needed in the solenoid to prod

Makovka662 [10]

Answer:

0.4344A

Explanation:

From Ampere's law, it can be shown that the magnetic field B inside a long solenoid is

$B= \mu_0NI$

Where

B= Magnetic field strenght at distance d

I= current

$\mu_0 =$ Permeability of free space ( $4\pi*10^{-7} Tm/A$ )

N= Number of loops

Our values are defined as follow,

$N=10000$

$B=5.25*10^{-5}$ T

$B'=5.25*10^{-5} * 104 = 5.46*10^{-3}T$

As a current required to become 104 times the Earth's magnetic field is required, we use B '

$B'= \mu_0NI$

$5.46*10^{-3}=4\pi*10^{-7}*10000*I$

$I=\frac{5.46*10^{-3}}{4\pi*10^{-7}*10000}$

$I=0.4344A$

<em>Therefore is needed 0.4344A in the solenoid to produce a magnetic field inside the solenoid, near its center, that is 104 times the Earth's magnetic field.</em>

4 0

1 year ago

When the sun’s rays are at an angle of 39°, the distance from the top of Dakota’s head to the tip of her shadow is 77 inches. Ab

slavikrds [6]

Answer:

Dakota is 48 inches tall.

Explanation:

We can solve this problem using trigonometry. Since the angle between Dakota and the ground is nearly 90°, we can construct a rectangle triangle, whose sides are Dakota, her shadow, and the distance between the top of her head to the tip of her shadow. Let the Dakota's height be D. Since the angle between the sun's rays and the ground is 39° and the distance between the tip of her shadow and Dakota's head is 77 inches, we can state that:

$\sin39\°=\frac{D}{77"}\\\\\implies D=77"\sin39\°\\\\D=48"$

So, this means that Dakota is 48 inches tall.

5 0

1 year ago