Physics, 26.09.2019 23:20 xxaurorabluexx

Your fhe brother (mass 144.1 kg) is canoeing on utah lake with his sister (mass 81.6 kg). he had the only paddle but managed to drop it in the lake. it has drifted just out of his reach along the long axis of the canoe. his sister has taken physics 121 and suggests that if they trade places she might be able to reach the paddle. due to the high "slime" content of the lake and the slick surface of the canoe, the canoe moves in the water without any friction or drag. the passengers sit 2.03 meters apart and the canoe has a mass of 48.7 kg. after the passengers switch places, how much closer to the paddle (which does not move) is the end of the canoe? (enter a positive number.)

Answers: 1

Show answers

Answers

Answer from: jjmo

The end of the canoe is 46.27 cm closer to the paddle.

Explanation:

This problem can be solved using the center of mass of the system.

As there are no external forces in the horizontal direction, and the external forces in the vertical direction, the gravitational force and the buoyancy, cancel each other, we know:

$\vec{F}_{net_{external}} = M \frac{d\vec{P}}{dt} = 0$

where M is the total mass of the system, and $\vec{P}$ is the linear momentum of the system. This implies:

$\frac{d\vec{P}}{dt} = 0$

$\vec{P} = constant$

the linear momentum of the system is:

$\vec{P} = M \vec{r}_{cm}$

where $\vec{r}_{cm}$ is the position of the center of mass. As the mass in this problem is constant, this implies that the position of the center of mass is conserved.

Finding the center of mass

For a system formed by i particles, each of mass m_i and position $\vec{r}_i$ , the center of mass can be found with the equation:

$\vec{r}_{cm} = \frac{\sum\limits_i m_i \vec{r}_i }{M}$

where M is the total mass of the system, found with the equation:

$M = \sum\limits_i m_i$

For this problem, the total mass of the system is :

$M = m_{brother} + m_{sister} + m_{canoe}$

$M = 144.1 \ kg + 81.6 \ kg + 48.7 \ kg$

$M = 274.4 \ kg$

To find the positions, we need an frame of reference. Putting the origin of coordinate at the position of the sister.

$\vec{r}_{sister_i} = 0 \ \hat{i}$

The brother is 2.03 meters apart in the positive direction:

$\vec{r}_{brother_i} = 2.03 m \ \hat{i}$

and the center of mass of the canoe must be at half this distance:

$\vec{r}_{canoe_i} = 1.015 m \ \hat{i}$

taking all this, the center of mass of the system is at :

$\vec{r}_{cm} = \frac{ 81.6 \ kg * 0 \ \hat{i} + 144.1 \ kg \ 2.03 m \ \hat{i} + 48.7 \ kg \ 1.015 m \ \hat{i} }{274.4 \ kg}$

$\vec{r}_{cm} = 1.2462 \ m\ \hat{i}$

Finding the displacement

After the switch, we found that the center of mass has to be displaced. If its displaced a distance d, we find that the new positions must be:

$\vec{r}_{sister_f} = 2.03 m \ \hat{i} + d \ \hat{i}$

$\vec{r}_{brother_f} = 0 \ \hat{i} + d \ \hat{i}$

$\vec{r}_{canoe_f} = 1.015 m \ \hat{i} + d \ \hat{i}$

where the brother and the sister had switched the original position. Now, the center of mass will be located at:

$\vec{r}_{cm} = 1.2462 \ m\ \hat{i}$

And the equation is :

$\vec{r}_{cm} = \frac{ 81.6 \ kg * (2.03 m \ \hat{i} + d \ \hat{i} ) + 144.1 \ kg \ d\ \hat{i} + 48.7 \ kg \ ( 1.015 m \ \hat{i} + d \ \hat{i}) }{274.4 \ kg}$

$\vec{r}_{cm} = 0.7838 \ m \ \hat{i} + \frac{ 81.6 \ kg d \ \hat{i} ) + 144.1 \ kg \ d\ \hat{i} + 48.7 \ kg \ d \ \hat{i}) }{274.4 \ kg}$

$\vec{r}_{cm} = 0.7838 \ m \ \hat{i} + \frac{ 81.6 \ kg + 144.1 \ kg + 48.7 \ kg \ }{274.4 \ kg} \ d \ \hat{i}$

$\vec{r}_{cm} = 0.7838 \ m \ \hat{i} + d \ \hat{i}$

$1.2462 \ m\ \hat{i} = 0.7838 \ m \ \hat{i} + d \ \hat{i}$

$d \hat{i} = 0.4627 \ m \ \hat{i}$

And this is how much closer the paddle is to the end of the canoe.

Answer from: Quest

the earths atmosphere is made up of nitrogen and oxygen. solids can turn into gasses through a process called sublimation. sublimation is the transition of a substance directly from the solid to the gas phase, without passing through the intermediate liquid phase.

hope this : d

Answer from: Quest

the five characteristics of adolescence are biological growth and development, and undefined status, increased decision making, increased pressure and the search of self.

Another question on Physics

Physics, 22.06.2019 01:40

In all trials, the magnitude of the final velocity for g1 + g2 was less than the magnitude of any initial velocity. as mass increased, what happened to the velocity? the velocity decreased. the velocity increased. the velocity of g1 + g2 could not be measured. the velocity was not affected by the mass increase.

Answers: 1

Answer

Physics, 22.06.2019 11:00

The star betelgeuse is about 600 light-years away. if it explodes tonight, a. we'll know because debris from the explosion will rain down on us from space.b. we'll know it immediately because it will be brighter than the full moon in the sky.c. we won't know about it until 600 years from now.d. none of the above.

Answers: 3

Answer

Physics, 22.06.2019 17:00

Since the energy was not raising the temperature of the water during these segments, what was the energy used to do instead? your answer must include an explanation of what is happening to the molecules.

Answers: 3

Answer

Physics, 22.06.2019 18:10

See the attachment and solve question 5th

Answers: 3

Answer

You know the right answer?

Your fhe brother (mass 144.1 kg) is canoeing on utah lake with his sister (mass 81.6 kg). he had the...

Questions