How Can Ricardo Calculate Carmelita's Mass Based on Their Movement in a Canoe?

[darkys]

i have this problem that I've been trying to figure out for a while, and can't seem to get it.

Ricardo, of mass 87 kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 28 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3.3 m apart and symmetrically located with respect to the canoe's center. Ricardo notices that the canoe moves 57.6 cm horizontally relative to a pier post during the exchange and calculates Carmelita's mass. What is it?

ive been trying this from many different ways. I've tried using the canoe after they move as the center of gravity, and then using x as the mass of the girl. I multiply the masses time the distance away from the center of gravity(the canoe) all divided by the mass, but its not coming out to the right answer. Can anyone help me with this?

 

[Andrew Mason]

i have this problem that I've been trying to figure out for a while, and can't seem to get it.

Ricardo, of mass 87 kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 28 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3.3 m apart and symmetrically located with respect to the canoe's center. Ricardo notices that the canoe moves 57.6 cm horizontally relative to a pier post during the exchange and calculates Carmelita's mass. What is it?

ive been trying this from many different ways. I've tried using the canoe after they move as the center of gravity, and then using x as the mass of the girl. I multiply the masses time the distance away from the center of gravity(the canoe) all divided by the mass, but its not coming out to the right answer. Can anyone help me with this?

The centre of mass of a system is defined as the point where:

$$\sum_{i=0}^n m_i\vec{x_i} = 0$$

where xi is the displacement of the centre of mass of each mass object in the system from the centre of mass of the system.

So set up an equation where there are three displacement vectors representing the displacement of the cm of each of the two people and the canoe from the cm of the system, both before and after the switch. Since the cm does not change, these are equal. You know that the sum of the displacements of C and R is the distance between the seats. You also know the difference between the positions of the cm of the canoe. So you have 3 equations, 3 variables. You should get a unique solution.

AM

 

[m2003]

I can offer some guidance on how to approach this problem. First, it's important to understand the concept of center of mass. The center of mass is the point at which an object's mass is evenly distributed, and it is the point around which an object will balance. In this case, the center of mass of the canoe is important because it will determine how much the canoe moves when Ricardo and Carmelita exchange seats.

To solve this problem, we can use the principle of conservation of momentum. This means that the total momentum before the exchange must be equal to the total momentum after the exchange. We can set up an equation using this principle:

M1V1 = M2V2

Where M1 and V1 are the mass and velocity of the canoe before the exchange, and M2 and V2 are the mass and velocity of the canoe after the exchange. Since the canoe is at rest before and after the exchange, we can simplify this equation to:

M1 = M2

This means that the mass of the canoe before the exchange is equal to the mass of the canoe after the exchange. We can also use the fact that the distance between the two seats is 3.3 m to set up another equation:

(M1 + M2) * 3.3 = M2 * 0.576

Where M1 and M2 are the masses of Ricardo and Carmelita, respectively. Solving these equations simultaneously will give us the mass of Carmelita.

Another approach could be to use the concept of torque. Torque is a measure of how much a force acting on an object causes that object to rotate. In this case, we can use the fact that the canoe rotates due to the exchange of seats to determine Carmelita's mass. We can set up the following equation:

M1 * d1 = M2 * d2

Where M1 and M2 are the masses of Ricardo and Carmelita, and d1 and d2 are the distances from the center of mass of the canoe to the two seats before and after the exchange, respectively. Solving this equation will also give us the mass of Carmelita.

I hope these explanations and approaches help you in solving this problem. Remember to always start with the basic principles and equations, and then apply them to the specific scenario given. Good luck!