two groups of paddlers meet in the middle of a lake. after a brief visit a person in canoe 1 pushes on canoe 2 with a force of 46 N . Mass of canoe 1 is 150 kg and mass of canoe 2 is 250 kg. find acceleration of each canoe
f = m a ___ a = f/m
c1 ___ a = 150/46
c2 ___ a = 250/46
answers are in m/s^2
To find the acceleration of each canoe, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
Let's assume the acceleration of canoe 1 is a1, and the acceleration of canoe 2 is a2.
For canoe 1:
Force pushing on canoe 2 = mass of canoe 1 * acceleration of canoe 1
46 N = 150 kg * a1
For canoe 2:
Force pushing back by canoe 1 = mass of canoe 2 * acceleration of canoe 2
46 N = 250 kg * a2
Now we can solve these two equations simultaneously to find the values of a1 and a2.
Dividing both sides of the first equation by 150 kg:
a1 = 46 N / 150 kg
a1 ≈ 0.307 m/s²
Dividing both sides of the second equation by 250 kg:
a2 = 46 N / 250 kg
a2 ≈ 0.184 m/s²
Therefore, the acceleration of canoe 1 is approximately 0.307 m/s², and the acceleration of canoe 2 is approximately 0.184 m/s².
To find the acceleration of each canoe, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Let's assume that the acceleration of both canoes is the same, denoted by 'a'. We'll use the following variables:
- Force exerted by the person in canoe 1 (F1) = 46 N
- Mass of canoe 1 (m1) = 150 kg
- Mass of canoe 2 (m2) = 250 kg
- Acceleration of both canoes (a)
According to Newton's second law, the force exerted on each canoe is equal to the product of its mass and acceleration. So we can write two equations:
For canoe 1: F1 = m1 * a
For canoe 2: F2 = m2 * a
Since the forces are exerted in opposite directions (canoe 1 pushes on canoe 2), the magnitude of the forces are equal. Therefore, F1 = F2. We can solve the equations simultaneously.
Given that F1 = F2 = 46 N, we have:
46 = 150 * a (equation 1)
46 = 250 * a (equation 2)
To find the acceleration, we can rearrange the equations as follows:
From equation 1, a = 46 / 150
From equation 2, a = 46 / 250
Calculating the values:
a = 0.3067 m/s² (acceleration of canoe 1)
a = 0.184 m/s² (acceleration of canoe 2)
Therefore, the acceleration of canoe 1 is approximately 0.3067 m/s², and the acceleration of canoe 2 is approximately 0.184 m/s².