A force of magnitude 7.50 N pushes three boxes with masses m_1 = 1.30 kg,m_2 = 3.20 kg, and m_3 = 4.90 kg .The mass is side by side.
1-Find the magnitude of the contact force between boxes 1 and 2, and
2-Find the magnitude of the contact force between boxes 2 and 3.
To find the magnitude of the contact forces between the boxes, we need to first analyze the forces acting on each box separately.
1. Magnitude of the contact force between boxes 1 and 2 (F12):
- Box 1 is being pushed by an external force of magnitude 7.50 N.
- Box 2 is being pulled by the contact force between Box 1 and Box 2.
- The two boxes are in contact, so the contact force between them is equal in magnitude but opposite in direction.
- According to Newton's Third Law of Motion, the contact force exerted by Box 2 on Box 1 is equal in magnitude but opposite in direction to the contact force exerted by Box 1 on Box 2.
So, to find the magnitude of F12, we need to calculate the force being exerted by Box 2 on Box 1.
To calculate this force, we can use Newton's Second Law of Motion: Force (F) = mass (m) * acceleration (a).
- The acceleration experienced by Box 1 is the same as Box 2 since they are in contact.
- The net force acting on Box 1 is the external force (7.50 N) minus the force exerted by Box 2. Therefore, F_net1 = 7.50 N - F12.
- Similarly, the net force acting on Box 2 is the force exerted by Box 2 (F12).
- The acceleration of both boxes is the same and can be denoted as a.
Using the equation:
F_net1 = m1 * a,
7.50 N - F12 = m1 * a ........(1)
Using the equation:
F_net2 = m2 * a,
F12 = m2 * a ..................(2)
We need to solve these two equations to find F12.
2. Magnitude of the contact force between boxes 2 and 3 (F23):
- Box 2 is being pulled by an external force of magnitude 7.50 N.
- Box 3 is being pulled by the contact force between Box 2 and Box 3.
- The two boxes are in contact, so the contact force between them is equal in magnitude but opposite in direction.
- According to Newton's Third Law of Motion, the contact force exerted by Box 3 on Box 2 is equal in magnitude but opposite in direction to the contact force exerted by Box 2 on Box 3.
So, to find the magnitude of F23, we need to calculate the force being exerted by Box 3 on Box 2.
To calculate this force, we can use Newton's Second Law of Motion again: Force (F) = mass (m) * acceleration (a).
- The acceleration experienced by Box 2 is the same as Box 3 since they are in contact.
- The net force acting on Box 2 is the external force (7.50 N) minus the force exerted by Box 3. Therefore, F_net2 = 7.50 N - F23.
- Similarly, the net force acting on Box 3 is the force exerted by Box 3 (F23).
- The acceleration of both boxes is the same and can be denoted as a.
Using the equation:
F_net2 = m2 * a,
7.50 N - F23 = m2 * a ........(3)
Using the equation:
F_net3 = m3 * a,
F23 = m3 * a ..................(4)
We need to solve these two equations to find F23.
To solve this problem, we need to apply Newton's second law of motion which states that the force applied to an object is equal to the object's mass multiplied by its acceleration. In this case, since the boxes are side by side, the acceleration of all the boxes will be the same.
1. Find the magnitude of the contact force between boxes 1 and 2:
We can start by finding the acceleration of the system using Newton's second law.
The force applied to the system is the same for all the boxes, given as 7.50 N.
Let's denote the acceleration of all the boxes as "a".
Using Newton's second law: F = m · a
For box 1: 7.50 N = m1 · a
Substituting the mass of box 1, m1 = 1.30 kg:
7.50 N = 1.30 kg · a
Now solve for "a":
a = 7.50 N / 1.30 kg
The acceleration of the system is 5.7692 m/s².
Now, to find the contact force between boxes 1 and 2, we can use the equation:
F12 = m1 · a
Substituting the mass of box 1, m1 = 1.30 kg, and the acceleration, a = 5.7692 m/s²:
F12 = 1.30 kg · 5.7692 m/s²
Calculating the magnitude of the contact force between boxes 1 and 2, F12:
F12 ≈ 7.5 N
Therefore, the magnitude of the contact force between boxes 1 and 2 is approximately 7.5 N.
2. Find the magnitude of the contact force between boxes 2 and 3:
To find the contact force between boxes 2 and 3, we can use the same equation:
F23 = m2 · a
Substituting the mass of box 2, m2 = 3.20 kg, and the acceleration, a = 5.7692 m/s²:
F23 = 3.20 kg · 5.7692 m/s²
Calculating the magnitude of the contact force between boxes 2 and 3, F23:
F23 ≈ 18.46 N
Therefore, the magnitude of the contact force between boxes 2 and 3 is approximately 18.46 N.