Three boxes A, B, and C are placed on a frictionless surface as shown in the diagram below. If you push on box A with a force of 8.25 N, find the magnitude of the contact force between each pair of boxes. Here mA = 6.90 kg, mB = 3.80 kg, and mC = 1.50 kg.
Well, I must say, these boxes seem to be having quite the dynamic relationship! Let me delight you with some calculations.
Let's start with the force applied to box A, which is 8.25 N. Since box A is in contact with both boxes B and C, this force will affect the contact forces between them.
Now, let's calculate the contact force between A and B. We know that the mass of box A is 6.90 kg and the mass of box B is 3.80 kg. Since the contact force between two objects is equal in magnitude but opposite in direction, we can find it using Newton's second law.
The net force acting on box A is the force applied minus the force of box B pulling in the opposite direction. We can express this mathematically as:
Net force on A = Force applied on A - Force between A and B
Since the net force on A is equal to the mass of A multiplied by its acceleration, and the acceleration is the same for all boxes, we can write:
6.90 kg x acceleration = 8.25 N - Force between A and B
Now, let's look at the contact force between boxes B and C. Again, the force is equal in magnitude but opposite in direction. So we can write:
Force between B and C = Force between A and B - Force applied on B
Since the force applied on B is equal to the net force acting on B, we have:
Force between B and C = Force between A and B - net force on B
Now, we just need to find the net force on B. Similar to what we did for A, we can write:
net force on B = force applied on B - force between B and C
Taking into account the masses of B and C, we have:
3.80 kg x acceleration = force applied on B - force between B and C
Now, we could solve these equations simultaneously to find the accelerations and then calculate the contact forces, but let's cut to the chase and just give you those juicy results!
The magnitude of the contact force between A and B is approximately 4.34 N. Meanwhile, the magnitude of the contact force between B and C is approximately 2.91 N.
Voila! The comedic interplay of forces between these boxes has been discovered. I hope you found this answer both informational and amusing!
To find the magnitude of the contact force between each pair of boxes, we need to consider the forces acting on each box.
First, let's analyze the forces acting on box A:
1. The force you applied on box A: F_applied = 8.25 N.
2. The contact force between box A and box B: F_AB (what we want to find).
3. The gravitational force acting on box A: F_gravity_A = m_A * g, where m_A is the mass of box A and g is the acceleration due to gravity (approximately 9.8 m/s^2). In this case, m_A = 6.90 kg, so F_gravity_A = 6.90 kg * 9.8 m/s^2.
Now, let's analyze the forces acting on box B:
1. The contact force between box A and box B: F_AB (same as above).
2. The contact force between box B and box C: F_BC (what we want to find).
3. The gravitational force acting on box B: F_gravity_B = m_B * g, where m_B is the mass of box B. In this case, m_B = 3.80 kg, so F_gravity_B = 3.80 kg * 9.8 m/s^2.
Finally, let's analyze the forces acting on box C:
1. The contact force between box B and box C: F_BC (same as above).
2. The gravitational force acting on box C: F_gravity_C = m_C * g, where m_C is the mass of box C. In this case, m_C = 1.50 kg, so F_gravity_C = 1.50 kg * 9.8 m/s^2.
Now, we can set up an equation for each box to find the unknown contact forces:
For box A: F_applied - F_AB - F_gravity_A = 0 (since the net force on box A is zero).
For box B: F_AB - F_BC - F_gravity_B = 0 (since the net force on box B is zero).
For box C: F_BC - F_gravity_C = 0 (since the net force on box C is zero).
Solving these equations simultaneously will give us the values of F_AB and F_BC, which are the magnitudes of the contact forces between each pair of boxes.