A force of magnitude 7.50 N pushes three boxes with masses m1=1.30kg m2=3.20kg, and m3=4.90kg. find the magnitude of the contact force between boxes 1 and 2. find the magnitude of the contact force between boxes 2 and 3.
the total mass is 1.3 + 3.2 + 4.9
the acceleration a = 7.5/that sum
therefore the force on the furthest box = m of that box * a
the force on the next box is that force + m that box * a
etc
To find the magnitude of the contact force between boxes 1 and 2, we need to first calculate the net force acting on the system.
Step 1: Calculate the total mass of the system.
m_total = m1 + m2 + m3
= 1.30 kg + 3.20 kg + 4.90 kg
= 9.40 kg
Step 2: Use Newton's second law of motion to find the net force.
net force = mass * acceleration
F_net = m_total * a
Since the acceleration is not given, we need to calculate it using the force provided.
F_net = F1 + F2 + F3
F_net = 7.50 N
Step 3: Substitute the known values into the formula and solve for acceleration.
F_net = m_total * a
7.50 N = 9.40 kg * a
a = 7.50 N / 9.40 kg
a ≈ 0.798 m/s^2
Step 4: Calculate the magnitudes of the contact forces.
To find the contact force between boxes 1 and 2, we need to consider only the forces acting on these two boxes.
F_contact1_2 = m1 * a
= 1.30 kg * 0.798 m/s^2
≈ 1.0374 N
To find the contact force between boxes 2 and 3, we use a similar calculation.
F_contact2_3 = m2 * a
= 3.20 kg * 0.798 m/s^2
≈ 2.5536 N
Therefore, the magnitude of the contact force between boxes 1 and 2 is approximately 1.0374 N, and the magnitude of the contact force between boxes 2 and 3 is approximately 2.5536 N.
To find the magnitude of the contact force between boxes 1 and 2, and between boxes 2 and 3, we need to apply 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.
1. To find the magnitude of the contact force between boxes 1 and 2, we can consider the motion of the two boxes as a system. The force applied by the external force (7.50 N) will be divided between the two boxes according to their masses. The contact force between the boxes will be equal in magnitude and opposite in direction.
Let's denote the contact force between boxes 1 and 2 as F12.
Applying Newton's second law to box 1:
m1 * a = F12
Applying Newton's second law to box 2:
m2 * a = -F12
Since the acceleration will be the same for both boxes in contact, we can equate the two equations:
m1 * a = -m2 * a
Simplifying the equation:
m1 * a + m2 * a = 0
a * (m1 + m2) = 0
a = 0
Since the acceleration is zero, it means that the contact force F12 is also zero. Therefore, there is no contact force between boxes 1 and 2.
2. To find the magnitude of the contact force between boxes 2 and 3, we again consider their motion as a system. The force applied by the external force (7.50 N) will now be divided between boxes 2 and 3.
Let's denote the contact force between boxes 2 and 3 as F23.
Applying Newton's second law to box 2:
m2 * a = F23
Applying Newton's second law to box 3:
m3 * a = -F23
Again, since the acceleration will be the same for both boxes in contact, we can equate the two equations:
m2 * a = -m3 * a
Simplifying the equation:
m2 * a + m3 * a = 0
a * (m2 + m3) = 0
a = 0
Similarly, since the acceleration is zero, it means that the contact force F23 is also zero. Therefore, there is no contact force between boxes 2 and 3.
In conclusion, the magnitude of the contact force between boxes 1 and 2 is zero, and the magnitude of the contact force between boxes 2 and 3 is also zero.