1) A box m1 = 9.30 kg is stacked on top of another box m2 = 20.0 kg, placed on the floor inside an elevator. When the elevator is accelerating downward with a magnitude of 3.72 m/s2, what is the normal force that box m1 exerts on box m2? What is the normal force that the elevator exerts on m2?
2) A force of magnitude F = 7.90 N pushes three boxes (from right to left) with masses m1 = 1.30 kg, m2 = 3.10 kg, and m3 = 4.70 kg, on a level surface. Find the contact force between boxes 1 and 2. Find the contact force between boxes 2 and 3. From right to left, Force F is pushing box1,box2,box3 attached together.
To solve these problems, 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.
1) To find the normal force that box m1 exerts on box m2, we need to consider the forces acting on box m1. These forces are the gravitational force (mg1) and the normal force (N1). Since the elevator is accelerating downward, the net force acting on m1 is given by the equation:
net force on m1 = m1 * acceleration
The net force is the difference between the gravitational force and the normal force:
mg1 - N1 = m1 * acceleration
We can rearrange the equation to solve for N1:
N1 = mg1 - m1 * acceleration
Substituting the given values:
m1 = 9.30 kg
m2 = 20.0 kg
acceleration = 3.72 m/s^2
g = 9.8 m/s^2 (acceleration due to gravity)
N1 = (9.30 kg * 9.8 m/s^2) - (9.30 kg * 3.72 m/s^2)
Similarly, to find the normal force that the elevator exerts on m2, we consider the forces acting on m2. These forces are the gravitational force (mg2) and the normal force (N2). Again, using Newton's second law, the net force on m2 is:
net force on m2 = m2 * acceleration
The net force is the difference between the gravitational force and the normal force:
mg2 - N2 = m2 * acceleration
Rearranging the equation to solve for N2:
N2 = mg2 - m2 * acceleration
By substituting the values and solving the equation, we can find N2.
2) To find the contact force between boxes 1 and 2, we need to consider the forces acting on box 1. These forces are the force pushing from right to left (F), the contact force with box 2 (N12), and the gravitational force (mg1). Using Newton's second law, the net force on box 1 is:
net force on box 1 = F - N12 - mg1 = m1 * acceleration
Since the boxes are not sliding or accelerating vertically, we know that the normal force between the boxes is equal to the gravitational force:
N12 = mg1
We can rearrange the equation to solve for N12:
N12 = F - mg1 - m1 * acceleration
By substituting the given values, we can calculate N12.
Similarly, to find the contact force between boxes 2 and 3, we need to consider the forces acting on box 2. These forces are the force pushing from right to left (F), the contact force with box 1 (N12), the contact force with box 3 (N23), and the gravitational force (mg2). The net force on box 2 is:
net force on box 2 = F - N12 - N23 - mg2 = m2 * acceleration
Again, we know that the normal force between the boxes is equal to the gravitational force:
N12 = N23 = mg2
We can rearrange the equation to solve for N23:
N23 = F - mg2 - m2 * acceleration
By substituting the given values, we can calculate N23.