Two boxes are stacked in an elevator that is accelerating downwards at 3.49m/s/s. A smaller 3.06kg box is on top and a larger 9.93kg box is on bottom. Find the magnitude and direction of the force that the smaller mass exerts on larger.

To find the magnitude and direction of the force that the smaller mass exerts on the larger, we need to consider Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.

Let's call the smaller mass (3.06 kg) M1 and the larger mass (9.93 kg) M2.

The force exerted by M1 on M2 will be equal in magnitude and opposite in direction to the force exerted by M2 on M1.

Given that the elevator is accelerating downwards at 3.49 m/s^2, we can calculate the net force on each object using Newton's second law:

F1 = M1 * a
= 3.06 kg * 3.49 m/s^2
= 10.6794 N

F2 = M2 * a
= 9.93 kg * 3.49 m/s^2
= 34.6017 N

According to Newton's third law, the magnitude of the force that M1 exerts on M2 is equal to the magnitude of the force that M2 exerts on M1, i.e., 34.6017 N. However, the direction of the force exerted by M1 on M2 is opposite to the direction of the force exerted by M2 on M1.

Therefore, the magnitude of the force that the smaller mass (M1) exerts on the larger mass (M2) is 34.6017 N, and the direction of this force is upward, opposite to the direction of the elevator's downward acceleration.

To find the magnitude and direction of the force that the smaller mass exerts on the larger mass, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = m * a).

Let's consider the forces acting on the larger mass: the gravitational force (weight) and the force exerted by the smaller mass.

1. Gravitational force on the larger mass:
The weight of an object can be calculated using the formula W = m * g, where W is the weight, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, the weight of the larger mass is W1 = (9.93 kg) * (9.8 m/s^2).

2. Net force acting on the larger mass:
The net force acting on the larger mass is the difference between the gravitational force and the force exerted by the smaller mass: F_net = F1 - F2.

3. Force exerted by the smaller mass on the larger mass:
Using Newton's second law, F2 = m2 * a, where F2 is the force exerted by the smaller mass, m2 is the mass of the smaller mass, and a is the acceleration of the elevator, which is equal to -3.49 m/s^2 (negative because it is accelerating downwards).

4. Substituting values into the equation:
F_net = F1 - F2
F_net = W1 - (m2 * a)

5. Calculate the magnitude and direction of the force:
Substitute the values for W1, m2, and a into the equation to find the net force acting on the larger mass.

Now that we have explained how to find the magnitude and direction of the force exerted by the smaller mass on the larger mass, you can go ahead and solve the equation to get the numerical answer.