A 6.40 kg block rests on a 12.5 kg block as shown in the diagram.

The interface between the lower mass and the table is frictionless, but
there is friction (static friction μS and kinetic friction μK) between the two
blocks. A horizontal force F
r
acts on the UPPER block and causes both
blocks to accelerate. The acceleration of both blocks when they begin to
slip is 2.0 2 s
m .
(i) Calculate the force F at the time when the blocks start to slip.
6.40 kg
12.5 kg
F
(ii) Calculate the coefficient of static friction μS.

3. A spaceship of mass 175,000 kg travels from the Earth to the Moon along a line that passes through the center of the

Earth and the center of the Moon. At what distance from the center of the Earth is the force due to the Earth twice the
magnitude of the force due to the Moon? If the spaceship has double the mass, will this position move toward the
earth or moon?

To calculate the force F at the time when the blocks start to slip, we can use Newton's second law of motion. This law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, we can consider the combined mass of both blocks as the object.

Step 1: Calculate the combined mass:
The combined mass of both blocks is the sum of their individual masses:
Combined mass = 6.40 kg + 12.5 kg = 18.9 kg

Step 2: Calculate the acceleration:
Given that the acceleration is 2.0 m/s^2, we can use this value in the equation:
Force = Mass × Acceleration
F = (18.9 kg) × (2.0 m/s^2)
F = 37.8 N

Therefore, the force F at the time when the blocks start to slip is 37.8 N.

To calculate the coefficient of static friction μS, we can use the formula that relates the force of friction to the normal force and the coefficient of friction. In this case, the normal force acting on the upper block is equal to its weight, as there is no vertical acceleration.

Step 1: Calculate the normal force:
The normal force acting on the upper block is equal to its weight, which can be found using the formula:
Weight = Mass × gravitational acceleration
Weight = 6.40 kg × 9.8 m/s^2
Weight ≈ 62.72 N

Step 2: Calculate the force of friction:
The force of friction can be calculated using the formula:
Force of friction = Coefficient of friction × Normal force
Since we are looking for the coefficient of static friction, we can rewrite this equation as:
Force of static friction = μS × Normal force

We know that the force of static friction is equal to the force applied:
Force of static friction = F = 37.8 N

Therefore, we can rewrite the equation as:
37.8 N = μS × 62.72 N

Step 3: Calculate the coefficient of static friction:
By rearranging the equation, we can solve for μS:
μS = (37.8 N) / (62.72 N)
μS ≈ 0.603

Therefore, the coefficient of static friction μS is approximately 0.603.