The figure is just mass A on top of mass B. There are no forces or anything shown.

Block A, of mass 3.2 kg, is on block B, of mass 7 kg, as shown in the above figure. The lower block is on a frictionless surface while the coefficient of static friction is 0.25 between the two blocks.

a) If they are moving at constant velocity, what is the frictional force between A and B?

b) What is the maximum horizontal force that can be applied to B without A slipping?

I'm not so clear on the topic of friction, so I don't understand how to find it.

frictional force is the normal force multiplied by the coefficient

in this case ... Ff = Ma * g * 0.25

the frictional force keeps A moving with B
... so the max acceleration (without slip) is ... Ma / Ff

the max force is the max acceleration multiplied by the sum of the masses
... f = m a

I figured out a) is 0 N because the velocity is constant

To solve this problem, let's break it down step-by-step:

a) If the blocks are moving at a constant velocity, it means that the net force acting on them is zero. Since there is no force shown in the figure, we can conclude that there is a frictional force between block A and block B that opposes the motion. The frictional force can be calculated using the equation:

Frictional force = Coefficient of static friction × Normal force

In this case, the normal force acting on block A is equal to its weight, which is given by:

Normal force = Mass A × Acceleration due to gravity

Normal force = 3.2 kg × 9.8 m/s^2

Now, we can substitute the given values into the frictional force equation:

Frictional force = 0.25 × (3.2 kg × 9.8 m/s^2)

Calculate the frictional force to find the answer.

b) To find the maximum horizontal force that can be applied to block B without block A slipping, we need to consider the limiting friction force. The limiting friction force is defined as:

Limiting friction force = Coefficient of static friction × Normal force

Once again, the normal force acting on block A is equal to its weight. We have already determined its value in the previous step. Now, you can substitute the given values into the equation for the limiting friction force:

Limiting friction force = 0.25 × (3.2 kg × 9.8 m/s^2)

Calculate the limiting friction force to find the answer.

Remember to double-check your numerical calculations and units.

To understand how to find the answers to the given questions, let's go step by step:

a) If the two blocks are moving at a constant velocity, it means that the frictional force between block A and block B is equal to the applied force. In this case, the applied force is equal to the force of friction.

To find the frictional force, we need to use the equation:

frictional force = coefficient of friction * normal force

The normal force is the force exerted by block B on block A, which is equal to the weight of block A (since the two blocks are at rest, the normal force cancels out the weight of block A).

normal force = weight of block A
normal force = mass of block A * acceleration due to gravity
normal force = 3.2 kg * 9.8 m/s^2

Next, we can calculate the frictional force:

frictional force = coefficient of friction * normal force
frictional force = 0.25 * (3.2 kg * 9.8 m/s^2)

b) The maximum horizontal force that can be applied to block B without block A slipping is equal to the maximum static friction force. The maximum static friction force can be calculated using the equation:

maximum static friction force = coefficient of static friction * normal force

Again, we need to find the normal force between the two blocks. In this case, it is equal to the weight of both blocks combined since they are at rest:

normal force = weight of block A + weight of block B
normal force = (mass of block A * acceleration due to gravity) + (mass of block B * acceleration due to gravity)
normal force = (3.2 kg * 9.8 m/s^2) + (7 kg * 9.8 m/s^2)

Finally, we can calculate the maximum horizontal force:

maximum static friction force = coefficient of static friction * normal force
maximum horizontal force = 0.25 * [(3.2 kg * 9.8 m/s^2) + (7 kg * 9.8 m/s^2)]

Note: It's important to remember that the coefficient of static friction is used when the two surfaces are at rest relative to each other, whereas the coefficient of kinetic friction is used when the two surfaces are in motion relative to each other. In this problem, since the blocks are moving at a constant velocity, the coefficient of static friction is applicable.

I hope this explanation helps you understand how to find the frictional force and the maximum horizontal force in this scenario.