Two crates, of mass 75 kg and 110 kg, are in contact and at rest on a horizontal surface. A 620-N force is exerted on the 75-kg crate. If the coefficient of kinetic friction is 0.15, calculate (a) the acceleration of the system, and (b) the force that each crate exerts on the other.

(c) Repeat with the crates reversed.

the boxes are horizontally aligned on a flat surface.

please help me... I don't get this problem:(

Tf did 1.47 come from

Well, it seems like you're in quite the box with this problem! But don't worry, I'm here to help and bring a little humor to the equation.

To solve this problem, we need to break it down into a few steps. Let's start with part (a), calculating the acceleration of the system.

The force exerted on the 75-kg crate is 620 N. However, due to the friction between the crate and the surface, we need to take that into account. The frictional force is given by the equation:

frictional force = coefficient of kinetic friction * normal force

The normal force is the force exerted by the surface on the crate, which is equal to the weight of the crate (mass * gravitational acceleration). So, for the 75-kg crate, the normal force is:

normal force = 75 kg * 9.8 m/s²

Now, we can calculate the frictional force using the coefficient of kinetic friction. The equation becomes:

frictional force = 0.15 * (75 kg * 9.8 m/s²)

Since the crate is being pushed with a force of 620 N, the net force acting on it is:

net force = 620 N - frictional force

Now, we can use Newton's second law, which states that the acceleration of an object is equal to the net force acting on it divided by its mass. In this case, the mass is 75 kg, so:

acceleration = (620 N - frictional force) / 75 kg

Alright, that's part (a) done! Now, let's move on to part (b) and find out the force that each crate exerts on the other.

When the two crates are in contact, they create a system where the net force acting on each crate should be the same. Since they have different masses, their accelerations will be different, but the force exerted on each other should be equal.

So, the force that the 75-kg crate exerts on the 110-kg crate is equal in magnitude and opposite in direction to the force that the 110-kg crate exerts on the 75-kg crate.

Therefore, the force that each crate exerts on the other is the same, but since they have different masses, the acceleration of each crate will differ.

Now, let's tackle part (c), where we have the crates reversed. The process is the same, but you'll need to switch the masses when calculating the force that each crate exerts on the other.

I hope this brings a little light-heartedness to the problem, but if you have any more questions, feel free to ask!

No problem! Let's break down the problem and solve it step by step.

(a) To find the acceleration of the system, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:

ΣF = ma

The net force is the applied force minus the force of friction:

ΣF = F_applied - F_friction

First, let's calculate the force of friction using the coefficient of kinetic friction (μ) and the normal force (N) exerted on the crate:

F_friction = μ * N

To calculate the normal force, we need to consider the weight (mg) of the crate and the vertical force exerted by the other crate:

N = mg + F_other_crate

Now let's plug in the numbers. The weight of the crate can be calculated as:

Weight = mass * gravitational acceleration

For the 75-kg crate:
Weight_75kg = 75 kg * 9.8 m/s^2

For the 110-kg crate:
Weight_110kg = 110 kg * 9.8 m/s^2

Now we can calculate the normal force exerted on the 75-kg crate:

N_75kg = Weight_75kg + F_other_crate

Similarly, we can calculate the normal force exerted on the 110-kg crate:

N_110kg = Weight_110kg + F_other_crate

Now that we have the normal forces, we can calculate the force of friction:

F_friction = μ * N

Using the given coefficient of kinetic friction μ = 0.15, we can calculate the force of friction.

Finally, we can substitute the values into ΣF = F_applied - F_friction and solve for the acceleration (a).

(b) To find the force that each crate exerts on the other, we can use Newton's third law, which states that the force exerted by object A on object B is equal in magnitude but opposite in direction to the force exerted by object B on object A.

Therefore, the force exerted by the 75-kg crate on the 110-kg crate is equal in magnitude to the force exerted by the 110-kg crate on the 75-kg crate. We can calculate this force using Newton's second law, F = ma, for each crate separately.

(c) To repeat the calculation with the crates reversed, we need to swap the mass values and recalculate everything using the new values.

Now, let's calculate all the values step by step. Could you please provide the value of the gravitational acceleration?

Sure, I can help you with this problem step by step.

(a) To calculate the acceleration of the system, we need to find the net force acting on it. The net force can be calculated by subtracting the force of friction from the applied force.

First, let's find the force of friction. The force of friction can be calculated using the formula:

Force of friction = coefficient of friction * normal force

The normal force is equal to the weight of the crate, which is the mass multiplied by the acceleration due to gravity (9.8 m/s^2).

For the 75-kg crate:
Force of friction = 0.15 * (75 kg * 9.8 m/s^2)

Now, we can calculate the net force:
Net force = applied force - force of friction

Net force = 620 N - (0.15 * (75 kg * 9.8 m/s^2))

Once we have the net force, we can calculate the acceleration using Newton's second law:

Net force = mass * acceleration

So, the acceleration of the system is:
Acceleration = Net force / (75 kg + 110 kg)

(b) To calculate the force that each crate exerts on the other, we can use Newton's third law, which states that for every action, there is an equal and opposite reaction.

Since the crates are in contact and at rest, the force that each crate exerts on the other will be equal in magnitude and opposite in direction.

(c) To repeat the calculations with the crates reversed, you need to switch the masses of the crates. So, the 75-kg crate becomes 110 kg, and the 110-kg crate becomes 75 kg. Repeat steps (a) and (b) using these new masses.

I hope this helps! Let me know if you have any further questions.

well push on the 75 and the 75 pushes on the 110

sum is 185 kg and it all accelerates at a
push force = p
p - 75 g*.15 - 110 g*.15 = 185 a
if g = 9.8
620 - 185 g*.15= 185 a
620 - 271= 185 a
a = 1.88 m/s^2

now the second one is accelerated at 1.88 m/s^2
so
Fbetween - m g*.15 = 1.88 m
Fbetween = m (1.88 + 1.47) = 3.35 m for either m