The coefficients of static and kinetic friction between a 476 N crate and the ware house floor are 0.615 abd 0.420, repectively. A worker gradually increases his horizontal push against this crate utnil it just begins to move and from them on maintains that same maximum push. What is the acceleration of the crate after it has begun to move?

Netforce=ma
mg(mus-muk)=ma
solve for a

so I got 476 (9.8) (0.615-0.420) = ma

but what is the other m ???

There is only one mass, M, and it equals the weight divided by g, which is 48.6 kg.

The equation you wrote is the correct one after motion starts.

The force needed to start it moving is
Mg *(mu,stat) = 292.7 N, After it starts moving, the friction force becomes
Mg*(mu,kin) = 199.9 N
The net accelerating force is then
292.7 - 199.9 = 92.8 N. Divide that by M = 48.6 kg for the acceleration.

so i got 1.91 is the right?

absolutely right!

Well, hello there! It seems like you're having a mathematical conundrum. But don't worry, I'm here to help...or at least make you laugh while doing it!

Now, to answer your question, the other "m" in your equation stands for the mass of the crate. You see, "m" represents the same variable on both sides of the equation because we're using Newton's second law, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration.

So, to find the acceleration of the crate, you need to know the mass of the crate. Once you have that little piece of the puzzle, you can plug it in to get your answer.

Remember, the coefficient of friction is just a factor that relates to the type of surfaces in contact, while the actual force depends on the mass of the crate.

I hope that clears things up while bringing a smile to your face!

To solve for the acceleration of the crate after it has begun to move, we can 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 (F = ma).

In this case, the net force on the crate is determined by the difference between the force of static friction (Fs) and the force of kinetic friction (Fk). When the crate is at rest, the maximum static friction is keeping it from moving. Once it starts moving, the force of kinetic friction comes into play.

Given that the coefficient of static friction (μs) is 0.615 and the coefficient of kinetic friction (μk) is 0.420, we can calculate the net force as follows:

Fs = μs * mg
Fk = μk * mg
Net force (F) = Fs - Fk

Here, m represents the mass of the crate. It is important to note that m will cancel out when we solve for acceleration.

To determine the mass of the crate (m), we can use the formula:

m = F / g

Where F is the weight of the crate (mg), and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Now, let's calculate the net force and the mass of the crate:

Net force (F) = (0.615 - 0.420) * 476 * 9.8 N
Mass (m) = (476 * 9.8 N) / 9.8 m/s^2

By plugging in the given values, we can find the net force and the mass of the crate. Then, we can substitute these values into the equation F = ma to solve for acceleration (a).