Calculate Frictional Force to Estimate Crate Mass

[zellster87]

Homework Statement

You see the boy next door trying to push a crate down the sidewalk. He can barely keep it moving, and his feet occasionally slip. You start to wonder how heavy the crate is. You call to ask the boy his mass, and he replies " 45.0 kg." From your recent physics class you estimate that the static and kinetic coefficients of friction are 0.900 and 0.4 for the boy's shoes, and 0.5 and 0.2 for the crate.

Estimate the mass of the crate.

Homework Equations

frictional force = mu * normal force

The Attempt at a Solution

I've tried rearanging the above force in order to fit with what I have. But I just cannot seem the relate the given data into one equation. An help will be much appreciated, thanks for your time.

 

[anathema]

Hello! It seems like you are on the right track. In order to estimate the mass of the crate, we can use the equation for frictional force you have mentioned. Let's break it down into two parts: the force due to the boy's shoes and the force due to the crate's shoes.

First, let's look at the force due to the boy's shoes. We can use the equation F = mu * N, where F is the frictional force, mu is the coefficient of friction, and N is the normal force (in this case, the force exerted by the sidewalk on the boy's shoes). We can rewrite this as N = F/mu. Now, we know that the boy's shoes have a coefficient of friction of 0.4, so we can plug that in and solve for N. N = F/0.4.

Next, let's look at the force due to the crate's shoes. We can use the same equation, but this time we will use the coefficient of friction for the crate's shoes (0.2). So, N = F/0.2.

Now, we can set these two equations equal to each other, since they are both equal to the normal force. So, F/0.4 = F/0.2. We can rearrange this to solve for F, the force of friction. F = (0.4/0.2) * F. This simplifies to F = 2F. This means that the force of friction on the crate is twice the force of friction on the boy's shoes.

Now, we can use this relationship to estimate the mass of the crate. Since the boy's mass is given as 45.0 kg, we know that the force of friction on his shoes is equal to 45.0 kg * 9.8 m/s^2 (the acceleration due to gravity). This gives us a force of friction of 441 N.

Since we know that the force of friction on the crate is twice this amount, we can estimate that the mass of the crate is around 90 kg. Of course, this is just an estimate and there may be other factors at play, but it gives us a good starting point to work with. I hope this helps! Let me know if you have any further questions.

 

[Moetasim]

As a scientist, it is important to use the appropriate equations and units to accurately solve a problem. In this case, we can use the equation for frictional force, which is equal to the coefficient of friction (mu) multiplied by the normal force. The normal force in this case would be the weight of the crate, which we can calculate using the boy's mass (45.0 kg) and the acceleration due to gravity (9.8 m/s^2).

Next, we can use the given coefficients of friction for both the boy's shoes and the crate to calculate the frictional force acting on the crate. Since the boy's feet are slipping occasionally, we can assume that the crate is in motion, so we will use the kinetic coefficient of friction (0.2) for the crate.

frictional force = mu * normal force

frictional force = (0.2)(45.0 kg)(9.8 m/s^2)

frictional force = 88.2 N

Now, using the same equation, we can solve for the normal force acting on the crate by setting the frictional force equal to the force of the boy pushing the crate (since he is just barely able to keep it moving).

frictional force = mu * normal force

88.2 N = (0.4)(45.0 kg)(9.8 m/s^2)

normal force = 110.3 N

Finally, we can calculate the weight of the crate (normal force) and use it to estimate the mass of the crate.

weight = mass * acceleration due to gravity

110.3 N = mass * 9.8 m/s^2

mass = 11.3 kg

Therefore, the estimated mass of the crate is 11.3 kg. It is important to note that this is an estimate, as there may be other factors (such as air resistance or uneven surfaces) that can affect the actual weight of the crate.