Finding Acceleration with Unknown Force & Mass

In summary, the acceleration of an object with a mass of m2-m1 would be the difference between the acceleration of an object with a mass of m1 and the acceleration of an object with a mass of m2, which is equal to F/8.2. Similarly, the acceleration of an object with a mass of m2+m1 would be the sum of the accelerations of an object with a mass of m1 and an object with a mass of m2, which is equal to F/16.2.
  • #1
mcdowellmg
55
0

Homework Statement



"A certain force gives an object of mass m1 an acceleration of 12.2 m/s^2 and an object of mass m2 an acceleration of 4 m/s^2. What acceleration would the force give to an object of mass m2-m1, and also of an object of mass m2+m1?"

Homework Equations



acceleration = force/mass

The Attempt at a Solution




I deduced that a = F/(m2-m1). From there, I calculated that a*m2 = a*m1, because the F is the same throughout. I worked a little algebra...4*m2 = 12.2*m1, so 4/12.2*m2 = m1. That means that m1 is .32787 of m2, and thus m2 - m1 would leave an "m3" that is .67213 of m2. I tried to apply this to the acceleration by calculating .67213*4...getting an acceleration of 2.7, but that would mean m3 is greater than m2 in mass...which could not be possible. I guess I am getting a little lost in my own (il)logic. Any ideas?

Thanks!
 
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  • #2
welcome to pf!

hi mcdowellmg! welcome to pf! :smile:

(try using the X2 and X2 icons just above the Reply box :wink:)
mcdowellmg said:
I deduced that a = F/(m2-m1).

uhh? what is a? :confused:

start again, and first convert the following words into two equations:
"A certain force gives an object of mass m1 an acceleration of 12.2 m/s^2 and an object of mass m2 an acceleration of 4 m/s^2.
 
  • #3
a is acceleration, sorry!

12.2*m1 = F and 4*m2 = F, so I know that 12.2*m1 = 4*m2, because F is the same throughout. After that, I'm stuck...and frustrated!

Thanks!
 
  • #4
mcdowellmg said:
a is acceleration, sorry!

12.2*m1 = F and 4*m2 = F, so I know that 12.2*m1 = 4*m2, because F is the same throughout. After that, I'm stuck...and frustrated!

Thanks!
So m1= F/12.2 and m2= F/4. Now m1- m2= F/12.2- F/4= F/?
 
  • #5
m2-m1 = F/8.2 ?

Am I not able to get an actual number?
 
  • #6
look at the question! :rolleyes:

it doesn't ask for m2 - m1, it only asks for the acceleration of such a mass

which is … ? :smile:
 
  • #7
Oops! So it is as simple as subtracting the accelerations to get 8.2? I find that hard to believe! I guess I made it too complicated. Thanks.
 
  • #8
yes and no

unfortunately, your previous equation was wrong :redface: …
HallsofIvy said:
So m1= F/12.2 and m2= F/4. Now m1- m2= F/12.2- F/4= F/?
mcdowellmg said:
m2-m1 = F/8.2

try it again …

carefully! :rolleyes:​
 

Related to Finding Acceleration with Unknown Force & Mass

1. What is acceleration and how is it related to force and mass?

Acceleration is the rate of change of an object's velocity. It is directly proportional to the net force acting on the object and inversely proportional to its mass. This means that a larger force will result in a greater acceleration, while a larger mass will result in a smaller acceleration.

2. How do you calculate acceleration when the force and mass are unknown?

To calculate acceleration when the force and mass are unknown, we can use Newton's second law of motion: F = ma. By measuring the object's acceleration and using the known value of the acceleration due to gravity (9.8 m/s^2), we can solve for the unknown force or mass.

3. Can you find acceleration without knowing the force or mass?

Yes, it is possible to find acceleration without knowing the force or mass. As mentioned before, we can use Newton's second law of motion to solve for the unknown force or mass. Additionally, if the object is in freefall, we can use the equation a = g to find the acceleration due to gravity without knowing the force or mass.

4. What are some common units of measurement for acceleration?

The most common unit of measurement for acceleration is meters per second squared (m/s^2). Other units include feet per second squared (ft/s^2) and kilometers per hour squared (km/h^2).

5. How does friction affect acceleration in this scenario?

Friction is a force that opposes motion and acts in the opposite direction of an object's velocity. In this scenario, friction would act to decrease the object's acceleration. This is because friction is a force that needs to be overcome by the applied force in order for the object to accelerate. Therefore, a greater amount of friction would result in a smaller acceleration.

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