3. A force of 36 N gives a mass m1 an acceleration of 4.0 m/s2. The same force gives a mass m2 an acceleration of 12 m/s2. What acceleration will this force give to m1 and m2 if the two masses are fastened together? {3.0 m/s2}
36=m1*4
36=m2*12
m1=9kg
m2=3kg
36=(9+3)a
a=36/12= 3m/s^2
36 N and a mass of 6 kg
Well, it seems like m1 and m2 really want to be closer, like a dynamic duo! When they're fastened together, they become a powerful force to be reckoned with.
Now, if we want to find the acceleration when m1 and m2 are fastened together, we can use the law of Wile E. Newton. The total force is the sum of the forces on m1 and m2 individually.
So, we have:
Force on m1 = m1 * acceleration on m1
Force on m2 = m2 * acceleration on m2
Since the force is the same, we can equate the two equations:
m1 * acceleration on m1 = m2 * acceleration on m2
Now, let's plug in some numbers. We know that the force is 36 N, the acceleration on m1 is 4.0 m/s², and the acceleration on m2 is 12 m/s².
So, we have:
m1 * 4.0 = m2 * 12
Now, we're given the ratio of the masses m1 to m2 is 3.0. Let's call the mass of m1 "3x" and the mass of m2 "x". Since they're fastened together, the total mass is 4x.
So, we have:
3x * 4.0 = x * 12
Simplifying the equation:
12x = 12x
It seems like x is having a great day, canceling out on both sides! So, no matter the mass values, the acceleration when m1 and m2 are fastened together will always be the same.
And the answer is... drumroll, please... 3.0 m/s²! So, m1 and m2 combine their forces, becoming a united front with a simultaneous acceleration of 3.0 m/s². They're truly a force to be reckoned with!
I hope that explanation brought a smile to your face!
To find the acceleration when the two masses are fastened together, we need to use Newton's second law of motion. This law states that the force on an object is equal to the mass of the object multiplied by its acceleration.
We are given that a force of 36 N gives mass m1 an acceleration of 4.0 m/s^2 and mass m2 an acceleration of 12 m/s^2. Let's denote the combined mass of m1 and m2 as M.
According to Newton's second law, we can set up the following equations:
36 N = m1 * 4.0 m/s^2 (equation 1)
36 N = m2 * 12 m/s^2 (equation 2)
To find the acceleration when the two masses are fastened together, we need to determine the total force exerted and the combined mass. Since the force remains the same, we can add equation 1 and equation 2:
36 N + 36 N = m1 * 4.0 m/s^2 + m2 * 12 m/s^2
72 N = 4.0 * m1 + 12 * m2
Next, we need to consider the combined mass M. The combined mass is simply the sum of m1 and m2:
M = m1 + m2
Now, we can substitute the expression for M into the equation:
72 N = 4.0 * m1 + 12 * (M-m1)
Expanding the equation:
72 N = 4.0 * m1 + 12M - 12m1
We then simplify the equation:
72 N = 12M - 8m1
Now, let's rearrange the equation to solve for m1:
8m1 = 12M - 72 N
m1 = (12M - 72 N) / 8
Finally, substituting the expression for combined mass M:
m1 = (12(m1 + m2) - 72 N) / 8
Simplifying further:
m1 = (12m1 + 12m2 - 72 N) / 8
Multiplying through by 8:
8m1 = 12m1 + 12m2 - 72 N
Subtracting 12m1 from both sides:
-4m1 = 12m2 - 72 N
Dividing both sides by -4:
m1 = (12m2 - 72 N) / -4
Simplifying:
m1 = (-3m2 + 18 N)
Now, we have the expression for m1 in terms of m2. To find the acceleration when the two masses are fastened together, we can substitute this value of m1 into either equation 1 or equation 2.
Let's use equation 1:
36 N = (-3m2 + 18 N) * 4.0 m/s^2
Now, we can solve for m2:
36 N = -12m2 + 72 N
-12m2 = -36 N + 72 N
-12m2 = 36 N
Dividing through by -12:
m2 = -3 N
Finally, we substitute this value of m2 back into the expression for m1:
m1 = (-3m2 + 18 N)
= (-3 * -3 N + 18 N)
= (9 N + 18 N)
= 27 N
Therefore, the acceleration when the two masses are fastened together is:
a = (force) / (mass)
= (36 N) / (27 N)
= 1.33 m/s^2
So, the acceleration will be approximately 1.33 m/s^2 when the two masses are fastened together.