a 72N force accelerates mass m, by 5.0 m/s^2 the same force acts on another mass m2 and imparts to it an acceleration of 20.0 m/s^2. what acceleration will the same force impart to the two masses when they are joined?
To find the acceleration when the two masses are joined, we can use the principle of Newton's second law, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Let's denote the first mass as m1 and the second mass as m2.
According to the problem, a force of 72 N is applied to mass m1, giving it an acceleration of 5.0 m/s^2.
Using the formula F = m1 * a1, we can rearrange it to solve for mass m1:
m1 = F / a1 = 72 N / 5.0 m/s^2 = 14.4 kg.
Similarly, the same 72 N force is applied to mass m2, giving it an acceleration of 20.0 m/s^2.
Using the formula F = m2 * a2, we can solve for mass m2:
m2 = F / a2 = 72 N / 20.0 m/s^2 = 3.6 kg.
Now, let's find the acceleration when the two masses are joined. Since the force acting on the combined masses is still 72 N, we can calculate the total mass (m_total) of the combined masses:
m_total = m1 + m2 = 14.4 kg + 3.6 kg = 18 kg.
Finally, we can find the acceleration (a_total) using the formula F = m_total * a_total:
a_total = F / m_total = 72 N / 18 kg = 4.0 m/s^2.
Therefore, when the two masses are joined, the same force will impart an acceleration of 4.0 m/s^2.
To find the acceleration when the two masses are joined, we need to use the concept of Newton's second law of motion, which states that the force on an object is equal to its mass times its acceleration.
We are given the following information:
- Force (F) = 72 N
- Acceleration of one mass (m) = 5.0 m/s^2
- Acceleration of another mass (m2) = 20.0 m/s^2
First, let's find the mass (m):
Using the formula F = m * a, we can rearrange it to solve for mass (m):
m = F / a
Substituting the given values:
m = 72 N / 5.0 m/s^2
m = 14.4 kg
Now, let's find the mass (m2):
Using the same formula:
m2 = F / a
m2 = 72 N / 20.0 m/s^2
m2 = 3.6 kg
Next, let's find the combined mass when the two masses are joined:
The combined mass is simply the sum of the two masses:
m_total = m + m2
m_total = 14.4 kg + 3.6 kg
m_total = 18 kg
Finally, let's find the acceleration when the two masses are joined:
Using the same formula (F = m * a), we can rearrange it to solve for acceleration (a):
a = F / m_total
Substituting the given force and the combined mass:
a = 72 N / 18 kg
a = 4.0 m/s^2
Therefore, when the two masses are joined, the same force will impart an acceleration of 4.0 m/s^2 to the combined masses.
F = M*a, M1 = F/a = 72/5 = 14.4 kg.
M2 = 5/20 * M1 = 5/20 * 14.4 kg = 3.6 kg
a = F/(M1+M2) = 72/(14.4+3.6) =