A resultant force of 20 N gives a body of mass m an acceleration of 8 m/s^2 and a body of mass m' acceleration of 24 m/s^2. What acceleration will this force cause the two masses to acquire if fastened together.
F = 20N
A1 = 8 m/s^2
A2 = 24 m/s^2
F = ma
M1 = F/A1
M1 = 20N/8 m/s^2
M1 = 2.25 kg
F = ma
M2 = F/A2
M2 = 20N/ 24 m/s^2
M2 = 0.83 kg
M1 + M2 = 3.33 kg
a = F/M
a = 20N / 3.33 kg
a = 6.01 m/s^2
F=20N
a1=8m/s^2
a2=24m/s^2
Let mass in first case be m1,
and mass in second case be m2.
1st case,
F=m1a2
m1=F/a1
=20/8
=5/2
2nd case,
F=m2a2
m2=F/a2
=20/24
=5/6
Total mass=m1+m2
=5/2 + 5/6
=10/3
a=F/total mass
=20/10/3
=20×3/10
=60/10
=6m/s^2.
F = 20N
A1 = 8 m/s^2
A2 = 24 m/s^2
F = ma
M1 = F/A1
M1 = 20N/8 m/s^2
M1 = 2.50 kg
F = ma
M2 = F/A2
M2 = 20N/ 24 m/s^2
M2 = 0.83 kg
M1 + M2 = 3.33 kg
a = F/M
a = 20N / 3.33 kg
a = 6.01 m/s^2
Correct 👍👍
Well, let me put on my thinking clown nose for this one! When you fasten those two masses together, you've got a classic case of teamwork. It's time for some physics acrobatics!
To find the combined acceleration, we need to consider the individual accelerations of the masses, let's call them m and m'.
Given that a force of 20 N causes mass m to accelerate at 8 m/s^2, we can use Newton's second law (F = ma) to find the mass m.
20 N = m * 8 m/s^2
Now, using the same force of 20 N and the new acceleration of 24 m/s^2 for mass m', we can find mass m'.
20 N = m' * 24 m/s^2
Once we know the masses m and m', we can find the combined acceleration by using the principle of conservation of momentum.
Now, let me do some clown calculations behind the curtain...
*drum roll*
Ta-da! The resulting acceleration when the masses are fastened together is the total force divided by the total mass.
Combined acceleration = 20 N / (m + m')
So, with the information given, we can't determine the specific acceleration without knowing the masses m and m'. If you provide that extra information, I would be delighted to calculate the final result for you!
To find the acceleration when the two masses are fastened together, we need to use the concept of Newton's second law, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Let's first calculate the individual accelerations of the two masses using the given information.
For the body with mass m:
Force (F1) = 20 N
Acceleration (a1) = 8 m/s^2
We can rearrange Newton's second law to solve for mass:
F1 = m * a1
m = F1 / a1
m = 20 N / 8 m/s^2
m = 2.5 kg
Similarly, for the body with mass m':
Force (F2) = 20 N
Acceleration (a2) = 24 m/s^2
Using Newton's second law:
F2 = m' * a2
m' = F2 / a2
m' = 20 N / 24 m/s^2
m' = 0.833 kg
Now that we have the masses of the two bodies, we can calculate the acceleration when they are fastened together.
When two masses are connected and move together, the net force acting on them is the sum of the individual forces:
Net Force (F_net) = F1 + F2
F_net = 20 N + 20 N
F_net = 40 N
The total mass of the combined system is the sum of the individual masses:
Total mass (m_total) = m + m'
m_total = 2.5 kg + 0.833 kg
m_total = 3.333 kg
Using Newton's second law:
F_net = m_total * a_total
a_total = F_net / m_total
a_total = 40 N / 3.333 kg
a_total = 12 m/s^2
Therefore, when the two masses are fastened together, the resultant force of 20 N will cause them to acquire an acceleration of 12 m/s^2.