Three bolocks are connected(mass_1 on the left connected to mass_2 with a string which is T_1. Mass_2 is connected to Mass_3 with a string, T_2. the force is holding on to T_3 which is connected to mass_3) and pulled to the right on a horizontal frictionless table by a force witha magnitude of T_3=65N. If m_1= 12 kg, m_2 =24 kg and m_3= 31 kg, what is a) acceleration of the sysem and b) tensions T_1 AND C) T_2 in the inerconnecting cords.
what is the formula I would use to find a? Is it a= F/m? for the tensions how would I find them?
I assume you are ignoring friction. If so, then acceleration=force/total mass.
Now, the tensions on each cord or spring pulling some masses is given by
tension=massespulled*acceleration.
The masses pulled is the mass being pulled. For instance, The string pulling mass1 and mass2 is
Tension=(M2+M1)*acceleration.
To find the acceleration of the system, you can use Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, the net force is the force applied by T3, and the mass is the sum of all three masses (m1 + m2 + m3).
a = F_net / total mass
Substituting the given values, we have:
a = T3 / (m1 + m2 + m3)
= 65 N / (12 kg + 24 kg + 31 kg)
To find the tensions T1 and T2 in the interconnecting cords, you can use the same reasoning. The tension in the string connecting m1 and m2 (T1) is equal to the total mass of m1 and m2 multiplied by the acceleration. Similarly, the tension in the string connecting m2 and m3 (T2) is equal to the total mass of m2 and m3 multiplied by the acceleration.
T1 = (m1 + m2) * a
T2 = (m2 + m3) * a
Substituting the given values, we have:
T1 = (12 kg + 24 kg) * a
T2 = (24 kg + 31 kg) * a
Now, you can substitute the value of acceleration (found in the previous step) in these equations to calculate the tensions T1 and T2.