Three blocks are located on a horizontal frictionless table. They are connected by a massless cord, as shown in the figure, and pulled to the right. The masses of the three blocks are m1 = 8 kg, m2 = 33 kg, and m3 = 49 kg. The pulling force is equal to T3 = 89 N. What is the acceleration of the system?
I know the equation is m(a+g). I keep getting the wrong answer. Help!
no friction, so why is gravity involved?
f = m a
89 = (8 + 33 + 49) a
To find the acceleration of the system, you need to consider the net force acting on the system. In this case, the net force is the tension force T3 pulling on block 3, minus the force due to the mass of the system.
Let's break down the steps to solve this problem:
1. Find the force due to the mass of the system:
The force due to the mass of the system is simply the sum of the individual masses multiplied by the acceleration due to gravity (g).
F_mass = (m1 + m2 + m3) * g
2. Find the net force:
The net force is the tension force T3 minus the force due to the mass of the system.
F_net = T3 - F_mass
3. Use Newton's second law to relate net force and acceleration:
Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
F_net = (m1 + m2 + m3) * a
4. Equate the net force found in step 2 to the net force in step 3 and solve for acceleration:
Set F_net from step 2 equal to F_net from step 3 and solve for acceleration (a).
T3 - F_mass = (m1 + m2 + m3) * a
Plugging in the known values:
89 N - (8 kg + 33 kg + 49 kg) * g = (8 kg + 33 kg + 49 kg) * a
You can now solve for acceleration (a).
Remember to use the correct value for the acceleration due to gravity (g), which is typically 9.8 m/s². Substitute that value into the equation and solve for the acceleration (a).