Two boxes, one acceleration
The acceleration of a system.
Pulling two boxes
You pull a box that is tied to a second box, on a smooth floor. Both boxes speed up together.
What mass do you think matters for how fast they speed up?
What this lesson covers
The idea
A system of connected objects accelerates like a single object of their total mass: a = F/(m1 + m2), where F is the external force on the system.
Pulling two boxes
You pull a box that is tied to a second box, on a smooth floor. Both boxes speed up together.
What mass do you think matters for how fast they speed up?
- The mass of both boxes together
- The mass of the first box only
- The mass of the string
Pull the system
Set the values asked for and read the acceleration.
Like one big object
The boxes moved together like a single object of mass m1 + m2. With a pull of 12 N and a total of 6 kg, the acceleration was 12 ÷ 6 = 2 m s⁻².
A system of connected objects accelerates like a single object of their total mass: a = F/(m1 + m2), where F is the external force on the system.
Notes
A connected system accelerates like one object of mass m1 + m2: a = F/(m1 + m2), with F the external force.
Check yourself
A force of 12 N pulls two boxes of 2 kg and 4 kg joined by a string. What is the acceleration of the system?
Answer: 2 m s⁻²
a = F/(m1 + m2) = 12 N ÷ 6 kg = 2 m s⁻².
A force of 20 N pulls two boxes of 3 kg and 2 kg joined by a string. What is the acceleration of the system?
Answer: 4 m s⁻²
a = F/(m1 + m2) = 20 N ÷ 5 kg = 4 m s⁻².
Which mass is used to find the acceleration of two boxes joined by a string?
Two connected boxes are pulled by an external force. How do they accelerate?
- The mass of Box 1 only. The system accelerates like a single object of the total mass.
- The total mass, m1 + m2 — correct. Yes!
- The difference of the masses, m1 − m2. The masses of connected objects add up: the total mass is m1 + m2.
- Each with the acceleration F divided by its own mass, differently. The boxes are joined, so they move together with one acceleration, F divided by m1 + m2.
- With no acceleration, because the tension balances F. The tension is an internal force. The external force F gives the system an acceleration.
- Like a single object of mass m1 + m2 — correct. Yes!