An empty shopping cart gains speed easily. The same cart loaded with bags, moved with the same net force, gains speed far more slowly. The force did not change. What did?
The last lesson changed the net force and held the mass. Now flip it: hold the net force and change only the mass.
Keep the net force at 18 N and change only the cart's mass.
With a mass of 6.0 kg, the acceleration is 3.0 m/s².
Double the mass to 12 kg, same net force: the acceleration halves, to 1.5 m/s².
Double it again, to 24 kg: the acceleration halves again, to 0.75 m/s².
So with the net force unchanged, doubling the mass of the cart halves its acceleration.
In general: with the net force held the same, increasing the mass causes the acceleration to decrease.
The mass of a cart increases while the net force on it stays the same. What happens to the cart's acceleration?
This is inertia in the numbers. Mass measures the tendency to keep the current velocity, so the same net force changes a larger mass's velocity more slowly.
A cart accelerates at 1.8 m/s². Its mass is doubled, and the net force on it stays the same. Enter the new acceleration in m/s².
An empty trailer accelerates at 3.6 m/s². Loaded, its total mass is three times as large, with the net force on it unchanged. Enter the new acceleration in m/s².
The pair of lessons now reads as one pattern: more net force, proportionally more acceleration; more mass, proportionally less.
An empty canoe accelerates at 3.3 m/s² under a steady net force. Loaded, its total mass is three times as large, and the net force on it is the same. What is its acceleration now?
Write down the values:
old acceleration = 3.3 m/s²; the mass is tripled; the net force is unchanged; new acceleration = ?
With the net force unchanged, tripling the mass cuts the acceleration to one third:
a = 3.3 ÷ 3 = 1.1
The loaded canoe's acceleration is 1.1 m/s².
A rowboat accelerates at 0.8 m/s². Its load is removed, halving its total mass, and the net force on it stays the same. Enter the new acceleration in m/s².
The net force on a wagon stays the same while its mass changes. Which statement is correct?
An airport luggage cart of mass 30 kg accelerates at 2.0 m/s² under a steady net force. Bags are stacked on until the total mass is 60 kg, with the net force unchanged. Enter the new acceleration in m/s².