Two carts roll toward each other: a 3.0 kg cart at 2.5 m/s rightward, and a 1.5 kg cart at 3.0 m/s leftward. Each cart has its own momentum. The system of both carts has one momentum of its own.
A system's total momentum is the sum of its objects' momenta, added with their signs. Signs need a declared positive direction, the same convention you used when you first signed momenta along a line: pick a positive direction, and motion the other way is negative.
Take rightward as positive. Every momentum in this problem now carries a sign.
The 3.0 kg cart moves right at 2.5 m/s: p_1 = +7.5 kg·m/s.
The 1.5 kg cart moves left at 3.0 m/s: p_2 = −4.5 kg·m/s.
The total momentum is the signed sum: p_total = p_1 + p_2.
Here, p_total = 7.5 + (−4.5) = +3.0 kg·m/s. The system's momentum points rightward.
The table below keeps the bookkeeping honest: one row per object, with mass, signed velocity, and signed momentum, and the total on the last row.
A wrong sign is the only way this calculation goes wrong. Sign each momentum from the declared positive direction before adding.
Take rightward as positive. A 3.0 kg cart moves right at 2.5 m/s and a 1.5 kg cart moves left at 3.0 m/s. Calculate the total momentum of the two-cart system.
Write down the values in the question:
Take rightward as positive.
m_1 = 3.0 kg, v_1 = +2.5 m/s
m_2 = 1.5 kg, v_2 = −3.0 m/s
p_total = ?
Find each momentum:
p_1 = 3.0 × 2.5
p_1 = +7.5 kg·m/s
p_2 = 1.5 × (−3.0)
p_2 = −4.5 kg·m/s
Write down the equation:
p_total = p_1 + p_2
Substitute in the values:
p_total = 7.5 + (−4.5)
Simplify:
p_total = +3.0 kg·m/s, rightward
The system's total momentum is +3.0 kg·m/s, pointing rightward.
The same two carts, now both moving rightward: the 3.0 kg cart at 2.5 m/s and the 1.5 kg cart at 3.0 m/s. Calculate the total momentum.
Both velocities are now positive:
p_1 = +7.5 kg·m/s
p_2 = +4.5 kg·m/s
Write down the equation:
p_total = p_1 + p_2
Substitute in the values:
p_total = 7.5 + 4.5
Simplify:
p_total = +12 kg·m/s, rightward
The system's total momentum is +12 kg·m/s, pointing rightward.
Take rightward as positive. A 3.5 kg wagon moves right at 3.0 m/s, and a 2.0 kg wagon moves left at 2.0 m/s. Enter the total momentum of the two-wagon system in kg·m/s.
Take eastward as positive. A 4.0 kg puck slides east at 1.5 m/s, and a 1.0 kg puck slides east at 3.5 m/s. Enter the total momentum of the two-puck system in kg·m/s.
Take rightward as positive. A 0.5 kg ball rolls right at 6.0 m/s, and a 1.0 kg ball rolls left at 3.0 m/s. Enter the total momentum of the two-ball system in kg·m/s.
Take northward as positive. A 2.5 kg cart moves northward at 4.0 m/s, and a 1.5 kg cart moves southward at 2.0 m/s. Enter the total momentum of the two-cart system in kg·m/s.
Take rightward as positive. Three carts roll on one track: a 1.0 kg cart moves right at 6.0 m/s, a 2.2 kg cart moves right at 2.5 m/s, and a 0.5 kg cart moves left at 5.0 m/s. Enter the total momentum of the three-cart system in kg·m/s.
Take eastward as positive. A 6.0 kg bowling ball rolls west at 3.0 m/s, and a 2.0 kg ball rolls east at 5.0 m/s. Enter the total momentum of the two-ball system in kg·m/s.