Linear momentum Transitional Reasoning Practice

Questions

1. 1.

   During a safety test, a stationary explosive capsule rests on a frictionless horizontal surface. An internal trigger detonates the capsule, splitting it into three fragments that slide across the surface. Immediately after detonation, fragment X of mass 2.0 kg travels due north at 4.0 m/s, and fragment Y of mass 3.0 kg travels due east at 2.0 m/s. Assuming no external horizontal forces act on the system, what is the magnitude of the linear momentum of the third fragment?

   • A) 2.0 kg·m/s
   • B) 10 kg·m/s
   • C) 14 kg·m/s
   • D) 24 kg·m/s
2. 2.

   In a bulk-handling facility, an empty cart of mass 15 kg glides along a straight horizontal track at a constant speed of 8.0 m/s with negligible friction. As it passes beneath a stationary chute, granular feed drops vertically into the cart until the combined mass of the cart and feed reaches 40 kg. Assuming the falling feed enters the cart with zero horizontal velocity, what is the magnitude of the linear momentum of the feed collected in the cart once it is fully loaded?

   • A) 45 kg·m/s
   • B) 75 kg·m/s
   • C) 120 kg·m/s
   • D) 200 kg·m/s
3. 3.

   A motorized rail trolley of mass 50 kg travels along a straight horizontal track with an initial velocity of 4.0 m/s east. A propulsion booster activates, exerting a net forward horizontal force whose magnitude increases linearly from 0 N to 120 N over a 5.0-second time interval. Assuming all resistive forces along the track are negligible, what is the magnitude of the trolley's linear momentum at the end of this 5.0-second interval?

   • A) 300 kg·m/s
   • B) 500 kg·m/s
   • C) 600 kg·m/s
   • D) 800 kg·m/s
4. 4.

   Two automated test sleds, sled X of mass 4.0 kg and sled Y of mass 9.0 kg, are positioned at rest on parallel, frictionless horizontal tracks. Starting at the same instant, each sled is propelled along its track by an identical constant net forward horizontal force of 18 N for a duration of 3.0 seconds. What is the ratio of the magnitude of the linear momentum of sled X to that of sled Y at the end of this 3.0-second interval?

   • A) 0.44
   • B) 1.0
   • C) 1.5
   • D) 2.25
5. 5.

   During a track test of an autonomous delivery rover, the 25 kg vehicle enters a horizontal turn traveling due north at 16 m/s. It completes the turn and exits traveling due east at 12 m/s. What is the magnitude of the change in the rover's linear momentum across this maneuver?

   • A) 500 kg·m/s
   • B) 100 kg·m/s
   • C) 700 kg·m/s
   • D) 400 kg·m/s
6. 6.

   During a field calibration test, a small atmospheric probe of mass 0.50 kg is launched from level ground across an open test range. At the peak of its trajectory, instruments record the magnitude of its linear momentum as 12 kg·m/s. Assuming air resistance is negligible, the probe returns to ground level with a final speed of 30 m/s. What was the magnitude of the vertical component of the probe's linear momentum at launch?

   • A) 3.0 kg·m/s
   • B) 6.0 kg·m/s
   • C) 9.0 kg·m/s
   • D) 15 kg·m/s
7. 7.

   An automated transport shuttle consisting of a 600 kg motorized cab and a 400 kg trailing wagon travels together along a straight horizontal track at a constant velocity of 5.0 m/s east. An internal mechanism acts between the two sections to partially brake the wagon, reducing its velocity to 2.0 m/s east while pushing the motorized cab forward along the same line. Assuming all external resistive forces along the track are negligible, what is the magnitude of the linear momentum of the motorized cab after this separation?

   • A) 1200 kg·m/s
   • B) 3000 kg·m/s
   • C) 3800 kg·m/s
   • D) 4200 kg·m/s
8. 8.

   During a harbor docking trial, an automated freight ferry with a total mass of $4.0 \times 10^4\text{ kg}$ moves toward a reinforced pier fender at a speed of 0.80 m/s. Upon striking the elastic fender, the ferry comes to a momentary stop and rebounds directly away from the pier along the same straight line at 0.30 m/s. What is the magnitude of the change in the ferry's linear momentum resulting from the interaction with the fender?

   • A) $4.4 \times 10^4\text{ kg}\cdot\text{m/s}$
   • B) $2.0 \times 10^4\text{ kg}\cdot\text{m/s}$
   • C) $3.2 \times 10^4\text{ kg}\cdot\text{m/s}$
   • D) $1.2 \times 10^4\text{ kg}\cdot\text{m/s}$
9. 9.

   A robotic inspection rover with a total mass of 20 kg moves across a flat factory floor with velocity components of 6.0 m/s along the x-axis and 8.0 m/s along the y-axis. Operators load additional diagnostic tools onto the rover, increasing its total mass by 5.0 kg, and reprogram it so that its new linear momentum has the same magnitude as its initial linear momentum but points entirely along the positive x-axis. What is the rover's new speed?

   • A) 8.0 m/s
   • B) 6.4 m/s
   • C) 4.8 m/s
   • D) 10.0 m/s
10. 10.

    In a logistics testing facility, a transport cart of mass 120 kg travels along a straight track at a constant velocity of 2.0 m/s. An engineer configures a lighter inspection cart of mass 40 kg on the same straight path such that its kinetic energy is three times that of the transport cart. Assuming resistive forces are negligible, what is the magnitude of the linear momentum of the inspection cart?

    • A) 80 kg·m/s
    • B) 120 kg·m/s
    • C) 160 kg·m/s
    • D) 240 kg·m/s

Answers and step-by-step solutions appear after you finish the test.