Impulse Transitional Reasoning Practice

Questions

1. 1.

   In an industrial surface-treatment facility, a calibration nozzle directs a continuous stream of spherical metal pellets perpendicularly against a rigid, stationary armor plate. The nozzle releases pellets of mass 0.025 kg at a steady rate of 50 pellets per second, each striking the plate at 20 m/s and rebounding along its incident line of motion at 12 m/s. Assuming external resistive forces during the rapid impacts are negligible, what is the magnitude of the total impulse delivered to the plate by the pellets over a 3.0-second testing interval?

   • A) 120 N·s
   • B) 75 N·s
   • C) 40 N·s
   • D) 30 N·s
2. 2.

   During an ice hockey match analysis, a tracking system records a 0.16 kg puck sliding across frictionless ice at 25 m/s before striking a straight, rigid boundary board. The puck impacts the board at an angle of 30° relative to the board's surface and rebounds elastically at the same speed of 25 m/s and at an angle of 30° relative to the surface. What is the magnitude of the impulse delivered to the puck by the board during the impact?

   • A) 4.0 N·s
   • B) 2.0 N·s
   • C) 6.9 N·s
   • D) 8.0 N·s
3. 3.

   During a barrier impact assessment, an accelerometer monitors a 1000 kg test car entering a staged crumple barrier at a speed of 16 m/s along a straight, horizontal track. The barrier exerts an opposing horizontal force in two consecutive stages, bringing the car completely to rest in a total time of 0.30 s. Telemetry indicates that the first stage lasts 0.10 s with an average retarding force of 70 kN, followed immediately by the second stage lasting 0.20 s. What is the average retarding force exerted by the barrier during the second stage?

   • A) 45 kN
   • B) 80 kN
   • C) 115 kN
   • D) 30 kN
4. 4.

   An aerospace test sled of mass 200 kg travels along a straight, horizontal track at an initial speed of 18 m/s before engaging an arresting cable system. The opposing horizontal force exerted by the cable increases linearly from zero to a peak value $F_{\text{max}}$ over 0.30 s and then decreases linearly back to zero over 0.50 s, bringing the sled completely to rest. Assuming other resistive forces are negligible, what is the peak force $F_{\text{max}}$ exerted on the sled during the arrest?

   • A) 4.5 kN
   • B) 9.0 kN
   • C) 14.4 kN
   • D) 24.0 kN
5. 5.

   A 0.50 kg sensor-equipped rubber ball strikes a rigid horizontal test platform vertically downward at 6.0 m/s and rebounds vertically upward at 4.0 m/s. High-speed telemetry reveals that the impact with the platform lasts for 0.040 s. Taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what is the magnitude of the impulse delivered to the ball by the normal force from the platform during the collision?

   • A) 4.8 N·s
   • B) 5.0 N·s
   • C) 5.2 N·s
   • D) 5.4 N·s
6. 6.

   An automated rail inspection cart of mass 5.0 kg moves along a straight, frictionless track with an initial velocity of +4.0 m/s. An onboard propulsion unit first fires along the direction of motion, delivering a forward impulse of +30 N·s to the cart. Immediately after this booster phase, a magnetic brake engages and applies a constant retarding force of 25 N opposite to the motion for 1.6 s. What is the final velocity of the cart after both phases are completed?

   • A) +10 m/s
   • B) -2.0 m/s
   • C) +18 m/s
   • D) +2.0 m/s
7. 7.

   In a sports biomechanics tracking trial, a 0.40 kg ball rolling due east across a horizontal surface at a constant speed of 12 m/s is redirected by an automated kicker. Immediately after the contact, the ball travels due north at a speed of 16 m/s. Assuming external friction during the brief impact is negligible, what is the magnitude of the impulse delivered to the ball by the kicker?

   • A) 8.0 N·s
   • B) 1.6 N·s
   • C) 11.2 N·s
   • D) 20.0 N·s
8. 8.

   An industrial test rig evaluates two shock-absorbing pads, Pad X and Pad Y, designed to safely arrest delicate cargo. A 3.0 kg module sliding horizontally on a frictionless track at 4.0 m/s impacts Pad X and is brought to rest in 0.060 s. In an identical trial, the same module impacts Pad Y at 4.0 m/s and is brought to rest in 0.020 s. What is the magnitude of the impulse delivered to the module by each pad, and what is the ratio of the average force exerted by Pad Y to that exerted by Pad X?

   • A) 12 N·s for both pads; ratio of average force is 3.0
   • B) 12 N·s for both pads; ratio of average force is 0.33
   • C) 4.0 N·s for Pad X and 12 N·s for Pad Y; ratio of average force is 3.0
   • D) 36 N·s for both pads; ratio of average force is 1.0
9. 9.

   In an automated logistics terminal, a 4.0 kg package slides along a frictionless horizontal track at an initial velocity of 6.0 m/s. To safely slow the package down, an arresting mechanism applies an opposing horizontal force that increases uniformly from 10 N to 30 N over a duration of 0.80 s. What is the speed of the package immediately after this braking force is applied?

   • A) 4.0 m/s
   • B) 3.0 m/s
   • C) 2.0 m/s
   • D) 0.0 m/s
10. 10.

    During a laboratory collision test, a 0.50 kg sensor-equipped puck slides across a frictionless horizontal surface at 8.0 m/s toward a fixed vertical barrier. The puck strikes the barrier perpendicularly and rebounds along its initial line of motion at 6.0 m/s. What is the magnitude of the impulse delivered to the puck by the barrier during the collision?

    • A) 1.0 N·s
    • B) 3.0 N·s
    • C) 4.0 N·s
    • D) 7.0 N·s

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