Work–energy theorem Transitional Reasoning Practice

Questions

1. 1.

   An automated guided trolley of mass 80 kg glides along a straight, frictionless horizontal surface at a steady speed of 3.0 m/s toward a docking station. To bring the trolley to a temporary halt, it engages an elastic spring buffer with a force constant of 2,000 N/m mounted at the end of the track. According to the work–energy theorem, what is the maximum compression of the spring buffer during this arrest process?

   • A) 0.36 m
   • B) 0.60 m
   • C) 0.85 m
   • D) 0.18 m
2. 2.

   A scientific field team drops an automated sensor pod of mass 5.0 kg from rest at a height of 9.6 m above a level, soft-sand deposit. The pod falls vertically and penetrates a distance of 0.40 m into the sand before coming to rest. Taking the acceleration due to gravity as 9.8 m/s$^2$ and neglecting air resistance, what is the magnitude of the average resistive force exerted by the sand on the pod according to the work–energy theorem?

   • A) 1176 N
   • B) 1225 N
   • C) 1274 N
   • D) 2450 N
3. 3.

   A performance engineer evaluates the energy consumption of a prototype electric hypercar accelerating along a straight, horizontal test track where resistive forces are negligible. Telemetry data reveals that the net work done on the car to accelerate it from rest to a benchmark speed $v$ is $W$. Under the same operating conditions, the car is then accelerated further from speed $v$ to a final speed of $3v$. According to the work–energy theorem, what is the additional net work required for this second acceleration phase in terms of $W$?

   • A) $2W$
   • B) $4W$
   • C) $6W$
   • D) $8W$
4. 4.

   A ballistic testing facility evaluates the stopping characteristics of a 0.050 kg projectile fired horizontally through two consecutive gelatin blocks. The projectile enters the first block of length 0.30 m at a speed of 40 m/s and emerges from it with a speed of 20 m/s. If the average retarding force exerted by the second block is half that of the first block, what distance does the projectile travel through the second block before coming to rest?

   • A) 0.20 m
   • B) 0.10 m
   • C) 0.30 m
   • D) 0.40 m
5. 5.

   An experimental maglev vehicle of mass 600 kg enters a deceleration zone with an initial speed of 30 m/s. A constant opposing magnetic braking force of 4,800 N acts on the vehicle along its line of motion until its kinetic energy is reduced to one-ninth of its initial value. According to the work–energy theorem, what distance does the vehicle travel while this braking force is applied?

   • A) 25 m
   • B) 37.5 m
   • C) 50 m
   • D) 56.25 m
6. 6.

   A warehouse worker pushes a 50 kg crate from rest at the bottom of an inclined ramp up to the top along a 5.0 m path that rises vertically by 2.0 m. Throughout the ascent, the worker applies a constant force of 320 N parallel to the incline, and the crate reaches a final speed of 4.0 m/s at the summit. Taking the acceleration due to gravity as 9.8 m/s$^2$, what is the magnitude of the constant kinetic friction force acting on the crate according to the work–energy theorem?

   • A) 240 N
   • B) 44 N
   • C) 80 N
   • D) 110 N
7. 7.

   A remote-controlled inspection drone of mass 2.0 kg glides horizontally along a frictionless guide rail at an initial speed of 6.0 m/s. An onboard linear booster engages over a short distance, doing 64 J of net work on the drone along its direction of travel. According to the work–energy theorem, what is the final speed of the drone after this boost?

   • A) 8.0 m/s
   • B) 12 m/s
   • C) 14 m/s
   • D) 10 m/s
8. 8.

   A construction hoist lifts a 400 kg load of bricks vertically from rest at ground level. After ascending through a vertical displacement of 15 m, the load reaches an upward speed of 5.0 m/s. Taking the acceleration due to gravity as 9.8 m/s2 and neglecting air resistance, what is the work done on the load solely by the hoisting cable's tension force during this motion?

   • A) 63,800 J
   • B) 58,800 J
   • C) 53,800 J
   • D) 5,000 J
9. 9.

   An 800 kg automated transport pod travelling at 15 m/s along a straight, horizontal track must be brought to a complete stop by an emergency arrestor system over a distance of 20 m. During this braking interval, aerodynamic drag performs -6,000 J of work on the pod. According to the work–energy theorem, what is the magnitude of the average retarding force exerted specifically by the arrestor system?

   • A) 4,200 N
   • B) 4,500 N
   • C) 4,800 N
   • D) 8,700 N
10. 10.

    A logistics cart with a mass of 2.0 kg enters a testing zone on a horizontal floor with an initial speed of 3.0 m/s. Across a straight 2.5 m segment, a constant horizontal towing force of 10 N pulls the cart forward while a constant kinetic friction force of 3.6 N opposes its motion. According to the work–energy theorem, what is the speed of the cart at the end of this 2.5 m segment?

    • A) 5.0 m/s
    • B) 4.0 m/s
    • C) 5.8 m/s
    • D) 7.0 m/s

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