Conservation of energy Transitional Reasoning Practice

Questions

1. 1.

   During a performance analysis of a ski jumper with a total mass of 60 kg, the athlete glides from rest down an inrun ramp from an initial vertical height of 20 m above the takeoff lip. Friction and air resistance dissipate 36% of the athlete's initial mechanical energy into thermal energy during the descent. Taking the acceleration due to gravity as 10 m/s², what is the jumper's speed at the instant of takeoff?

   • A) 16 m/s
   • B) 20 m/s
   • C) 12 m/s
   • D) 8 m/s
2. 2.

   During a safety evaluation of an outdoor adventure zip-line, a rider with equipment having a combined mass of 80 kg launches from rest at an upper platform located 45 m above the ground. The rider travels along the cable and reaches the lower platform, situated 15 m above the ground, with a speed of 20 m/s just before the arrival brake engages. Taking the acceleration due to gravity as 10 m/s², how much mechanical energy was dissipated by air resistance and cable friction during this descent?

   • A) 24 000 J
   • B) 16 000 J
   • C) 8 000 J
   • D) 20 000 J
3. 3.

   A transit authority tests an energy-recovery system on an electric bus of mass 12 000 kg operating on a level road. When braking from an initial speed of 20 m/s to rest, 60% of the vehicle's kinetic energy is captured and stored in a mechanical flywheel, while the remaining 40% is dissipated as thermal energy. The stored energy is subsequently delivered to the drivetrain to propel the bus up an incline with its primary motor turned off. Assuming negligible friction and air resistance, and taking $g = 10\text{ m/s}^2$, what is the maximum vertical height the bus can ascend using only this stored energy?

   • A) 12 m
   • B) 20 m
   • C) 8 m
   • D) 24 m
4. 4.

   A warehouse freight mechanism uses a counterweight system to move cargo between levels. A counterweight of mass 600 kg is connected by a light, inextensible cable passing over a frictionless pulley to an elevator cabin of mass 400 kg. If the system is released from rest and the counterweight descends vertically through a distance of 3.0 m, what is the kinetic energy of the cabin at that moment? (Assume air resistance and cable mass are negligible, and take g = 10 m/s².)

   • A) 6,000 J
   • B) 3,600 J
   • C) 2,400 J
   • D) 1,200 J
5. 5.

   In a hydroelectric power station, water flows from an elevated reservoir at a height of 40 m above a turbine, starting with negligible speed. Upon passing through the turbine, the water is discharged at the base level at a speed of 10 m/s. If the generator converts 80% of the mechanical energy extracted from the water into electrical energy, how much electrical energy is produced per kilogram of water? (Take g = 10 m/s² and assume energy losses outside the turbine generator are negligible.)

   • A) 240 J
   • B) 280 J
   • C) 320 J
   • D) 350 J
6. 6.

   An athlete of mass 60 kg tests a training trampoline. At the maximum downward depression of the bounce, the trampoline mat is pushed down by 0.50 m below its equilibrium level, and the athlete is momentarily stationary. Upon rebound, the athlete leaves the mat and ascends to a peak height of 2.50 m above the equilibrium level before momentarily stopping in the air. Assuming air resistance and mechanical dissipation in the mat are negligible, what was the elastic potential energy stored in the trampoline at the lowest point of the bounce? (Take g = 10 m/s².)

   • A) 1500 J
   • B) 1800 J
   • C) 1200 J
   • D) 2100 J
7. 7.

   In a materials testing laboratory, a pendulum hammer of mass 20 kg is released from rest from an initial height of 1.5 m to measure the fracture toughness of a metal sample placed at the lowest point of the swing. During the impact, 140 J of mechanical energy is absorbed by the specimen to break it. Assuming pivot friction and air resistance are negligible, what maximum height does the hammer reach on its follow-through swing after fracturing the sample? (Take g = 10 m/s².)

   • A) 0.70 m
   • B) 0.80 m
   • C) 1.05 m
   • D) 1.20 m
8. 8.

   A testing facility evaluates an emergency vertical arrestor cable on a descending cargo container of mass 400 kg. While traveling downward at 3.0 m/s at a height of 8.0 m above the ground, the container engages the arrestor mechanism. The mechanism exerts a constant upward resistive force until the container is brought momentarily to rest at a height of 2.0 m above the ground. Assuming air resistance is negligible and taking the acceleration due to gravity as 10 m/s², what is the magnitude of the constant resistive force exerted by the arrestor?

   • A) 4300 N
   • B) 4000 N
   • C) 3700 N
   • D) 3000 N
9. 9.

   A student releases a 0.25 kg block from rest from a height of 2.0 m down an inclined track. During the descent, 1.0 J of mechanical energy is dissipated as thermal energy due to friction before the block reaches a smooth horizontal floor. If the block subsequently collides with and compresses a horizontal ideal spring of spring constant 200 N/m, what is the maximum compression of the spring? (Take g = 10 m/s².)

   • A) 0.14 m
   • B) 0.22 m
   • C) 0.20 m
   • D) 0.40 m
10. 10.

    A roller-coaster cart with a mass of 500 kg passes point X at a height of 30 m above the ground with a speed of 10 m/s. It moves along a frictionless track and reaches point Y at a height of 15 m above the ground. Assuming air resistance is negligible and taking the acceleration due to gravity as 10 m/s², what is the kinetic energy of the cart as it passes point Y?

    • A) 100 kJ
    • B) 75 kJ
    • C) 175 kJ
    • D) 50 kJ

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