Conservation of energy Transitional Reasoning Download PDF

Questions

1. 1.

   An electric vehicle with a mass of 1200 kg travels down a mountain road, descending through a vertical height of 50 m. The driver maintains a constant speed of 15 m/s throughout the descent by utilizing the vehicle's regenerative braking system, which converts mechanical energy into stored electrical energy. During this descent, aerodynamic drag and rolling resistance dissipate 180 kJ of mechanical energy as thermal energy. Assuming gravitational acceleration is $g = 10\text{ m/s}^2$, how much electrical energy is recovered and stored in the vehicle's battery during the descent?

   • A) 780 kJ
   • B) 600 kJ
   • C) 285 kJ
   • D) 420 kJ
2. 2.

   During a high-altitude adventure test, a 70 kg bungee jumper steps off a stationary platform suspended high above a canyon. The jumper is attached to an elastic cord with an unstretched natural length of 20 m that behaves like an ideal spring. Ignoring air resistance and the mass of the cord, the jumper falls freely until the cord begins to stretch, and momentarily comes to rest at a lowest point 40 m below the platform. Taking $g = 10\text{ m/s}^2$, what is the effective spring constant of the bungee cord?

   • A) 140 N/m
   • B) 70 N/m
   • C) 35 N/m
   • D) 280 N/m
3. 3.

   During a track and field analysis, a 60 kg pole vaulter sprints horizontally along a runway at 9.0 m/s with their center of mass initially 1.0 m above the ground. Upon planting the pole, the athlete's kinetic energy is converted into elastic potential energy of the bending pole and then into gravitational potential energy, while the athlete performs an additional 570 J of muscular work during the push-off. Assuming energy losses due to air resistance and pole vibration are negligible, and that the vaulter clears the bar with negligible kinetic energy, what is the maximum height above the ground reached by the athlete's center of mass? (Take g = 10 m/s².)

   • A) 6.0 m
   • B) 5.0 m
   • C) 5.1 m
   • D) 7.0 m
4. 4.

   A civil engineering team uses a dynamic penetrometer to test the firmness of a construction site foundation. A 20 kg cylindrical steel weight is released from rest from a height of 1.8 m above the surface of the ground and drives vertically into the soil until it comes to rest at a depth of 0.20 m. Assuming air resistance is negligible and taking the acceleration due to gravity as 10 m/s$^2$, what is the magnitude of the average resistive force exerted by the soil on the weight during penetration?

   • A) 1800 N
   • B) 2000 N
   • C) 2200 N
   • D) 3600 N
5. 5.

   A roller-coaster engineering team tests a frictionless track model in which a 0.50 kg cart is released from rest at an unknown height above the ground. The cart descends along the track and enters a vertical circular loop having a radius of 0.80 m. If the cart successfully traverses the loop and registers a speed of 4.0 m/s at the very top of the loop, from what height above the ground was it released? (Assume energy losses due to friction and air resistance are negligible, and take g = 10 m/s².)

   • A) 1.6 m
   • B) 2.4 m
   • C) 3.2 m
   • D) 0.8 m
6. 6.

   A laboratory apparatus consists of a 3.0 kg cart resting on a smooth horizontal track, connected by a light, inextensible string over an ideal pulley to a hanging 1.0 kg mass. The system is released from rest, allowing the hanging mass to descend vertically through a distance of 1.8 m before striking the floor. Assuming all frictional and rotational losses are negligible and taking the acceleration due to gravity as 10 m/s$^2$, what is the speed of the cart just before the hanging mass hits the floor?

   • A) 2.1 m/s
   • B) 3.0 m/s
   • C) 4.2 m/s
   • D) 6.0 m/s
7. 7.

   A vertical test rig uses a spring with a spring constant of 500 N/m to launch a 2.0 kg sensor package upward. The spring is initially compressed downward by 0.40 m from its uncompressed equilibrium length and released from rest. As the spring decompresses and pushes the package upward to its uncompressed length, friction along the launch column dissipates 7.0 J of mechanical energy into thermal energy. Taking the acceleration due to gravity as 10 m/s$^2$, what is the speed of the package at the instant it detaches from the spring?

   • A) 3.0 m/s
   • B) 4.0 m/s
   • C) 6.0 m/s
   • D) 5.0 m/s
8. 8.

   A 400 kg inspection cart travels along a maintenance track at a theme park, passing the lowest section of the track with a horizontal speed of 20 m/s before ascending an incline toward an observation ridge 12 m above the base. During the climb, resistive forces convert 12 kJ of mechanical energy into thermal energy. Taking the acceleration due to gravity as 10 m/s$^2$, what is the speed of the cart when it reaches the observation ridge?

   • A) 8 m/s
   • B) 10 m/s
   • C) 12 m/s
   • D) 14 m/s
9. 9.

   An environmental monitoring capsule with a mass of 2.0 kg is dropped from rest from a research drone hovering at an altitude of 180 m. As it descends through the atmosphere, an onboard sensor records its downward speed as 40 m/s at an altitude of 60 m, immediately before its retrieval parachute deploys. Taking the acceleration due to gravity as 10 m/s$^2$, how much mechanical energy was dissipated by air resistance during this descent?

   • A) 400 J
   • B) 1200 J
   • C) 2000 J
   • D) 800 J
10. 10.

    In an engineering safety test, a 2.0 kg test carriage is released from rest at a height of 3.2 m on a curved guide track. During its descent to the horizontal base, friction dissipates 14 J of mechanical energy as thermal energy. Upon reaching the frictionless horizontal track, the carriage strikes and compresses a bumper spring with a spring constant of 400 N/m until momentarily coming to a stop. Taking the acceleration due to gravity as 10 m/s$^2$, what is the maximum compression of the bumper spring?

    • A) 0.50 m
    • B) 0.57 m
    • C) 0.35 m
    • D) 0.62 m