Mechanical energy Knowledge-Based Download PDF

Questions

1. 1.

   During a descent, gravity does 120 J of work on a skydiver while air resistance does -30 J of work. What is the change in the total mechanical energy of the skydiver-Earth system during this descent?

   • A) +90 J
   • B) -30 J
   • C) -120 J
   • D) +150 J
2. 2.

   Two identical spheres, X and Y, are projected from the same height above the ground with the same initial speed $v$, with sphere X directed vertically upward and sphere Y directed horizontally. Neglecting air resistance, how do the total mechanical energies of spheres X and Y relative to the ground compare immediately after projection?

   • A) Sphere X has greater mechanical energy because its initial velocity is directed upward against gravity.
   • B) Sphere Y has greater mechanical energy because its motion is not opposed by gravitational force at launch.
   • C) Spheres X and Y have the same mechanical energy because mechanical energy is a scalar quantity depending only on speed and height.
   • D) Sphere X has greater mechanical energy because upward projection requires an additional component of kinetic energy.
3. 3.

   An electric motor lifts a 5.0 kg crate vertically upward through a height of 6.0 m at a constant speed. Assuming air resistance is negligible and taking $g$ = 10 m/s², what is the change in the total mechanical energy of the crate-Earth system?

   • A) 0 J
   • B) 150 J
   • C) 300 J
   • D) 600 J
4. 4.

   The total mechanical energy of a physical system is conserved during a process if which of the following conditions is satisfied?

   • A) The net external force acting on the system is equal to zero.
   • B) Only conservative forces perform work on or within the system.
   • C) The kinetic energy of the system remains constant throughout the process.
   • D) The total work performed by all forces on the system is equal to zero.
5. 5.

   A ball is thrown vertically upward from ground level with an initial speed of 20 m/s. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, at what height above the ground is its kinetic energy equal to its gravitational potential energy?

   • A) 5 m
   • B) 10 m
   • C) 15 m
   • D) 20 m
6. 6.

   A 4.0 kg cart travels at a speed of 6.0 m/s on a frictionless horizontal surface toward an ideal horizontal spring with a spring constant of 900 N/m. Assuming mechanical energy is conserved, what is the maximum compression of the spring when it brings the cart momentarily to rest?

   • A) 0.16 m
   • B) 0.28 m
   • C) 0.40 m
   • D) 0.80 m
7. 7.

   A 0.40 kg glider attached to an ideal horizontal spring with a spring constant of 250 N/m moves on a frictionless track. At an instant when its speed is 1.5 m/s and the spring is stretched by 0.080 m, what is the total mechanical energy of the glider-spring system?

   • A) 0.45 J
   • B) 0.80 J
   • C) 1.70 J
   • D) 1.25 J
8. 8.

   An object with a mass of 3.0 kg has a total mechanical energy of 150 J. At a point where its potential energy is 54 J, what is the speed of the object?

   • A) 4.0 m/s
   • B) 6.0 m/s
   • C) 8.0 m/s
   • D) 10 m/s
9. 9.

   A 0.50 kg toy car moves along a horizontal surface at a speed of 4.0 m/s before entering a rough patch where friction does -1.5 J of work on the car. Taking the horizontal surface as the reference level for gravitational potential energy, what is the final mechanical energy of the car?

   • A) 1.5 J
   • B) 2.0 J
   • C) 2.5 J
   • D) 5.5 J