Mechanical energy Transitional Reasoning Download PDF

Questions

1. 1.

   A student performs an impact experiment by releasing a solid 0.50 kg steel sphere from rest from a height of 1.8 m above the surface of a container of sand. The sphere penetrates vertically into the sand, coming to rest at a depth of 0.20 m below the surface. Assuming air resistance is negligible and taking the acceleration due to gravity as 10 m/s², what is the magnitude of the average resistive force exerted by the sand on the sphere?

   • A) 40 N
   • B) 45 N
   • C) 50 N
   • D) 60 N
2. 2.

   An acrobatic gymnast of mass 50 kg moves vertically upward after launching from a trampoline. As the gymnast passes an elevation of 1.8 m above the trampoline bed, a high-speed tracking system records their vertical speed as 8.0 m/s. Assuming air resistance is negligible and taking $g = 10\text{ m/s}^2$, at what height above the trampoline bed will the gymnast's gravitational potential energy be four times their kinetic energy?

   • A) 2.5 m
   • B) 4.0 m
   • C) 3.2 m
   • D) 5.0 m
3. 3.

   A safety testing apparatus drops a 2.0 kg package from rest from a vertical height of 0.60 m above the uncompressed top plate of a vertical buffer spring. The spring has an ideal force constant of 400 N/m, and energy losses due to air resistance and mechanical damping are negligible. Taking $g = 10\text{ m/s}^2$, what is the maximum downward compression of the spring during this impact?

   • A) 0.05 m
   • B) 0.20 m
   • C) 0.24 m
   • D) 0.30 m
4. 4.

   In a mechanics experiment, a 2.0 kg cart on a smooth horizontal track is connected by a light inextensible cord over an ideal pulley to a hanging 3.0 kg counterweight. The system is released from rest, allowing the counterweight to fall vertically while pulling the cart horizontally. Assuming friction and air resistance are negligible and taking g = 10 m/s², what is the kinetic energy of the 2.0 kg cart after the counterweight has fallen through a distance of 1.5 m?

   • A) 18 J
   • B) 27 J
   • C) 30 J
   • D) 45 J
5. 5.

   A 1000 kg roller coaster train enters an emergency braking section at an elevation of 14 m above the station platform with a speed of 8.0 m/s. As the train descends to an elevation of 4.0 m, the brakes exert resistive forces that remove 60 kJ of mechanical energy from the train. Assuming track friction outside the brakes and air resistance are negligible, and taking $g = 10\text{ m/s}^2$, what is the speed of the train as it exits this section?

   • A) 6.0 m/s
   • B) 10 m/s
   • C) 12 m/s
   • D) 14 m/s
6. 6.

   A motorized winch lifts a 4.0 kg crate vertically upward from rest with a constant acceleration of $2.0\text{ m/s}^2$ through a height of 5.0 m. Assuming air resistance is negligible and taking $g = 10\text{ m/s}^2$, what is the total increase in the mechanical energy of the crate over this displacement?

   • A) 200 J
   • B) 240 J
   • C) 160 J
   • D) 40 J
7. 7.

   A physics student launches a 0.50 kg projectile from ground level with an initial speed of 10 m/s at an angle to the horizontal. As the projectile reaches the highest point of its trajectory, a sensor records its speed as 6.0 m/s. Assuming air resistance is negligible and taking the ground as the reference level for gravitational potential energy, what is the gravitational potential energy of the projectile at this highest point?

   • A) 16 J
   • B) 25 J
   • C) 9 J
   • D) 34 J
8. 8.

   A student investigates energy transformations using a 0.25 kg glider attached to an ideal horizontal spring of force constant 50 N/m on a frictionless air track. The glider is pulled a distance of 0.20 m from its equilibrium position and released from rest. Assuming no energy is lost to the surroundings, what is the speed of the glider at the instant its kinetic energy equals its elastic potential energy?

   • A) 1.4 m/s
   • B) 2.0 m/s
   • C) 2.8 m/s
   • D) 4.0 m/s
9. 9.

   A laboratory cart with a mass of 2.0 kg travels along a frictionless curved track. As it passes point X at an elevation of 2.3 m above the floor, its speed is 3.0 m/s. Assuming air resistance is negligible and taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what is the kinetic energy of the cart as it reaches point Y at an elevation of 1.5 m?

   • A) 9.0 J
   • B) 16.0 J
   • C) 25.0 J
   • D) 30.0 J