Inclined planes Transitional Reasoning Download PDF

Questions

1. 1.

   A safety engineer tests an emergency braking mechanism on a 500 kg service trolley travelling down a straight, frictionless ramp inclined at 30° above the horizontal. The trolley enters the test zone with a downward speed of 12 m/s, and the braking mechanism exerts a constant force directed parallel to and up the incline to bring it to a complete stop over a distance of 36 m. Taking $g = 10\text{ m/s}^2$ and $\sin 30^\circ = 0.50$, what is the magnitude of the braking force applied to the trolley?

   • A) 1000 N
   • B) 1500 N
   • C) 2500 N
   • D) 3500 N
2. 2.

   A test package with a mass of 5.0 kg is given a brief push down a straight ramp inclined at 37° above the horizontal, after which it continues sliding down the ramp at a constant speed. An operator now wishes to push this same package up the ramp at the same constant speed by applying a force parallel to the incline. Taking $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$, what is the magnitude of the pushing force required?

   • A) 60 N
   • B) 50 N
   • C) 40 N
   • D) 30 N
3. 3.

   Two sorting containers with masses of 2.0 kg and 4.0 kg are placed in direct contact on a frictionless ramp inclined at 30° above the horizontal, with the 2.0 kg container positioned lower on the slope. A motorized guide applies a constant force of 48 N directed parallel to and up the ramp against the 2.0 kg container, accelerating both containers up the incline. Taking $g = 10\text{ m/s}^2$, what is the magnitude of the contact force exerted by the 2.0 kg container on the 4.0 kg container?

   • A) 18 N
   • B) 32 N
   • C) 20 N
   • D) 16 N
4. 4.

   An engineering student launches a small test sled up a rough ramp inclined at an angle of 37° above the horizontal to investigate how friction affects uphill and downhill motion. The coefficient of kinetic friction between the sled and the ramp surface is 0.25. After ascending to a momentary stop, the sled slides back down the ramp. What is the ratio of the magnitude of the sled's acceleration during its ascent to the magnitude of its acceleration during its descent? (Take $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$.)

   • A) 1.00
   • B) 1.33
   • C) 2.00
   • D) 4.00
5. 5.

   A 5.0 kg crate is pulled up an inclined loading ramp angled at 37° above the horizontal by a motorized cable oriented parallel to the ramp surface. The coefficient of kinetic friction between the crate and the ramp surface is 0.20. If the cable exerts a constant tension of 50 N on the crate, what is the magnitude of the crate's acceleration up the ramp? (Take g = 10 m/s², sin 37° = 0.60, and cos 37° = 0.80.)

   • A) 4.0 m/s²
   • B) 5.6 m/s²
   • C) 0.8 m/s²
   • D) 2.4 m/s²
6. 6.

   An industrial test crate with a mass of 10 kg is placed on a rough loading ramp inclined at an angle of 37° above the horizontal. The coefficients of static and kinetic friction between the crate and the ramp surface are 0.85 and 0.70, respectively. Taking $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$, what is the magnitude of the friction force acting on the crate?

   • A) 80 N
   • B) 68 N
   • C) 56 N
   • D) 60 N
7. 7.

   A laboratory cart of mass 3.0 kg rests on a frictionless track inclined at 30° above the horizontal and is connected to a light, inextensible cord passing over an ideal pulley at the top of the incline. The other end of the cord supports a suspended 2.0 kg counterweight hanging vertically. When the system is released from rest, what is the magnitude of the tension in the cord? (Take $g = 10\text{ m/s}^2$.)

   • A) 15 N
   • B) 18 N
   • C) 20 N
   • D) 24 N
8. 8.

   A logistics technician stabilizes a 20 kg cargo crate on a smooth, frictionless ramp inclined at an angle of 37° above the horizontal. A mechanical actuator holds the crate stationary by applying a steady pushing force directed purely horizontally toward the ramp. Given that $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$, what is the magnitude of this horizontal pushing force?

   • A) 120 N
   • B) 150 N
   • C) 160 N
   • D) 200 N
9. 9.

   A postal worker places a 5.0 kg parcel on a straight sorting ramp inclined at an angle of 37° above the horizontal. As the parcel slides down the rough surface, it experiences kinetic friction with a coefficient of $\mu_k = 0.25$. Given that $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$, what is the magnitude of the acceleration of the parcel down the ramp?

   • A) 4.0 m/s²
   • B) 6.0 m/s²
   • C) 6.5 m/s²
   • D) 8.0 m/s²
10. 10.

    A student investigates forces on an inclined plane by placing a 3.0 kg block on a smooth, frictionless ramp tilted at an angle of 30° above the horizontal. A pulling force directed parallel to and up the incline is applied to the block so that it accelerates up the ramp at 2.0 m/s². Taking the acceleration due to gravity as 10 m/s², what is the magnitude of this pulling force?

    • A) 6.0 N
    • B) 9.0 N
    • C) 15 N
    • D) 21 N