Inclined planes Transitional Reasoning Practice

Questions

1. 1.

   A 10 kg tool chest rests on a loading ramp inclined at $37^\circ$ above the horizontal, where the coefficient of static friction between the chest and the ramp is 0.50. A worker uses a tensioned safety strap aligned parallel to the ramp to pull upward on the chest with a constant force of 75 N. Under these conditions, the chest remains stationary on the ramp. What is the magnitude and direction of the static friction force exerted by the ramp on the chest? (Take $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$.)

   • A) 40 N directed down the ramp
   • B) 15 N directed up the ramp
   • C) 15 N directed down the ramp
   • D) 40 N directed up the ramp
2. 2.

   In a materials-testing experiment, a 2.0 kg block X and a 3.0 kg block Y are placed in contact on a ramp inclined at $37^\circ$ to the horizontal, with block X positioned higher up the ramp, directly behind block Y. The coefficient of kinetic friction is 0.10 between block X and the ramp, and 0.60 between block Y and the ramp. When the blocks are released from rest and slide together down the ramp, what is the magnitude of the contact force exerted between them? (Take $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$.)

   • A) 4.8 N
   • B) 6.4 N
   • C) 3.6 N
   • D) 2.4 N
3. 3.

   A fixed triangular wedge features two frictionless inclined surfaces meeting at an apex: the left surface is inclined at $37^\circ$ above the horizontal, and the right surface is inclined at $53^\circ$. A 3.0 kg block on the left incline is connected by a light, inextensible cord passing over an ideal pulley at the apex to a 4.0 kg block on the right incline. When the system is released from rest, what is the magnitude of the tension in the connecting cord? (Take $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\sin 53^\circ = 0.80$.)

   • A) 14 N
   • B) 18 N
   • C) 24 N
   • D) 32 N
4. 4.

   At an automated sorting terminal, a 5.0 kg parcel slides downward along a straight chute inclined at $37^\circ$ above the horizontal. A mechanical brake engages, exerting a constant retarding force of 12 N directed upward along the surface of the chute. The coefficient of kinetic friction between the parcel and the chute is 0.20. What is the magnitude of the parcel's acceleration as it continues sliding down the chute? (Take $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$.)

   • A) 1.2 m/s2
   • B) 2.0 m/s2
   • C) 2.4 m/s2
   • D) 3.6 m/s2
5. 5.

   A technician places a 5.0 kg equipment case on an adjustable ramp inclined at $37^\circ$ above the horizontal, where the coefficient of static friction between the case and the ramp is 0.25. An automated positioning rod exerts an upward force parallel to the ramp's surface to prevent the case from sliding downward. What is the minimum magnitude of this force required to maintain the case at rest? (Take $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$.)

   • A) 10 N
   • B) 20 N
   • C) 30 N
   • D) 40 N
6. 6.

   A testing facility uses an inclined plane to evaluate an automated material-handling system. A 6.0 kg cart on a frictionless track inclined at 30° above the horizontal is connected by a light cord passing over an ideal pulley to a hanging counterweight of mass $M$. When released, the cart accelerates up along the track at 1.0 m/s2. What is the mass $M$ of the hanging counterweight? (Take $g = 10\text{ m/s}^2$ and $\sin 30^\circ = 0.50$.)

   • A) 4.0 kg
   • B) 3.6 kg
   • C) 3.0 kg
   • D) 2.4 kg
7. 7.

   During a field trial, a 2.0 kg instrument package is launched with an initial velocity up a ramp inclined at 53° above the horizontal. The coefficient of kinetic friction between the package and the ramp surface is 0.50. What is the magnitude of the package's acceleration while it slides upward along the ramp? (Take $g = 10\text{ m/s}^2$, $\sin 53^\circ = 0.80$, and $\cos 53^\circ = 0.60$.)

   • A) 11 m/s2
   • B) 5.0 m/s2
   • C) 8.0 m/s2
   • D) 10 m/s2
8. 8.

   At an automated distribution center, a pneumatic actuator exerts a constant horizontal force to push a 4.0 kg carton up a smooth ramp inclined at 37° above the horizontal. The carton accelerates up along the surface of the ramp at 2.0 m/s2. What is the magnitude of the horizontal force applied by the actuator? (Take $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$.)

   • A) 24 N
   • B) 30 N
   • C) 40 N
   • D) 50 N
9. 9.

   A laboratory technician tests a 10 kg container on an experimental ramp inclined at $37^\circ$ above the horizontal. A motorized cable exerts a tension force parallel to the ramp's surface, pulling the container up the incline at a constant velocity. If the coefficient of kinetic friction between the container and the ramp is 0.20, what is the magnitude of the tension force exerted by the cable? (Take $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$.)

   • A) 60 N
   • B) 76 N
   • C) 44 N
   • D) 80 N
10. 10.

    A logistics worker releases a 4.0 kg crate from rest at the top of a straight loading ramp inclined at $30^\circ$ above the horizontal. The crate accelerates uniformly down the ramp, traveling a distance of 6.0 m along its surface in 2.0 s. Assuming $g = 10$ m/s2, what is the magnitude of the kinetic friction force exerted by the ramp on the crate?

    • A) 12.0 N
    • B) 14.0 N
    • C) 20.0 N
    • D) 8.0 N

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