Inclined planes Knowledge-Based Practice

Questions

1. 1.

   Two blocks with masses of 2.0 kg and 3.0 kg are placed in contact on a frictionless ramp inclined at $30^\circ$ above the horizontal, with the 2.0 kg block positioned lower on the ramp. If a constant force of 35 N directed parallel to and up the ramp is applied to the 2.0 kg block, what is the magnitude of the contact force exerted on the 3.0 kg block? (Assume $g = 10\text{ m/s}^2$ and $\sin 30^\circ = 0.50$.)

   • A) 14 N
   • B) 15 N
   • C) 21 N
   • D) 25 N
2. 2.

   A 5.0 kg block rests on a rough ramp inclined at $37^\circ$ above the horizontal. If the coefficient of static friction between the block and the ramp is 0.90, what is the magnitude of the friction force acting on the block? (Assume $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$.)

   • A) 45 N
   • B) 36 N
   • C) 30 N
   • D) 40 N
3. 3.

   A 2.0 kg block is projected up a rough ramp inclined at $30^\circ$ above the horizontal. While sliding up the ramp, a constant kinetic friction force of 4.0 N opposes its motion. What is the magnitude of the block's acceleration as it moves up the ramp? (Assume $g = 10\text{ m/s}^2$ and $\sin 30^\circ = 0.50$.)

   • A) $7.0\text{ m/s}^2$
   • B) $3.0\text{ m/s}^2$
   • C) $5.0\text{ m/s}^2$
   • D) $2.0\text{ m/s}^2$
4. 4.

   A 5.0 kg crate is pushed up a rough ramp inclined at $30^\circ$ above the horizontal by a constant force of 45 N directed parallel to the incline. If a kinetic friction force of 10 N opposes the motion, what is the magnitude of the crate's acceleration? (Assume $g = 10\text{ m/s}^2$ and $\sin 30^\circ = 0.50$.)

   • A) $1.0\text{ m/s}^2$
   • B) $2.0\text{ m/s}^2$
   • C) $4.0\text{ m/s}^2$
   • D) $7.0\text{ m/s}^2$
5. 5.

   A wooden block rests on an inclined plane whose angle of inclination is slowly increased until the block just begins to slip at an angle of $37^\circ$ above the horizontal. What is the coefficient of static friction between the block and the incline? (Assume $\sin 37^\circ = 0.60$ and $\cos 37^\circ = 0.80$.)

   • A) 0.75
   • B) 0.60
   • C) 0.80
   • D) 1.33
6. 6.

   A 6.0 kg crate is held at rest on a frictionless incline angled at $53^\circ$ above the horizontal by a constant horizontal force $F$. What is the magnitude of $F$? (Assume $g = 10\text{ m/s}^2$, $\sin 53^\circ = 0.80$, and $\cos 53^\circ = 0.60$.)

   • A) 36 N
   • B) 45 N
   • C) 48 N
   • D) 80 N
7. 7.

   A 3.0 kg block resting on a frictionless incline angled at $30^\circ$ to the horizontal is connected by a light string over a frictionless pulley to a freely hanging 2.0 kg mass. What is the magnitude of the acceleration of the system when it is released from rest? (Assume $g = 10\text{ m/s}^2$ and $\sin 30^\circ = 0.50$.)

   • A) 4.0 m/s2
   • B) 2.5 m/s2
   • C) 2.0 m/s2
   • D) 1.0 m/s2
8. 8.

   A 4.0 kg crate slides down a rough ramp inclined at an angle of $37^\circ$ above the horizontal with an acceleration of $2.0\text{ m/s}^2$. What is the magnitude of the kinetic friction force acting on the crate? (Assume $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$.)

   • A) 8.0 N
   • B) 12 N
   • C) 16 N
   • D) 24 N
9. 9.

   A block of mass 5.0 kg is pulled up a frictionless plane inclined at an angle of $30^\circ$ above the horizontal. What magnitude of force applied parallel to the incline is required to move the block up the plane at a constant velocity? (Assume $g = 9.8\text{ m/s}^2$.)

   • A) 49 N
   • B) 42.4 N
   • C) 12.3 N
   • D) 24.5 N

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