Friction (static and kinetic) Transitional Reasoning Practice

Questions

1. 1.

   In an automated parcel-sorting facility, a 3.0 kg package is projected up a straight ramp inclined at 37° above the horizontal with an initial speed of 8.0 m/s. The coefficients of static and kinetic friction between the package and the ramp are $\mu_s = 0.80$ and $\mu_k = 0.25$, respectively. Taking the acceleration due to gravity as 10 m/s$^2$, what distance does the package travel along the ramp before coming to a stop, and what is its subsequent motion? (Take $\sin 37^\circ = 0.60$ and $\cos 37^\circ = 0.80$.)

   • A) 8.0 m, and it slides back down the ramp
   • B) 5.3 m, and it remains at rest on the ramp
   • C) 4.0 m, and it remains at rest on the ramp
   • D) 4.0 m, and it slides back down the ramp
2. 2.

   In a mechanics experiment, a 4.0 kg wooden block is projected across a level floor with an initial speed of 6.0 m/s and slides a distance of 9.0 m before coming to rest solely under the influence of friction. For this surface interface, the coefficient of static friction is 1.5 times the coefficient of kinetic friction. Taking the acceleration due to gravity as 10 m/s$^2$, what minimum horizontal force must subsequently be exerted on the stationary block to start it moving again?

   • A) 8.0 N
   • B) 12 N
   • C) 18 N
   • D) 20 N
3. 3.

   During a vehicle safety trial on a dry horizontal track, a test car travels at an initial velocity of 20 m/s before the driver applies the brakes to come to a complete stop. When the anti-lock braking system operates effectively, the rolling tires do not slip, allowing the vehicle to utilize the maximum static friction coefficient of 0.80. If the system fails and the wheels lock, the tires skid across the asphalt with a kinetic friction coefficient of 0.50. Taking the acceleration due to gravity as 10 m/s$^2$, what is the difference between the minimum stopping distance when skidding and the minimum stopping distance when braking without skidding?

   • A) 10 m
   • B) 15 m
   • C) 25 m
   • D) 40 m
4. 4.

   During an equipment mobility test, a technician pulls a 20 kg crate across a flat horizontal surface using a strap angled at 37° above the horizontal with a constant pulling force of 100 N. The coefficient of kinetic friction between the crate and the surface is 0.30, and the acceleration due to gravity is 10 m/s$^2$. What is the magnitude of the horizontal acceleration of the crate while it slides? (Take $\sin 37^\circ = 0.60$ and $\cos 37^\circ = 0.80$.)

   • A) 1.9 m/s$^2$
   • B) 1.0 m/s$^2$
   • C) 2.9 m/s$^2$
   • D) 0.1 m/s$^2$
5. 5.

   An engineering team evaluates the stability of a 10 kg equipment container resting on an adjustable loading ramp inclined at 30° above the horizontal. The coefficient of static friction between the container and the ramp surface is 0.70, the coefficient of kinetic friction is 0.50, and the acceleration due to gravity is 10 m/s². If the container is released from rest, which statement correctly describes the motion of the container and the magnitude of the friction force exerted on it by the ramp? (Take sin 30° = 0.50 and cos 30° = 0.87.)

   • A) The container accelerates down the ramp, and the friction force has a magnitude of 43.5 N.
   • B) The container remains at rest, and the friction force has a magnitude of 60.9 N.
   • C) The container accelerates down the ramp, and the friction force has a magnitude of 50.0 N.
   • D) The container remains at rest, and the friction force has a magnitude of 50.0 N.
6. 6.

   A 4.0 kg component rests on top of a 6.0 kg tray that can slide across a frictionless horizontal surface. The coefficients of static and kinetic friction between the component and the tray are 0.50 and 0.35, respectively, and the acceleration due to gravity is 10 m/s$^2$. A technician applies a constant horizontal pulling force of 65 N directly to the 6.0 kg tray. What is the magnitude and direction of the friction force exerted by the tray on the component?

   • A) 26 N in the direction of the tray's motion
   • B) 20 N in the direction of the tray's motion
   • C) 14 N in the direction of the tray's motion
   • D) 14 N opposite to the direction of the tray's motion
7. 7.

   A 2.0 kg block resting on a rough horizontal workbench is connected to a hanging 3.0 kg mass by an inextensible, light cord passing over an ideal pulley. The coefficients of static and kinetic friction between the block and the workbench are 0.60 and 0.50, respectively. If the system is released from rest and the acceleration due to gravity is 10 m/s$^2$, what is the magnitude of the acceleration of the two-block system?

   • A) 0 m/s$^2$
   • B) 3.6 m/s$^2$
   • C) 4.0 m/s$^2$
   • D) 6.0 m/s$^2$
8. 8.

   In an automated distribution center, a 5.0 kg parcel is gently placed from rest onto a horizontal conveyor belt moving to the right at a constant speed of 2.0 m/s. The coefficient of kinetic friction between the belt and the parcel is 0.40, the coefficient of static friction is 0.50, and the acceleration due to gravity is 10 m/s$^2$. Which of the following correctly gives the magnitude and direction of the frictional force exerted by the belt on the parcel while it is speeding up, as well as the magnitude of the frictional force once the parcel travels at the constant speed of the belt?

   • A) 20 N to the left while speeding up, and 25 N once at constant speed
   • B) 20 N to the right while speeding up, and 0 N once at constant speed
   • C) 25 N to the right while speeding up, and 20 N once at constant speed
   • D) 20 N to the right while speeding up, and 25 N once at constant speed
9. 9.

   In an investigation of frictional forces, a student holds a 0.60 kg wooden block stationary against a rough vertical wall by applying a perpendicular horizontal pushing force of 20 N. The coefficient of static friction between the block and the wall is 0.50, and the acceleration due to gravity is 10 m/s$^2$. If the student subsequently increases the horizontal pushing force to 30 N while the block remains at rest, how do the magnitude of the normal force exerted by the wall and the magnitude of the frictional force change?

   • A) The normal force increases from 20 N to 30 N, and the frictional force increases from 10 N to 15 N.
   • B) The normal force remains 20 N, and the frictional force increases from 6.0 N to 10 N.
   • C) The normal force and the frictional force both remain unchanged at 20 N and 6.0 N, respectively.
   • D) The normal force increases from 20 N to 30 N, while the frictional force remains unchanged at 6.0 N.
10. 10.

    A stationary 40 kg crate rests on a rough horizontal warehouse floor where the coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.35. A technician applies a horizontal force of 150 N to the crate, but it does not budge. Another worker then assists by increasing the total horizontal pushing force to 250 N, causing the crate to overcome static friction and slide across the floor. Taking the acceleration due to gravity as 10 m/s$^2$, what are the magnitudes of the friction force exerted by the floor on the crate during the first attempt and while it slides during the second attempt, respectively?

    • A) 200 N and 140 N
    • B) 150 N and 250 N
    • C) 200 N and 200 N
    • D) 150 N and 140 N

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