Friction (static and kinetic) Transitional Reasoning Download PDF

Questions

1. 1.

   During a safety evaluation on a straight, horizontal test track, a 1500 kg test car travels at an initial speed of 20 m/s before the driver applies the brakes to come to a complete stop. The coefficients of static and kinetic friction between the tires and the dry pavement are 0.80 and 0.50, respectively. Taking the acceleration due to gravity as 10 m/s², what is the difference between the distance required to stop during a locked-wheel skid and the minimum distance achieved through optimal threshold braking without skidding?

   • A) 15 m
   • B) 10 m
   • C) 25 m
   • D) 40 m
2. 2.

   At an airport luggage facility, an 8.0 kg package is placed gently from rest onto a horizontal conveyor belt moving at a constant speed of 3.0 m/s. The coefficient of static friction between the belt and the package is 0.40, and the coefficient of kinetic friction is 0.25. Taking the acceleration due to gravity as 10 m/s², what is the horizontal distance traveled by the package relative to the floor before it stops slipping on the belt?

   • A) 1.1 m
   • B) 2.4 m
   • C) 3.6 m
   • D) 1.8 m
3. 3.

   A 2.0 kg package rests on a rough ramp inclined at an angle $\theta$ above the horizontal, where $\sin\theta = 0.60$ and $\cos\theta = 0.80$. The coefficients of static and kinetic friction between the package and the ramp surface are 0.50 and 0.40, respectively. A technician applies an external force directed parallel to and up the incline to prevent the package from sliding down. Taking $g = 10\text{ m/s}^2$, what is the minimum magnitude of this upward parallel force required to keep the package at rest?

   • A) 5.6 N
   • B) 4.0 N
   • C) 12 N
   • D) 20 N
4. 4.

   A 4.0 kg block rests on a rough horizontal workbench and is connected by a light, inextensible cord passing over a frictionless pulley to a hanging 2.0 kg counterweight. The coefficients of static and kinetic friction between the block and the bench surface are 0.45 and 0.20, respectively. The system is released from rest with the connecting cord taut. Taking the acceleration due to gravity as 10 m/s², what is the magnitude of the acceleration of the system?

   • A) 2.0 m/s²
   • B) 3.0 m/s²
   • C) 0.33 m/s²
   • D) 3.3 m/s²
5. 5.

   A logistics worker drags a 5.0 kg crate along a level warehouse floor by pulling on a strap with a constant force of 50 N directed at an angle of 37° above the horizontal. The coefficients of static and kinetic friction between the crate and the floor are 0.60 and 0.50, 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 crate's acceleration?

   • A) $6.0\text{ m/s}^2$
   • B) $3.0\text{ m/s}^2$
   • C) $5.6\text{ m/s}^2$
   • D) $8.0\text{ m/s}^2$
6. 6.

   In a laboratory investigation, a 2.0 kg block is placed on top of a 6.0 kg cart that rests on a frictionless horizontal track. The coefficient of static friction between the block and the top surface of the cart is 0.30, and the coefficient of kinetic friction is 0.20. A student pulls the lower cart horizontally with a force of gradually increasing magnitude. Taking $g = 10\text{ m/s}^2$, what is the maximum pulling force that can be applied to the cart without causing the upper block to slip?

   • A) 6.0 N
   • B) 16 N
   • C) 18 N
   • D) 24 N
7. 7.

   A flatbed truck carries an unsecured 20 kg crate on its horizontal bed, where the coefficients of static and kinetic friction between the crate and the bed surface are 0.40 and 0.25, respectively. As the truck speeds up forward along a straight, level road with a constant acceleration of 3.0 m/s², the crate is observed to remain on the bed. Taking the acceleration due to gravity as 10 m/s², what are the magnitude and direction of the friction force exerted by the truck bed on the crate?

   • A) 60 N, directed forward
   • B) 60 N, directed backward
   • C) 80 N, directed forward
   • D) 50 N, directed backward
8. 8.

   A 5.0 kg crate is sliding to the right along a rough horizontal floor with an instantaneous speed of 6.0 m/s. At this moment, a worker applies a constant horizontal pulling force of 25 N directed to the left. The coefficients of static and kinetic friction between the crate and the floor are 0.40 and 0.30, respectively. Taking the acceleration due to gravity as 10 m/s², what is the magnitude of the crate's acceleration while it is still moving to the right?

   • A) 2.0 m/s²
   • B) 5.0 m/s²
   • C) 9.0 m/s²
   • D) 8.0 m/s²
9. 9.

   A 2.0 kg textbook is held against a vertical rough wall by applying a horizontal pushing force of 40 N perpendicular to the wall. The coefficient of static friction between the book and the wall is 0.60, and the coefficient of kinetic friction is 0.40. Taking the acceleration due to gravity as 10 m/s², what is the state of motion of the book and the magnitude of the friction force exerted by the wall on it?

   • A) It accelerates downward, and the upward friction force is 16 N.
   • B) It remains stationary, and the upward friction force is 20 N.
   • C) It remains stationary, and the upward friction force is 24 N.
   • D) It accelerates upward, and the upward friction force is 24 N.
10. 10.

    A student investigates the forces acting on a 4 kg crate initially at rest on a horizontal floor, where the coefficients of static and kinetic friction are 0.50 and 0.30, respectively. In the first trial, the student applies a horizontal pushing force of 15 N to the crate. In the second trial, the horizontal pushing force is increased to 28 N. Taking the acceleration due to gravity as 10 m/s², what are the magnitudes of the friction force acting on the crate in the first and second trials, respectively?

    • A) 15 N and 12 N
    • B) 20 N and 12 N
    • C) 15 N and 20 N
    • D) 20 N and 28 N