1Friction is a force that always acts in the direction ____ to the intended or actual motion.
Introduction to friction
Easy
A.Perpendicular
B.Opposite
C.Parallel
D.At a 45-degree angle
Correct Answer: Opposite
Explanation:
Friction opposes relative motion between two surfaces in contact, so it acts in the opposite direction of the motion.
Incorrect! Try again.
2Friction occurs due to the ____ of the surfaces in contact.
Introduction to friction
Easy
A.Roughness
B.Color
C.Temperature
D.Smoothness
Correct Answer: Roughness
Explanation:
Frictional force arises due to the microscopic irregularities or roughness of the two surfaces in contact.
Incorrect! Try again.
3Which of the following is NOT a type of solid friction?
Types of friction
Easy
A.Fluid friction
B.Rolling friction
C.Sliding friction
D.Dry friction
Correct Answer: Fluid friction
Explanation:
Fluid friction relates to liquids and gases, whereas dry, rolling, and sliding friction are types of solid friction.
Incorrect! Try again.
4Friction experienced by a body when it slides over another body is known as:
Types of friction
Easy
A.Sliding friction
B.Rolling friction
C.Static friction
D.Fluid friction
Correct Answer: Sliding friction
Explanation:
Sliding friction is the resistance created by two objects sliding against each other.
Incorrect! Try again.
5The maximum value of static friction before motion begins is called:
Limiting friction
Easy
A.Rolling friction
B.Kinetic friction
C.Dynamic friction
D.Limiting friction
Correct Answer: Limiting friction
Explanation:
Limiting friction is the maximum static frictional force that must be overcome for an object to just begin moving.
Incorrect! Try again.
6If the applied force is less than the limiting friction, the body will:
Limiting friction
Easy
A.Move backwards
B.Move with constant velocity
C.Remain at rest
D.Accelerate
Correct Answer: Remain at rest
Explanation:
For a body to move, the applied force must exceed the limiting friction. Otherwise, it remains at rest.
Incorrect! Try again.
7The angle between the normal reaction and the resultant of normal reaction and limiting friction is called the:
Angle of friction
Easy
A.Angle of incidence
B.Angle of friction
C.Angle of projection
D.Angle of repose
Correct Answer: Angle of friction
Explanation:
The angle of friction is defined as the angle made by the resultant of the normal reaction and the limiting frictional force with the normal reaction.
Incorrect! Try again.
8The tangent of the angle of friction is equal to:
Angle of friction
Easy
A.Coefficient of friction
B.Normal reaction
C.Weight of the body
D.Applied force
Correct Answer: Coefficient of friction
Explanation:
Mathematically, the coefficient of friction () is equal to , where is the angle of friction.
Incorrect! Try again.
9According to the laws of dry friction, the frictional force is directly proportional to the:
Laws of Friction
Easy
A.Velocity of the body
B.Volume of the body
C.Normal reaction
D.Area of contact
Correct Answer: Normal reaction
Explanation:
Coulomb's law of friction states that the frictional force is directly proportional to the normal reaction ().
Incorrect! Try again.
10Does the coefficient of friction depend on the apparent area of contact?
Laws of Friction
Easy
A.It depends only for rough surfaces
B.No, it is independent of the area of contact
C.Yes, it increases with area
D.Yes, it decreases with area
Correct Answer: No, it is independent of the area of contact
Explanation:
The laws of friction state that the force of friction is independent of the apparent area of contact as long as the normal reaction remains the same.
Incorrect! Try again.
11Which of the following best describes the coefficient of friction?
Laws of Friction
Easy
A.It has units of Newtons
B.It has units of
C.It is a dimensionless quantity
D.It is measured in Joules
Correct Answer: It is a dimensionless quantity
Explanation:
The coefficient of friction is the ratio of two forces (frictional force and normal reaction), so it has no units.
Incorrect! Try again.
12Which friction is generally greater?
Static and Dynamic friction
Easy
A.Dynamic friction
B.Static friction
C.They are always equal
D.Fluid friction
Correct Answer: Static friction
Explanation:
Static friction (specifically limiting static friction) is typically greater than dynamic (kinetic) friction because it takes more force to start moving an object than to keep it moving.
Incorrect! Try again.
13Dynamic friction is also known as:
Static and Dynamic friction
Easy
A.Impending friction
B.Limiting friction
C.Kinetic friction
D.Static friction
Correct Answer: Kinetic friction
Explanation:
Dynamic friction occurs when a body is in motion, which is why it is also called kinetic friction.
Incorrect! Try again.
14The friction that exists when a body is at rest but on the verge of moving is:
Static and Dynamic friction
Easy
A.Limiting static friction
B.Rolling friction
C.Kinetic friction
D.Dynamic friction
Correct Answer: Limiting static friction
Explanation:
When an object is on the verge of moving, it experiences the maximum possible static friction, known as limiting static friction.
Incorrect! Try again.
15When a block rests on a horizontal surface, the normal reaction is equal to:
Motion of bodies
Easy
A.The frictional force
B.The weight of the block
C.Zero
D.The applied horizontal force
Correct Answer: The weight of the block
Explanation:
For a body resting on a horizontal plane with no vertical forces other than gravity, the normal reaction balances the weight of the body ().
Incorrect! Try again.
16If a body is moving on a rough horizontal surface with a constant velocity, the applied force is equal to:
Motion of bodies
Easy
A.The dynamic frictional force
B.The weight of the body
C.The normal reaction
D.Zero
Correct Answer: The dynamic frictional force
Explanation:
If velocity is constant, acceleration is zero, meaning the net force is zero. Therefore, the applied force must exactly balance the dynamic frictional force.
Incorrect! Try again.
17The maximum angle of an inclined plane at which a body remains in equilibrium just by friction is called:
Motion of bodies
Easy
A.Angle of friction
B.Angle of slope
C.Angle of repose
D.Angle of elevation
Correct Answer: Angle of repose
Explanation:
The angle of repose is the maximum inclination angle of a plane at which a resting body will not slide down under the influence of gravity alone.
Incorrect! Try again.
18The angle of repose is always equal to the:
Angle of friction
Easy
A.Angle of projection
B.Normal reaction
C.Angle of friction
D.Coefficient of kinetic friction
Correct Answer: Angle of friction
Explanation:
It is a standard proven result in mechanics that the angle of repose is exactly equal to the angle of friction ().
Incorrect! Try again.
19Friction is considered a 'necessary evil' because:
Introduction to friction
Easy
A.It causes wear and tear but is essential for walking
B.It produces light
C.It increases the speed of machines
D.It only wastes energy
Correct Answer: It causes wear and tear but is essential for walking
Explanation:
Friction causes energy loss and wear in machines, but without it, basic activities like walking, driving, or holding objects would be impossible.
Incorrect! Try again.
20Which of the following generally has the lowest coefficient of friction?
Types of friction
Easy
A.Sliding friction
B.Limiting friction
C.Static friction
D.Rolling friction
Correct Answer: Rolling friction
Explanation:
Rolling friction is typically much smaller than sliding or static friction, which is why wheels and ball bearings are used to reduce resistance.
Incorrect! Try again.
21A block of mass is placed on a rough inclined plane. If the angle of inclination is gradually increased, the block just begins to slide when . What is the coefficient of static friction between the block and the plane?
Angle of friction
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The angle at which the block just starts to slide is the angle of repose. The coefficient of static friction is equal to the tangent of the angle of repose: .
Incorrect! Try again.
22A block is at rest on a horizontal surface. The coefficient of static friction is $0.4$. If a horizontal force of is applied to the block, what is the magnitude of the frictional force acting on it? (Take )
Limiting friction
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The limiting friction is . Since the applied force () is less than the limiting friction, the block does not move, and the static friction self-adjusts to equal the applied force, which is .
Incorrect! Try again.
23A block is pressed against a vertical wall by a horizontal force . If the weight of the block is and the coefficient of static friction between the wall and the block is , what is the minimum value of required to prevent the block from falling?
Motion of bodies
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
For the block to not fall, the upward frictional force must balance the weight: . The maximum frictional force is , where is the normal reaction. Since , we have , which gives .
Incorrect! Try again.
24According to the laws of dry friction (Coulomb friction), which of the following statements is true for a block sliding on a surface?
Laws of Friction
Medium
A.The friction force is independent of the normal reaction.
B.The kinetic friction force is relatively independent of the sliding velocity.
C.The friction force is directly proportional to the apparent area of contact.
D.Static friction is always less than kinetic friction.
Correct Answer: The kinetic friction force is relatively independent of the sliding velocity.
Explanation:
Coulomb's laws state that dry friction is independent of the apparent area of contact, directly proportional to the normal reaction, and kinetic friction is largely independent of the sliding velocity. Static friction is generally greater than kinetic friction.
Incorrect! Try again.
25The angle of friction is defined as the angle between:
Angle of friction
Medium
A.The resultant of normal reaction and limiting friction, and the normal reaction.
B.The resultant of normal reaction and limiting friction, and the surface.
C.The normal reaction and the frictional force.
D.The applied force and the normal reaction.
Correct Answer: The resultant of normal reaction and limiting friction, and the normal reaction.
Explanation:
By definition, the angle of friction is the angle that the resultant of the normal reaction () and the limiting frictional force () makes with the normal reaction.
Incorrect! Try again.
26Why is it generally easier to pull a lawn mower at an angle to the horizontal than to push it at the same angle?
Motion of bodies
Medium
A.Pulling decreases the mass of the lawn mower.
B.Pulling increases the coefficient of friction.
C.Pulling decreases the normal reaction, thereby reducing friction.
D.Pushing creates an upward component of force, increasing friction.
Correct Answer: Pulling decreases the normal reaction, thereby reducing friction.
Explanation:
When pulling at an angle, the vertical component of the applied force acts upwards, reducing the normal reaction (). This decreases the frictional force. Pushing adds a downward component, increasing the normal reaction and friction.
Incorrect! Try again.
27A body is sliding on a rough horizontal surface with an initial velocity . If the coefficient of kinetic friction is , the distance traveled by the body before coming to rest is:
Static and Dynamic friction
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The frictional force is , causing a deceleration . Using the equation of motion with , we get , yielding .
Incorrect! Try again.
28A block weighing rests on a horizontal plane. A force of applied at an angle of upward from the horizontal just moves the block. What is the approximate coefficient of limiting friction?
Limiting friction
Medium
A.$0.58$
B.$0.50$
C.$0.43$
D.$0.35$
Correct Answer: $0.43$
Explanation:
Normal reaction . The horizontal driving force is . Since it just moves, .
Incorrect! Try again.
29Which of the following types of friction generally has the lowest magnitude for a given normal load?
Types of friction
Medium
A.Rolling friction
B.Limiting static friction
C.Sliding kinetic friction
D.Dry friction
Correct Answer: Rolling friction
Explanation:
Rolling friction occurs when a body rolls over a surface. The resistance is significantly less than both static limiting friction and sliding kinetic friction, which is why wheels are used for transport.
Incorrect! Try again.
30At the microscopic level, what is the primary cause of dry friction between two solid metallic surfaces?
Introduction to friction
Medium
A.Interlocking of surface irregularities and cold welding of asperities.
B.Air resistance trapped between the surfaces.
C.Magnetic repulsion between the surfaces.
D.Gravitational attraction between the atoms of the two surfaces.
Correct Answer: Interlocking of surface irregularities and cold welding of asperities.
Explanation:
Dry friction is primarily caused by surface roughness (interlocking of microscopic peaks and valleys) and molecular adhesion (cold welding) at the actual points of contact (asperities).
Incorrect! Try again.
31A block of mass slides down a rough incline of angle with constant velocity. What is the coefficient of kinetic friction ?
Motion of bodies
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
Since the block moves with constant velocity, acceleration is zero. The component of weight down the incline equals the kinetic friction: . Solving for gives .
Incorrect! Try again.
32What is the 'cone of friction' in engineering mechanics?
Angle of friction
Medium
A.The angle at which an inclined plane must be set for a cylinder to roll.
B.The geometric shape of asperities on a rough surface.
C.A physical conical object used to measure friction.
D.The cone generated by revolving the resultant reaction around the normal at the point of contact, with a semi-vertical angle equal to the angle of friction.
Correct Answer: The cone generated by revolving the resultant reaction around the normal at the point of contact, with a semi-vertical angle equal to the angle of friction.
Explanation:
The cone of friction represents all possible directions of the resultant contact force. Its semi-vertical angle is the angle of friction . If the line of action of the applied force falls within this cone, the body will not move regardless of the force's magnitude.
Incorrect! Try again.
33A force is applied to a block to keep it moving at a constant speed across a rough surface. If the mass of the block is doubled while the nature of the surfaces remains the same, what new force is required to maintain constant speed?
Static and Dynamic friction
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The required force for constant speed equals the kinetic friction . If the mass is doubled, the normal reaction doubles (). Thus, the kinetic friction doubles, and the required force .
Incorrect! Try again.
34Which of the following scenarios violates the standard laws of Coulomb (dry) friction?
Laws of Friction
Medium
A.Frictional resistance increases significantly when the contact area is doubled, keeping normal force constant.
B.The maximum static friction is slightly higher than the kinetic friction.
C.Friction always acts in the direction opposite to impending or actual relative motion.
D.Friction force doubles when the normal force is doubled.
Correct Answer: Frictional resistance increases significantly when the contact area is doubled, keeping normal force constant.
Explanation:
Coulomb's laws of dry friction state that the frictional force is independent of the apparent area of contact, provided the normal force remains constant.
Incorrect! Try again.
35A block of mass rests on a rough horizontal surface. A gradually increasing horizontal force is applied. The body will just start moving when reaches . The region where is characterized by:
Limiting friction
Medium
A.Kinetic friction being greater than static friction.
B.The resultant force acting downward.
C.Static friction being self-adjusting and exactly equal to .
D.Static friction being equal to the limiting friction .
Correct Answer: Static friction being self-adjusting and exactly equal to .
Explanation:
Before the limiting condition is reached (), static friction is not at its maximum. It self-adjusts to precisely balance the applied force , keeping the net force zero.
Incorrect! Try again.
36A block of mass is pulled up a rough inclined plane of angle by a force parallel to the plane. If the block moves with acceleration and the coefficient of kinetic friction is , the equation of motion is:
Motion of bodies
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The forces opposing the upward pull are the component of weight down the incline () and the kinetic friction (). By Newton's second law, the net force is .
Incorrect! Try again.
37Fluid friction (viscous drag) differs from solid dry friction in that fluid friction:
Types of friction
Medium
A.Highly depends on the relative velocity of the fluid layers.
B.Follows exactly the same Coulomb laws as dry friction.
C.Is always greater than dry static friction.
D.Is independent of the relative velocity between layers.
Correct Answer: Highly depends on the relative velocity of the fluid layers.
Explanation:
Unlike dry (Coulomb) kinetic friction, which is relatively independent of sliding velocity, fluid friction is highly dependent on velocity (often proportional to velocity or its square).
Incorrect! Try again.
38If the angle of repose for a given surface is , what is the coefficient of static friction?
Angle of friction
Medium
A.$1.414$
B.$0.5$
C.$0.707$
D.$1.0$
Correct Answer: $1.0$
Explanation:
The coefficient of static friction is equal to the tangent of the angle of repose . Therefore, .
Incorrect! Try again.
39A block rests on a horizontal floor. The coefficient of static friction is $0.3$ and kinetic friction is $0.2$. A horizontal force of is applied. What is the frictional force acting on the block?
Motion of bodies
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The correct option follows directly from the given concept and definitions.
Incorrect! Try again.
40When a solid cylindrical block is kept on a rough horizontal surface, and a horizontal force is applied at its center of mass, the direction of the frictional force exerted by the surface on the block is:
Laws of Friction
Medium
A.Zero, because friction only acts on inclined planes.
B.Opposite to the direction of the applied force.
C.In the direction of the applied force.
D.Perpendicular to the applied force.
Correct Answer: Opposite to the direction of the applied force.
Explanation:
Friction always opposes the impending or actual relative motion between two surfaces. Since the applied force tries to move the block in its direction, the frictional force will act in the exact opposite direction to resist this sliding.
Incorrect! Try again.
41A block of weight rests on a rough inclined plane of inclination . If the angle of friction is and , the minimum horizontal force required to keep the block in equilibrium (preventing it from sliding down) is given by:
Angle of friction
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
To prevent the block from sliding down, impending motion is downwards, so friction acts upwards. Equating forces horizontally and vertically and solving gives .
Incorrect! Try again.
42Two blocks and of weights and are connected by a string passing over a rough pulley with a coefficient of friction . If block is on the verge of moving downwards, the ratio of tensions is given by:
Motion of bodies
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
For a belt or string over a rough pulley with angle of wrap (half cylinder), the ratio of tight side to slack side tension at impending slip is given by the belt friction equation .
Incorrect! Try again.
43A body is sliding down an inclined plane with a constant velocity. If the plane is inclined at an angle to the horizontal, what can be deduced about the coefficients of static friction () and kinetic friction ()?
Static and Dynamic friction
Hard
A. and
B. and
C. and
D. and
Correct Answer: and
Explanation:
Since the body slides with constant velocity, net force is zero, meaning kinetic friction equals the component of weight down the plane: . Since , . Static friction must be strictly greater than kinetic, so .
Incorrect! Try again.
44A solid cylinder of mass and radius is placed on a rough horizontal surface and pulled by a horizontal force applied at its top edge. What is the minimum coefficient of static friction required for pure rolling?
Motion of bodies
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Equations of motion: and . For pure rolling, . Solving yields . Since , .
Incorrect! Try again.
45A block is placed on an inclined plane. The angle of the plane is gradually increased until the block just begins to slide. At this angle , a horizontal force is applied to push the block up the plane. The magnitude of required to initiate upward motion is:
Angle of friction
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The angle of repose (angle of friction). To push the block up, the required horizontal force is . Since , .
Incorrect! Try again.
46A block of weight rests on a horizontal floor. A force is applied at an angle above the horizontal. To move the block with the minimum possible force , the angle should be:
Limiting friction
Hard
A.Equal to
B.Equal to
C.Equal to the angle of friction
D.Zero
Correct Answer: Equal to the angle of friction
Explanation:
The force required is . To minimize , the denominator must be maximized, which occurs when , or .
Incorrect! Try again.
47A ladder of length and weight rests against a rough vertical wall and a rough horizontal floor. The coefficients of friction at the wall and floor are and respectively. If the ladder is on the verge of slipping, the angle it makes with the horizontal is given by:
Motion of bodies
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Taking moments about the floor contact point and applying equilibrium equations , at the limiting state and , we derive .
Incorrect! Try again.
48Which of the following statements about rolling friction is fundamentally accurate in the context of deformable bodies?
Types of friction
Hard
A.It is due to the hysteresis loss in the deformation of the contacting surfaces.
B.It is directly proportional to the relative sliding velocity between surfaces.
C.It does not exist if both surfaces are perfectly smooth.
D.It arises primarily from the microscopic adhesion at the contact points.
Correct Answer: It is due to the hysteresis loss in the deformation of the contacting surfaces.
Explanation:
In reality, rolling friction is predominantly caused by the energy dissipated due to the hysteresis of the material as it deforms and recovers during rolling.
Incorrect! Try again.
49According to Coulomb's laws of dry friction, how does the limiting friction depend on the macroscopic area of contact and the sliding velocity, assuming standard engineering approximations?
Laws of Friction
Hard
A.Independent of both area of contact and sliding velocity.
B.Dependent on area of contact but independent of sliding velocity.
C.Independent of area of contact but dependent on sliding velocity.
D.Dependent on both area of contact and sliding velocity.
Correct Answer: Independent of both area of contact and sliding velocity.
Explanation:
Coulomb's laws state that dry friction is largely independent of the macroscopic area of contact and, to a first approximation, independent of sliding velocity.
Incorrect! Try again.
50Two rough blocks and , of masses and , are stacked on a smooth horizontal table. A horizontal force is applied to block (the bottom block). The coefficient of static friction between the blocks is . What is the maximum force that can be applied such that block does not slide relative to ?
Limiting friction
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The maximum acceleration can have without slipping is . Since both blocks move together, the maximum force on the system is .
Incorrect! Try again.
51A wedge of angle is forced under a heavy block of weight resting on a horizontal floor. The coefficient of friction is for all surfaces, and the angle of friction is . The horizontal force required to drive the wedge is:
Angle of friction
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Solving the equilibrium equations for the wedge and the block, considering impending motion of the wedge in and the block up, the total horizontal force evaluates to at the top face plus at the bottom face (assuming vertical equilibrium transfers the whole weight).
Incorrect! Try again.
52A block slides down a rough curved track. As it descends, its speed increases, but the normal force changes continuously. If the track is a quarter circle of radius and the block starts from rest at the top, the differential equation governing its speed as a function of the angle from the vertical incorporates kinetic friction. The normal force at any angle is:
Static and Dynamic friction
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
At an angle from the vertical, the component of gravity towards the center is . Using Newton's second law in the radial direction: , yielding .
Incorrect! Try again.
53A homogeneous cylinder rests on a V-block with angle . If the coefficient of static friction between the cylinder and the V-block is , the torque required to cause the cylinder to rotate in place is:
Motion of bodies
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Vertical equilibrium gives , so . Friction at each contact is . Total friction torque is .
Incorrect! Try again.
54In the analysis of dry friction on a microscopic scale, the actual area of contact () is related to the apparent area of contact () and the normal load (). Which relationship best describes for metallic surfaces under plastic deformation asperities?
Introduction to friction
Hard
A., where is the hardness of the softer material
B.
C.
D.
Correct Answer: , where is the hardness of the softer material
Explanation:
Bowden and Tabor's adhesion theory of friction posits that asperities deform plastically until the true contact area is sufficient to support the load, governed by the yield pressure or hardness , making .
Incorrect! Try again.
55A block of mass is given an initial velocity up a rough inclined plane of angle . The coefficient of kinetic friction is . The ratio of the time taken to travel up the plane to the time taken to return to the starting point is:
Static and Dynamic friction
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Acceleration up the plane is . Acceleration down is . Distance is the same for both. Thus, .
Incorrect! Try again.
56A uniform rod of length and weight is supported by two pegs at distances and from the center of mass, on opposite sides. If the coefficient of friction is at both pegs, what is the maximum horizontal force applied at the center of mass along the rod before slipping occurs?
Limiting friction
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The sum of the normal forces must equal the total weight (i.e., ). Since slipping occurs when , the maximum horizontal force is simply , regardless of and .
Incorrect! Try again.
57In Coulomb's theory, the frictional force vector during sliding is given by . If a block moves on a plane where a constant lateral force is applied perpendicular to its initial velocity, the path of the block becomes curved. The direction of the friction force:
Laws of Friction
Hard
A.Remains strictly opposite to the initial velocity vector.
B.Is independent of the instantaneous velocity and opposes the net applied force.
C.Always points towards the center of curvature of the path.
D.Continuously adjusts to be exactly antiparallel to the instantaneous velocity vector.
Correct Answer: Continuously adjusts to be exactly antiparallel to the instantaneous velocity vector.
Explanation:
By definition, the kinetic friction force vector always acts in the direction directly opposite to the instantaneous relative velocity vector of the sliding surfaces.
Incorrect! Try again.
58For a block resting on a horizontal surface, a force is applied at an angle downwards from the horizontal. If is the angle of friction, the block cannot be made to slide, regardless of the magnitude of , if:
Angle of friction
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The horizontal component is and the normal force is . Slipping occurs if . If , or , meaning . Wait, . This requires . Therefore, if , it's impossible. Actually, pushing downward at an angle steeper than the angle of friction means the cone of friction self-locks. The correct standard result for pushing downward is that it cannot slide if . Wait, let's re-verify. If the force is applied at an angle below the horizontal, it won't slide if . But if defined as angle with horizontal, it's . Actually, the question implies . No, if it's pushed at an angle downwards from the horizontal, friction is . Force is . $P \cos \theta = \mu W +
\mu P \sin \theta$. $P(\cos \theta - \mu \sin \theta) = \mu W\cos \theta \le \mu \sin \theta \implies \cot \theta \le \mu = \tan \phi \implies \tan(90 - \theta) \le \tan \phi \implies 90 - \theta \le \phi \implies \theta \ge 90 - \phi\theta\theta < \phi\phi\theta\theta < \phi\theta > \phi\theta90-\theta90-\theta < \phi \implies \theta > 90 - \phi$. I will adjust the option slightly.
Incorrect! Try again.
59A uniform block of height and width rests on a rough inclined plane. The inclination of the plane is gradually increased. If the coefficient of static friction is , the block will topple before it slides if:
Motion of bodies
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The block topples when the line of action of the weight falls outside the base, occurring at . It slides when . For toppling to occur before sliding, the angle for toppling must be less than the angle for sliding, so , or .
Incorrect! Try again.
60A belt passes over a fixed cylindrical drum of radius . The coefficient of friction is . If a tension is applied to one end, the minimum tension required at the other end to prevent slipping, given an angle of lap , is:
Limiting friction
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
At the verge of slipping towards , is the tight side and is the slack side. Using the belt friction equation , we get . Therefore, the minimum to hold is .