Mechanics

A small bead can slide without friction on a circular hoop that is in a vertical plane and has a radius of 0.100 m. The hoop rotates at a constant rate of 4.00 rev/s about a vertical diameter (Fig. P5.107). (a) Find the angle $\mathit{\beta }$ at which the bead is in vertical equilibrium. (It has a radial acceleration toward the axis.) (b) Is it possible for the bead to “ride” at the same elevation as the center of the hoop? (c) What will happen if the hoop rotates at 1.00 rev/s?

Two objects, with masses  5.00 kg and 2.00 kg , hang 0.600 m  above the floor from the ends of a cord that is  6.00 m long and passes over a frictionless pulley. Both objects start from rest. Find the maximum height reached by the  2.00 kg object.

You are riding in an elevator on the way to the 18th floor of your dormitory. The elevator is accelerating upward with $\mathit{w}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{90}\mathbf{ }\mathit{m}\mathbf{/}{\mathit{s}}^{\mathbf{2}}$ . Beside you is the box containing your new computer; the box and its contents have a total mass of 36.0 kg . While the elevator is accelerating upward, you push horizontally on the box to slide it at constant speed toward the elevator door. If the coefficient of kinetic friction between the box and the elevator floor is ${\mathit{\mu }}_{\mathbf{k}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{32}$ , what magnitude of force must you apply?

A block is placed against the vertical front of a cart (Fig. P5.95). What acceleration must the cart have so that block A does not fall? The coefficient of static friction between the block and the cart is ${\mathit{\mu }}_{\mathbf{s}}$ . How would an observer on the cart describe the behavior of the block?

Block A, with weight 3w, slides down an inclined plane S of slope angle 36.9° at a constant speed while plank B, with weight w, rests on top of A. The plank is attached by a cord to the wall (Fig. P5.97). 

(a) Draw a diagram of all the forces acting on block A. 

(b) If the coefficient of kinetic friction is the same between A and B and between S and A, determine its value.

Jack sits in the chair of a Ferris wheel that is rotating at a constant 0.100 rev/s. As Jack passes through the highest point of his circular path, the upward force that the chair exerts on him is equal to one-fourth of his weight. What is the radius of the circle in which Jack travels? Treat him as a point mass

Consider a wet roadway banked as in Example 5.22 (Section 5.4), where there is a coefficient of static friction of 0.30 and a coefficient of kinetic friction of 0.25 between the tires and the roadway. The radius of the curve is R = 50 m . (a) If the bank angle is $\mathit{\beta }\mathbf{=}\mathbf{25}\mathbf{°}$ , what is the maximum speed the automobile can have before sliding up the banking? 

(b) What is the minimum speed the automobile can have before sliding down the banking?

Blocks A, B, and C are placed as in Fig. P5.101 and connected by ropes of negligible mass. Both A and B weigh 25.0 N each, and the coefficient of kinetic friction between each block and the surface is 0.35. Block C descends with constant velocity. 

(a) Draw separate free-body diagrams showing the forces acting on A and on B. 

(b) Find the tension in the rope connecting blocks A and B. 

(c) What is the weight of block C? 

(d) If the rope connecting A and B were cut, what would be the acceleration of C?

You are riding in a school bus. As the bus rounds a flat curve at constant speed, a lunch box with mass 0.500 kg, suspended from the ceiling of the bus by a string 1.80 m long, is found to hang at rest relative to the bus when the string makes an angle of 30.0° with the vertical. In this position the lunch box is 50.0 m from the curve’s center of curvature. What is the speed v of the bus?

You throw a rock downward into water with a speed of 3 mg/k, where k is the coefficient in Eq. (5.5). Assume that the relationship between fluid resistance and speed is as given in Eq. (5.5), and calculate the speed of the rock as a function of time.

A 4.00-kg block is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended as shown in Fig. P5.104 and the tension in the upper string is 80.0 N. 

(a) What is the tension in the lower cord? 

(b) How many revolutions per minute does the system make? 

(c) Find the number of revolutions per minute at which the lower cord just goes slack. 

(d) Explain what happens if the number of revolutions per minute is less than that in part (c).

On the ride “Spindletop” at the amusement park Six Flags Over Texas, people stood against the inner wall of a hollow vertical cylinder with radius 2.5 m. The cylinder started to rotate, and when it reached a constant rotation rate of 0.60 rev/s, the floor dropped about 0.5 m. The people remained pinned against the wall without touching the floor. 

(a) Draw a force diagram for a person on this ride after the floor has dropped. (b) What minimum coefficient of static friction was required for the person not to slide downward to the new position of the floor? 

(c) Does your answer in part (b) depend on the person’s mass? (Note: When such a ride is over, the cylinder is slowly brought to rest. As it slows down, people slide down the walls to the floor.)

A 70-kg person rides in a 30-kg cart moving at 12 m/s at the top of a hill that is in the shape of an arc of a circle with a radius of 40 m. (a) What is the apparent weight of the person as the cart passes over the top of the hill? (b) Determine the maximum speed that the cart can travel at the top of the hill without losing contact with the surface. Does your answer depend on the mass of the cart or the mass of the person? Explain.

A small bead can slide without friction on a circular hoop that is in a vertical plane and has a radius of 0.100 m. The hoop rotates at a constant rate of 4.00 rev/s about a vertical diameter (Fig. P5.107). (a) Find the angle $\mathit{\beta }$ at which the bead is in vertical equilibrium. (It has a radial acceleration toward the axis.) (b) Is it possible for the bead to “ride” at the same elevation as the center of the hoop? (c) What will happen if the hoop rotates at 1.00 rev/s?

A physics major is working to pay her college tuition by performing in a traveling carnival. She rides a motorcycle inside a hollow, transparent plastic sphere. After gaining sufficient speed, she travels in a vertical circle with radius 13.0 m. She has mass 70.0 kg, and her motorcycle has mass 40.0 kg. (a) What minimum speed must she have at the top of the circle for the motorcycle tires to remain in contact with the sphere? (b) At the bottom of the circle, her speed is twice the value calculated in part (a). What is the magnitude of the normal force exerted on the motorcycle by the sphere at this point?

A physics major is working to pay her college tuition by performing in a traveling carnival. She rides a motorcycle inside a hollow, transparent plastic sphere. After gaining sufficient speed, she travels in a vertical circle with radius 13.0 m. She has mass 70.0 kg, and her motorcycle has mass 40.0 kg. (a) What minimum speed must she have at the top of the circle for the motorcycle tires to remain in contact with the sphere? (b) At the bottom of the circle, her speed is twice the value calculated in part (a). What is the magnitude of the normal force exerted on the motorcycle by the sphere at this point?

In your physics lab, a block of mass m is at rest on a horizontal surface. You attach a light cord to the block and apply a horizontal force to the free end of the cord. You find that the block remains at rest until the tension T in the cord exceeds 20.0 N. For T>20 N, you measure the acceleration of the block when T is maintained at a constant value, and you plot the results (Fig. P5.109). The equation for the straight line that best fits your data is $\mathbf{a}\mathbf{=}\mathbf{[}\mathbf{0}\mathbf{.}\mathbf{182}\mathbf{\hspace{0.33em}}\mathbf{m}\mathbf{/}\mathbf{(}\mathbf{N}\mathbf{\cdot }{\mathbf{s}}^{\mathbf{2}}\mathbf{\left)}\mathbf{\right]}\mathbf{T}\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{842}\mathbf{\hspace{0.33em}}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$. For this block and surface, what are (a) the coefficient of static friction and (b) the coefficient of kinetic friction? (c) If the experiment were done on the earth’s moon, where g is much smaller than on the earth, would the graph of a versus T still be fit well by a straight line? If so, how would the slope and intercept of the line differ from the values in Fig. P5.109? Or, would each of them be the same?

In your physics lab, a block of mass m is at rest on a horizontal surface. You attach a light cord to the block and apply a horizontal force to the free end of the cord. You find that the block remains at rest until the tension T in the cord exceeds 20.0 N. For $\mathit{T}\mathbf{>}\mathbf{20}\mathit{N}$, you measure the acceleration of the block when T is maintained at a constant value, and you plot the results (Fig. P5.109). The equation for the straight line that best fits your data is $\mathit{a}\mathbf{ }\mathbf{=}\mathbf{[}\mathbf{0}\mathbf{.}\mathbf{182}\mathbf{m}\mathbf{/}\left(N-s^2\right)\mathbf{]}\mathit{T}\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{842}\mathit{m}\mathbf{/}{\mathit{s}}^{\mathbf{2}}$. For this block and surface, what are (a) the coefficient of static friction and (b) the coefficient of kinetic friction? (c) If the experiment were done on the earth’s moon, where g is much smaller than on the earth, would the graph of a versus T still be fit well by a straight line? If so, how would the slope and intercept of the line differ from the values in Fig. P5.109? Or, would each of them be the same?

A road heading due east passes over a small hill. You drive a car of mass   at constant speed   over the top of the hill, where the shape of the roadway is well approximated as an arc of a circle with radius  . Sensors have been placed on the road surface there to measure the downward force that cars exert on the surface at various speeds. The table gives values of this force versus speed for your car:

Treat the car as a particle. (a) Plot the values in such a way that they are well fitted by a straight line. You might need to raise the speed, the force, or both to some power. (b) Use your graph from part (a) to calculate   and  . (c) What maximum speed can the car have at the top of the hill and still not lose contact with the road?

Question: A road heading due east passes over a small hill. You drive a car of mass m at constant speed v over the top of the hill, where the shape of the roadway is well approximated as an arc of a circle with radius R. Sensors have been placed on the road surface there to measure the downward force that cars exert on the surface at various speeds. The table gives values of this force versus speed for your car:

Treat the car as a particle. (a) Plot the values in such a way that they are well fitted by a straight line. You might need to raise the speed, the force, or both to some power. (b) Use your graph from part (a) to calculate m and R. (c) What maximum speed can the car have at the top of the hill and still not lose contact with the road?

You are an engineer working for a manufacturing company. You are designing a mechanism that uses a cable to drag heavy metal blocks a distance of 8.00 m  along a ramp that is sloped at $\mathbf{40}\mathbf{.}\mathbf{0}\mathbf{°}$ above the horizontal. The coefficient of kinetic friction between these blocks and the incline is ${\mathit{\mu }}_{\mathbf{k}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{350}$. Each block has a mass of 2170 kg. The block will be placed on the bottom of the ramp, the cable will be attached, and the block will then be given just enough of a momentary push to overcome static friction. The block is then to accelerate at a constant rate to move the 8.00 m in 4.20 s . The cable is made of wire rope and is parallel to the ramp surface. The table gives the breaking strength of the cable as a function of its diameter; the safe load tension, which is 20% of the breaking strength; and the mass per meter of the cable:

What is the minimum diameter of the cable that can be used to pull a block up the ramp without exceeding the safe load value of the tension in the cable? Ignore the mass of the cable, and select the diameter from those listed in the table. (b) You need to know safe load values for diameters that aren’t in the table, so you hypothesize that the breaking strength and safe load limit are proportional to the cross-sectional area of the cable. Draw a graph that tests this hypothesis, and discuss its accuracy. What is your estimate of the safe load value for a cable with diameter $\frac{\mathbf{9}}{\mathbf{16}}$ in.? (c) The coefficient of static friction between the crate and the ramp is ${\mathit{\mu }}_{\mathbf{s}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{620}$, which is nearly twice the value of the coefficient of kinetic friction. If the machinery jams and the block stops in the middle of the ramp, what is the tension in the cable? Is it larger or smaller than the value when the block is moving? (d) Is the actual tension in the cable, at its upper end, larger or smaller than the value calculated when you ignore the mass of the cable? If the cable is 9.00 m long, how accurate is it to ignore the cable’s mass?

Question: You are an engineer working for a manufacturing company. You are designing a mechanism that uses a cable to drag heavy metal blocks a distance of 8.00m along a ramp that is sloped at 40.0^o above the horizontal. The coefficient of kinetic friction between these blocks and the incline is ${\mathit{\mu }}_{\mathbf{k}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{350}$. Each block has a mass of 2170kg. The block will be placed on the bottom of the ramp, the cable will be attached, and the block will then be given just enough of a momentary push to overcome static friction. The block is then to accelerate at a constant rate to move the 8.00m in 4.20s. The cable is made of wire rope and is parallel to the ramp surface. The table gives the breaking strength of the cable as a function of its diameter; the safe load tension, which is 20% of the breaking strength; and the mass per meter of the cable:

What is the minimum diameter of the cable that can be used to pull a block up the ramp without exceeding the safe load value of the tension in the cable? Ignore the mass of the cable, and select the diameter from those listed in the table. (b) You need to know safe load values for diameters that aren’t in the table, so you hypothesize that the breaking strength and safe load limit are proportional to the cross-sectional area of the cable. Draw a graph that tests this hypothesis, and discuss its accuracy. What is your estimate of the safe load value for a cable with diameter $\frac{\mathbf{9}}{\mathbf{16}}$ in.? (c) The coefficient of static friction between the crate and the ramp is ${\mathit{\mu }}_{\mathbf{s}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{620}$, which is nearly twice the value of the coefficient of kinetic friction. If the machinery jams and the block stops in the middle of the ramp, what is the tension in the cable? Is it larger or smaller than the value when the block is moving? (d) Is the actual tension in the cable, at its upper end, larger or smaller than the value calculated when you ignore the mass of the cable? If the cable is 9.00 m long, how accurate is it to ignore the cable’s mass?

A wedge with mass  M rests on a frictionless, horizontal tabletop. A block with mass   is placed on the wedge (Fig. P5.112a). There is no friction between the block and the wedge. The system is released from rest. 

(a) Calculate the acceleration of the wedge and the horizontal and vertical components of the acceleration of the block.            

(b) Do your answers to part (a) reduce to the correct results when M is very large? 

(c) As seen by a stationary observer, what is the shape of the trajectory of the block?

Question: A wedge with mass M rests on a frictionless, horizontal tabletop. A block with mass m is placed on the wedge (Fig. P5.112a). There is no friction between the block and the wedge. The system is released from rest. 

(a) Calculate the acceleration of the wedge and the horizontal and vertical components of the acceleration of the block.         

(b) Do your answers to part (a) reduce to the correct results when M is very large? 

(c) As seen by a stationary observer, what is the shape of the trajectory of the block?

A wedge with mass M rests on a frictionless, horizontal table top. A block with mass   is placed on the wedge, and a horizontal force $\overrightarrow{\mathbf{F}}$ is applied to the wedge (Fig. P5.112b). What must the magnitude of   be if the block is to remain at a constant height above the tabletop?

Question: A wedge with mass M rests on a frictionless, horizontal table top. A block with mass m is placed on the wedge, and a horizontal force $\overrightarrow{\mathbf{F}}$ is applied to the wedge (Fig. P5.112b). What must the magnitude of $\overrightarrow{\mathbf{F}}$ be if the block is to remain at a constant height above the tabletop?

Double Atwood’s Machine. In Fig. P5.114 masses  ${\mathbf{m}}_{\mathbf{1}}$ and ${\mathbf{m}}_{\mathbf{2}}$ are connected by a light string A over a light, frictionless pulley B. The axle of pulley B is connected by a light string C over a light, frictionless pulley D to a mass ${\mathbf{m}}_{\mathbf{3}}$ . Pulley D is suspended from the ceiling by an attachment to its axle. The system is released from rest. In terms of  ${\mathbf{m}}_{\mathbf{1}}\mathbf{,}{\mathbf{m}}_{\mathbf{2}}\mathbf{,}{\mathbf{m}}_{\mathbf{3}\mathbf{,}}$ and g, what are (a) the acceleration of block ${\mathbf{m}}_{\mathbf{3}}$ ; (b) the acceleration of pulley B; (c) the acceleration of block ${\mathbf{m}}_{\mathbf{1}}$ ; (d) the acceleration of block  ${\mathbf{m}}_{\mathbf{2}}$; (e) the tension in string A; (f) the tension in string C? (g) What do your expressions give for the special case of  ${\mathbf{m}}_{\mathbf{1}}\mathbf{=}{\mathbf{m}}_{\mathbf{2}}$ and  ${\mathbf{m}}_{\mathbf{3}}\mathbf{=}{\mathbf{m}}_{\mathbf{1}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}$? Is this reasonable?

A ball is held at rest at position A in Fig. P5.115 by two light strings. The horizontal string is cut, and the ball starts swinging as a pendulum. Position B is the farthest to the right that the ball can go as it swings back and forth. What is the ratio of the tension in the supporting string at B to its value at A before the string was cut?

Friction and climbing SHOES. Shoes made for the sports of bouldering and rock climbing are designed to provide a great deal of friction between the foot and the surface of the ground. Such shoes on the smooth rock might have a coefficient of static friction of 1.2 and a coefficient of kinetic friction of   .

For a person wearing these shoes, what’s the maximum angle (with respect to the horizontal) of a smooth rock that can be walked on without slipping? (a) $\mathbf{42}\mathbf{°}$ ; (b) $\mathbf{50}\mathbf{°}$; (c) $\mathbf{64}\mathbf{°}$; (d) larger than $\mathbf{90}\mathbf{°}$ .

Friction and climbing SHOES. Shoes made for the sports of bouldering and rock climbing are designed to provide a great deal of friction between the foot and the surface of the ground. Such shoes on the smooth rock might have a coefficient of static friction of 1.2 and a coefficient of kinetic friction of 0.90.

If the person steps onto a smooth rock surface that’s inclined at an angle large enough that these shoes begin to slip, what will happen? (a) She will slide a short distance and stop; (b) she will accelerate down the surface; (c) she will slide down the surface at constant speed; (d) we can’t tell what will happen without knowing her mass.

Friction and climbing SHOES. Shoes made for the sports of bouldering and rock climbing are designed to provide a great deal of friction between the foot and the surface of the ground. Such shoes on smooth rock might have a coefficient of static friction of 1.2 and a coefficient of kinetic friction of 0.90.

A person wearing these shoes stands on a smooth, horizontal rock. She pushes against the ground to begin running. What is the maximum horizontal acceleration she can have without slipping? (a) 20g; (b) 00.75g ; (c) 0.90g; (d) 1.2g.

Question: Double Atwood’s Machine. In Fig. P5.114 masses ${\mathit{m}}_{\mathbf{1}}$ and ${\mathit{m}}_{\mathbf{2}}$ are connected by a light string A over a light, frictionless pulley B. The axle of pulley B is connected by a light string C over a light, frictionless pulley D to a mass ${\mathit{m}}_{\mathbf{3}}$. Pulley D is suspended from the ceiling by an attachment to its axle. The system is released from rest. In terms of ${\mathit{m}}_{\mathbf{1}}$, ${\mathit{m}}_{\mathbf{2}}$, ${\mathit{m}}_{\mathbf{3}}$, and g, what are (a) the acceleration of block ${\mathit{m}}_{\mathbf{3}}$; (b) the acceleration of pulley B; (c) the acceleration of block ${\mathit{m}}_{\mathbf{1}}$; (d) the acceleration of block ${\mathit{m}}_{\mathbf{2}}$; (e) the tension in string A; (f) the tension in string C? (g) What do your expressions give for the special case of ${\mathit{m}}_{\mathbf{1}}\mathbf{=}{\mathit{m}}_{\mathbf{2}}$ and ${\mathit{m}}_{\mathbf{3}}\mathbf{=}{\mathit{m}}_{\mathbf{1}}\mathbf{+}{\mathit{m}}_{\mathbf{2}}$? Is this reasonable?

The sign of many physical quantities depends on the choice of coordinates. For example, ${\mathbf{a}}_{\mathbf{y}}$ for free-fall motion can be negative or positive, depending on whether we choose upward or downward as positive. Is the same true of work? In other words, can we make positive work negative by a different choice of coordinates? Explain.

An elevator is hoisted by its cables at constant speed. Is the total work done on the elevator positive, negative, or zero? Explain.

A rope tied to a body is pulled, causing the body to accelerate. But according to Newton’s third law, the body pulls back on the rope with a force of equal magnitude and opposite direction. Is the total work done then zero? If so, how can the body’s kinetic energy change? Explain.

Question: A factory worker pushes 30.0-kg crate a distance of 4.5 m along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic friction between the crate and the floor is 0.25. (a) What magnitude of force must the worker apply? (b) How much work is done on the crate by this force? (c) How much work is done on the crate by friction? (d) How much work is done on the crate by the normal force? (e) What is the total work done on the crate?

If it takes total work W to give an object a speed v and kinetic energy K, starting from rest, what will be the object’s speed (in terms of v) and kinetic energy (in terms of K) if we do twice as much work on it, again starting from rest?

If there is a net nonzero force on a moving object, can the total work done on the object be zero? Explain, using an example.

In Example 5.5 (Section 5.1), how does the work done on the bucket by the tension in the cable compare with the work done on the cart by the tension in the cable?

In the conical pendulum of Example 5.20 (Section 5.4), which of the forces do work on the bob while it is swinging?

For the cases shown in Fig. Q6.8, the object is released from rest at the top and feels no friction or air resistance. In which (if any) cases will the mass have (i) the greatest speed at the bottom and (ii) the most work done on it by the time it reaches the bottom?

Does a car’s kinetic energy change more when the car speeds up from 10 to 15 m/s or from 15 to 20 m/s? Explain.

You push your physics book 1.5 m along a horizontal table-top with a horizontal push of 2.40 N while the opposing force of friction is 0.600 N. How much work does each of the following forces do on the book: (a) your 2.40 N- push, (b) the friction force, (c) txhe normal force from the tabletop, and (d) gravity (e) What is the net work done on the book.

Using a cable with a tension of 1350 N, a tow truck pulls a car 5.00 Km along a horizontal roadway. (a) How much work does the cable do on the car if it pulls horizontally? If it pulls at $\mathbf{35}\mathbf{°}$  above the horizontal? (b) How much work does the cable do on the two trucks in both cases of part (a)? (c) How much work does gravity do on the car in part (a)? 

Suppose the worker in Exercise 6.3 pushes downward at an angle of  $\mathbf{30}\mathbf{°}$ below the horizontal (a) What magnitude of force must the worker apply to move the crate at constant velocity? (b) How much work is done on the crate by this force when the crate is pushed at a distance of 4.5 m? (c) How much work is done on the crate by friction during this displacement? (d) How much work is done on the crate by the normal force? (e) What is the total work done on the crate?

A 75.0-kg painter climbs a ladder that is 2.75 m long and leans against a vertical wall. The ladder makes a  $\mathbf{30}\mathbf{°}$ angle with the wall. (a) How much work does gravity do on the painter? (b) Does the answer to part (a) depend on whether the painter climbs at constant speed or accelerates up the ladder?

Two tugboats pull a disabled tanker. Each tug exerts a constant force of 1.80x10⁶ N one $\mathbf{14}\mathbf{°}$  west of north and the other  $\mathbf{14}\mathbf{°}$ east of north, as they pull the tanker 0.75 km toward the north. What is the total work they do on the supertanker?

Two blocks are connected by a very light string passing over a massless and frictionless pulley (Fig. E6.7). Traveling at constant speed, the 20.0-N block moves 75.0 cm to the right and the 12.0-N block moves 75.0 cm downward. How much work is done (a) on the 12.0-N block by (i) gravity and (ii) the tension in the string? (b) How much work is done on the 20.0-N block by (i) gravity, (ii) the tension in the string, (iii) friction, and (iv) the normal force? (c) Find the total work done on each block. 

A force $\overrightarrow{\mathbf{F}}$ is in the x-direction and has a magnitude that depends on x. Sketch a possible graph of F versus x such that the force does zero work on an object that moves from ${\mathit{x}}_{\mathbf{1}}$ to ${\mathit{x}}_{\mathbf{2}}$, even though the force magnitude is not zero at all x in this range.

A falling brick has a mass of 1.5 kg and is moving straight downward with a speed of 5.0 m/s. A 1.5-kg physics book is sliding across the floor with a speed of 5.0 m/s. A 1.5-kg melon is traveling with a horizontal velocity component 3.0 m/s to the right and a vertical component 4.0 m/s upward. Do all of these objects have the same velocity? Do all of them have the same kinetic energy? For both questions, give your reasoning.