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If the coefficient of static friction between the block and the ramp is 0.4, fi…

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Wize University Physics Textbook (Master) > Newton's Laws of Motion: Forces and Dynamics

Inclined Surfaces

3 Activities

Wize University Physics Textbook (Master) > Newton's Laws of Motion: Forces and Dynamics

Friction

4 Activities

If the coefficient of static friction between the block and the ramp is 0.40.4, find the minimum angle such that the block will slide down the slope.


More Inclined Surfaces Questions:
Problems on Work and Energy
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
(a) What is the speed of the block as it slides along the horizontal surface after having left the spring?
(b) How far does the block travel up the incline before starting to slide back down?
Forces: Block on slope with friction
A mass of 5 kg5\ kg is stationary on the surface of an inclined surface with angle of θ\theta and coefficient of kinetic friction of 0.30.3 and coefficient of static friction of 0.50.5. You start increasing the angle of the inclines surface.
Problems on Work and Energy
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
(a) What is the speed of the block as it slides along the horizontal surface after having left the spring?
(b) How far does the block travel up the incline before starting to slide back down?
trapezoid and friction
Two blocks are attached by a rope over a pulley and are placed on an incline as shown below. A force F is applied to prevent the top block from moving toward the right. If the static and kinetic coefficients of friction of all surfaces are 0.15 and 0.08 respectively, what is the minimum magnitude of F required to prevent being pulled to the right? (Hint: always start these problems with a free-body diagram!)
Two blocks of mass m and M are connected via pulley with a configuration as shown. The surfaces are frictionless. If M=15 kg and m=8 kg and θ1=30 and θ2=60\theta_1=30\ {\rm and}\ \theta_2=60
Find the acceleration
What is the tension in the string?
A 1.2 kg is at rest on a spring at the base of a 35 degree inclined plane. If the spring constant is 105 N/m, and the spring is compressed by 12 cm, how far will it travel up the incline when it is release?
Stacked blocks on a pulley and slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Stacked blocks on a pulley and slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Stacked blocks on a pulley and slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Stacked blocks on a pulley and slope
Practice: Stacked Blocks on Pulley with Slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Problems on Work and Energy
Practice: Block with Spring and Ramp
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
(a) What is the speed of the block as it slides along the horizontal surface after having left the spring?
Forces: Block on slope with friction
A mass of 5 kg5\ kg is stationary on the surface of an inclined surface with angle of θ\thetaand coefficient of kinetic friction of 0.30.3 and coefficient of static friction of 0.50.5. You start increasing the angle of the inclines surface.
Two masses on a pulley on a slope
Two blocks of mass m and M are connected via pulley with a configuration as shown. The surfaces are frictionless. If M=15 kg and m=8 kg and θ1=30 and θ2=60\theta_1=30\ {\rm and}\ \theta_2=60,
Find the acceleration of the system.
What is the tension in the string?
Minimum sliding angle
If the coefficient of static friction between the block and the ramp is 0.40.4, find the minimum angle such that the block will slide down the slope. Give your answer to two sig figs in degrees.
I over-packed a box and it weighs 50kg. I'm pulling it across a rough surface at an angle of 45 degrees above the horizontal with a force of 280N. The coefficient of kinetic friction of the floor is 0.50. I pull for 10 seconds, which causes the box speed up from rest. Then I release it, and it continues to slide, as it slows to a halt.
a) What is its maximum speed?
b) How long until it stops?
Stacked blocks on a pulley and slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Inclined pully system
Two blocks are connected by a pulley system. One block (10 kg) rests on a plane inclined at 35º to the horizontal, while the other block (9.0 kg) hangs off the edge of the incline. The coefficient of friction between the block and the table is 0.30. The blocks are released from rest, what are their accelerations and what is the tension?
Practice: Springs and slopes
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
Component vectors practice 2
A block of weight 30 N is sitting on an incline of 19 degrees.
a) What are the components of the block's weight in the directions parallel to, and perpendicular to, the slope?
b) What is the mass of this block?
Forces: Inclined surfaces
Consider a segment of a light rail train banked at 4.0 degrees from horizontal spanning a turn with a radius of curvature of 450 meters. Neglect friction. What speed was this light rail designed for? (in m/s, rounded to 1 decimal place)
This question is adapted from Chapter 6, problem #75 in the Openstax Physics textbook, which is free and open-source: https://openstax.org/details/books/university-physics-volume-1
Slide and collide
A 5.00kg box is sliding down a 20.0m tall slide that makes an angle of 60.0o with the ground. The coefficient of friction for the slide is 0.750.
At the bottom of the slide it slides on a frictionless surface and collides with a 2.50kg stationary mass.
If the coefficient of static friction between the 2.00kg block and the ramp is 0.4000.400, find the minimum angle such that the block will slide down the slope (in degrees).
Problems on Work and Energy
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
(a) What is the speed of the block as it slides along the horizontal surface after having left the spring?
(b) How far does the block travel up the incline before starting to slide back down?
Work on wagon
A 20kg wagon rests on an inclined plane with angle 30°. The wagon is pulled by a 200N tension force along the plane and is displaced by 2 m. The coefficient of kinetic friction between the surfaces is 0.30.
a) Draw a free-body diagram for the wagon.
b) Find the work done by each force on the wagon.
Block on Slope with Friction
A mass of 5.0 kg5.0\ kg is stationary on the surface of an inclined surface with angle of θ\thetaand coefficient of kinetic friction of 0.300.30 and coefficient of static friction of 0.500.50. You start increasing the angle of the inclines surface.
a) At what angle does the mass start to slide down? (Round to the nearest whole number)
b) If you set the system at an angle which is 5 degrees more than the angle you found in part a), how much time does it take for the speed of the mass to reach 2.0 m/s2.0\ m/s? (Units are in seconds, write the answer so that it has one digit)
A block with mass m is set to move up an inclined plane.
a) Assume there is no friction, how far will the block slide before come to a stop?
b) Now, assume there is friction between the block and the plane, how far will the block go up the plane?
1) Two masses are attached together by a rope as shown in the picture. If the system is released from the rest, what is the direction of the motion and acceleration for each mass? (Imagine there is no friction between masses and the inclined surface) M2 = 2M1 = 2kg
Two blocks of mass m and M are connected via pulley with a configuration as shown. The surfaces are frictionless. If M=15 kg and m=8 kg and θ1=30 and θ2=60\theta_1=30\ {\rm and}\ \theta_2=60
Find the acceleration
What is the tension in the string?
Practice: Inclined Plane Theory
Inclined Plane
Sliding down an inclined plane is another example of motion with constant acceleration.
Source of the motion is still gravity of earth but only part of it is affecting the sliding of the object
trapezoid and friction
Two blocks are attached by a rope over a pulley and are placed on an incline as shown below. A force F is applied to prevent the top block from moving toward the right. If the static and kinetic coefficients of friction of all surfaces are 0.15 and 0.08 respectively, what is the minimum magnitude of F required to prevent being pulled to the right? (Hint: always start these problems with a free-body diagram!)
Practice: Inclined Plane
A box of 10 Kg10\ Kg is released from rest at t=0 st=0\ sfrom the top of a frictionless inclined surface with θ=45°\theta=45\degree. If the box is initially at the top of inclined surface with height of 2 m2\ mrespect to the bottom of the ramp, at what time the box gets to the ground?
Practice: Friction
A 10-kg box is initially at rest on flat surface. A horizontal force of 28 Newton is applied on it. The static and kinetic coefficient of friction between the box and the floor is 0.32 and 0.18. What is the magnitude of the friction force?
Work Done by Multiple Forces
A 20 kg wagon rests on an inclined plane with angle 30°. The wagon is pulled by a 200 N tension force along the plane and is displaced by 2 m. The coefficient of kinetic friction between the surfaces is 0.3.
a) draw all the forces.
b) Find the work done by each force on the box.
Two different boxes of masses m1 = 125kg and m2 = 45kg are sliding down a rough inclined plane angled at θ=35∘\theta = 35^\circ , as seen in the figure. The coefficient of kinetic friction between m1 and the plane is 0.3. The coefficient between m2 and the plane is 0.5. Find the acceleration of the two boxes and the contact force between them.
A 1400-kg truck ascends a steep road at a speedy 60 km/h, against a 450-N force of air resistance. If the engine supplies energy to the drive wheels at the rate of 38 kW, what is the slope of the road?
A fixed triangular wedge has two inclined surfaces forming a double inclines plane. Two masses m1 = 5 kg and m2 = 10 kg are attached to a massless pulley connected with an inextensible string. The inclined surface I1 and I2 make an angle α1=60∘\alpha_1=60^\circ and α2=30∘\alpha_2=30^\circ with the horizontal respectively. The coefficient of kinetic friction is μ=0.01.\mu=0.01. Assume g = 10 m/s2.
a) Draw a free body diagram.
b) Is the system stationary? If not what will be the net acceleration?
A 1.2 kg is at rest on a spring at the base of a 35 degree inclined plane. If the spring constant is 105 N/m, and the spring is compressed by 12 cm, how far will it travel up the incline when it is release?
A stationary snow/water skier starts to slid down an icy slope inclined 11° until it hits the water. Initially skier is 200 meter away from the surface on the inclined surface. When he hits the water, the skier comes to full stop in 80 meters on the surface of water.
a) What is the acceleration of the skier on the icy slope?
b) How long does it take for the skier to hit the water?
A car travelling at 25 m/s on an uphill with θ = 20° slope runs out of the gas. a) How far up the hill it can move before starting to roll back down?
b) How long does it take for the car to get to the turning point?
a) Dave is trying to push a 60kg box up a greased ramp inclined 30°, pushing with a force of 350N. He pushes the box perfectly horizontally, rather than up the ramp, because he’s not terribly bright. What is the box’s acceleration?
b) If Dave forgot his grease at home, the ramp would have μsmax=0.10\mu_{\rm smax}=0.10 and μk=0.05.\mu_k=0.05. He still insists on pushing the box horizontally, with the same force. What would the box’s acceleration be now?
I'm moving and packed all my books into a box that weighs 17kg. I pull the box on a weightless dolly with a force of 60N at an angle of 30° to the horizontal surface. What is the acceleration of the box?
If the coefficient of static friction between the block and the ramp is 0.40.4, find the minimum angle such that the block will slide down the slope.
Forces: Inclined surface
A 40kg wagon attached to a rope is pulled up a hill at an incline of 19° to the horizontal. If the wagon starts from rest and takes 50 seconds to move 92 m up the hill, what is the force of tension in the rope? Find the acceleration of the block.
More Friction Questions:
Kinematics: Friction
Alice decides to push her little brother Bob on ice. Bob weights 3030 kg. Initially, the force Alice is applying on Bob is not enough to start the motion. Alice gradually increases the force on Bob until he starts to slide. After that, Alice keeps pushing Bob (with the same force that she was applying when Bob started to move) for the next 33 s and then lets him go. Bob is going to stop a little bit later. The coefficient of kinetic friction between Bob's shoes and ice is 0.10.1 and the coefficient of static friction between his shoes and ice is 0.20.2.
a) Find Bob's speed at the moment when Alice lets him go.
b) How long does it take for Bob to stop completely after Alice lets him go?
Kinematics: Friction
Alice decides to push her little brother Bob on ice. Bob weights 3030 kg. Initially, the force Alice is applying on Bob is not enough to start the motion. Alice gradually increases the force on Bob until he starts to slide. After that, Alice keeps pushing Bob (with the same force that she was applying when Bob started to move) for the next 33 s and then lets him go. Bob is going to stop a little bit later. The coefficient of kinetic friction between Bob's shoes and ice is 0.10.1 and the coefficient of static friction between his shoes and ice is 0.20.2.
a) Find Bob's speed at the moment when Alice lets him go.
b) How long does it take for Bob to stop completely after Alice lets him go?
trapezoid and friction
Two blocks are attached by a rope over a pulley and are placed on an incline as shown below. A force F is applied to prevent the top block from moving toward the right. If the static and kinetic coefficients of friction of all surfaces are 0.15 and 0.08 respectively, what is the minimum magnitude of F required to prevent being pulled to the right? (Hint: always start these problems with a free-body diagram!)
Friction and a spring
Practice: Friction and a Spring
A spring with a spring constant k=340 N/m is used to launch a 1.5kg block along the horizontal surface whose coefficient of sliding friction is 0.27. If the spring is compressed 18cm, how far does the block slide?
Kinematics: Friction
Alice decides to push her little brother Bob on ice. Bob weights 3030 kg. Initially, the force Alice is applying on Bob is not enough to start the motion. Alice gradually increases the force on Bob until he starts to slide. After that, Alice keeps pushing Bob (with the same force that she was applying when Bob started to move) for the next 33 s and then lets him go. Bob is going to stop a little bit later. The coefficient of kinetic friction between Bob's shoes and ice is 0.10.1 and the coefficient of static friction between his shoes and ice is 0.20.2.
a) Find Bob's speed at the moment when Alice lets him go.
b) How long does it take for Bob to stop completely after Alice lets him go?
Practice: Pulley
You set up a pulley system as shown. There is kinetic friction acting on the top block (μk=0.175\mu_k=0.175) which has mass 4.5 kg. The vertical block has mass 10.0 kg.
A block is sliding on gym floor. The coefficient of static and kinetic friction between the block and the floor are 0.400.40and 0.0700.070 respectively.
a) Draw and label a FBD for both the initial state and the final state.
b) If the block is initially traveling at 3.0 m/s3.0\ m/s, find the total distance the block must travel to stop.
Forces: Friction
Consider a hardcover textbook that you are pressing against a wall. Your pushing force against the book is horizontal, and perpendicular to the wall. The book has a mass of 2.0 kg and the coefficients of kinetic and static friction between the book and the wall are 0.30 and 0.40, respectively.
a) How much force do you have to apply to just barely keep the book from falling?
b) How much force would you have to apply if you were instead pushing upwards and into the wall, at an angle of 20 degrees above horizontal?
Driving in a circle
You are driving around a sharp corner, going clockwise. There is a box in the middle of your back seat. If you are driving fast enough, the box will slide to a side of your car. Which side will it slide to? Why?
(Hint: even if questions do not ask you to draw a sketch or picture, you should draw one anyway! It makes life easier for both you and the exam marker.)
Practice: Box in back of truck
You are driving a flatbed truck. A large box is on the flatbed, at rest relative to the truck. Driving at a speed of 120 km/h, you suddenly need to hit the brakes, slowing down to 100 km/h in 0.64 seconds, because somebody cut you off.
a) What must the coefficient of static friction be to ensure the box does not slip? Is this a realistic coefficient of friction?
b) What does the mass need to be? (Does it matter?)
Newton's third
Let m = 2.50kg and M = 3.00kg. The following situation is given:
The coefficient of kinetic friction between masses is μk,Mm =0.840\mu_{k,Mm}\ =0.840 and between M and the ground is μk,MG = 0.230\mu_{k,MG}\ =\ 0.230.
The coefficient of static friction between masses is μs,Mm=0.950\mu_{s,Mm}=0.950 and between M and the ground is μs,MG =0.320\mu_{s,MG}\ =0.320.
Alice and Bob, arguing and fighting over the usage of the imperial system, are facing each other and pushing. Alice is facing +x, and Bob is facing -x. They are both on a slippery surface and are sliding along together at a steady 4m/s. Which of the following statements are true?
Two cats are on a slanted roof, and they are both not moving. Cat 1 is 2.0kg, and Cat 2 is 3.0kg. Which cat is experiencing the highest frictional force?
I over-packed a box and it weighs 50kg. I'm pulling it across a rough surface at an angle of 45 degrees above the horizontal with a force of 280N. The coefficient of kinetic friction of the floor is 0.5. I pull for 10 seconds, the box speeds up from rest, I release it and it continues to slide to a halt. What is its maximum speed?
Friction and a spring
A spring with a spring constant k=340 N/m is used to launch a 1.5kg block along the horizontal surface whose coefficient of sliding friction is 0.27. If the spring is compressed 18cm, how far does the block slide?
Tugboats (defining systems)
A tugboat of mass 13300 kg has an engine that exerts a force of 112 kN forward while it pulls a much larger boat behind it. This system experiences 16.1 kN of forces resisting motion (think of this as the "friction" between the boat and the water, although there would be more than friction going on in this case).
a) If the acceleration of the system is 0.700 m/s2m/s^2, what is the mass of the larger boat?
b) Calculate the force exerted by the tugboat on the larger boat, assuming that 14.7 kN of the resistive forces are experienced by the larger boat.
The magnitude of the force of static friction is linearly proportional to the applied external force.
work done by force of friction
A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total work done on the block over the same distance?
The mass of the bar is 4 kg. The coefficient of static friction between the bar and the floor is 0.3. Neglect friction between the bar and the wall.
(a) If α=20°\alpha = 20\degree what is the magnitude of the friction force exerted on the bar by the floor?
(b) What is the maximum angle α\alphafor which the bar will not slip
Work done by friction
When a body slides against a rough horizontal surface, the work done by friction is ___________
An object with mass of 4 kg is moving on a frictionless surface in X direction. It enters a rough region with μ=0.3\mu=0.3. If the velocity of the object is 5msı^5\frac{m}{s}\hat\imath , a) what will be its displacement in the rough region? b) What is its velocity half-way through the region? c) Is the motion speeding up or slowing down?
In the following figure, m2 is located on a frictionless surface. If the coefficient of static friction between m1 and m2 is μ\mu,
what is the minimum force required so that m1 and m2 remain stationery?
trapezoid and friction
Two blocks are attached by a rope over a pulley and are placed on an incline as shown below. A force F is applied to prevent the top block from moving toward the right. If the static and kinetic coefficients of friction of all surfaces are 0.15 and 0.08 respectively, what is the minimum magnitude of F required to prevent being pulled to the right? (Hint: always start these problems with a free-body diagram!)
The Work-Energy Theorem: Friction
A car parked on a 32- degree steep hill loses its traction and starts to come down. It travels 160 meters on the hill until it reaches speed of 72 km/h. What is the kinetic coefficient of friction between the car and the surface?
Practice: Friction
A 10-kg box is initially at rest on flat surface. A horizontal force of 28 Newton is applied on it. The static and kinetic coefficient of friction between the box and the floor is 0.32 and 0.18. What is the magnitude of the friction force?
Practice: Alice Pushes Her Brother Bob
Alice decides to push her little brother Bob on ice. Bob weights 30kg. Initially, the force Alice is applying on Bob is not enough to start the motion. Alice increases the force on Bob gradually until he starts to slide. After that, Alice keeps pushing Bob with the same force that she were applying when Bob started moving for the next 3s and then lets him go. Bob is going to stop a little bit later. The coefficient of kinetic friction between Bob's shoes and ice is 0.10.1and the coefficient of static friction between his shoes and ice is 0.2.
a) Find speed of Bob when Alice letting him go.
A bus moving at 40 km/h negotiates a 130m radius banked turn designed for 60 km/h. What coefficient of friction is needed to keep the bus on the road?
Uniform Circular Motion
A 1000kg car rounds a circular track with radius 10m. If μsmax⁡=0.81,\mu _{s\max }=0.81,what is the maximum speed the car can travel?
Practice: Condition of Static Equilibrium
A 3.0 m ladder of mass 12 kg rests against a frictionless wall. The coefficient of friction between the ladder and the floor is 0.60. What is the smallest angle that the ladder can make with the ground if the ladder is to remain at rest? (in degrees) Neglect the friction between the ladder and the wall.
a) Dave is trying to push a 60kg box up a greased ramp inclined 30°, pushing with a force of 350N. He pushes the box perfectly horizontally, rather than up the ramp, because he’s not terribly bright. What is the box’s acceleration?
b) If Dave forgot his grease at home, the ramp would have μsmax=0.10\mu_{\rm smax}=0.10 and μk=0.05.\mu_k=0.05. He still insists on pushing the box horizontally, with the same force. What would the box’s acceleration be now?
Dave is driving his truck, now loaded with his 60kg box full of precious and delicate Ming vases. Unfortunately, he did not secure the box in any way to the bed of the truck, thinking that his truck’s filthy floor was `sticky enough' to stop the box moving. μsmax=0.45\mu_{\rm smax}=0.45 between the truck floor and the box. He drives at a constant 20 m/s and sees a red light coming up. What is the minimum distance he needs to give himself to stop so that the box does not move?
I over-packed a box and it weighs 50kg. I'm pulling it across a rough surface at an angle of 45 degrees above the horizontal with a force of 280N. The coefficient of kinetic friction of the floor is 0.5. I pull for 10 seconds, the box speeds up from rest, I release it and it continues to slide to a halt. What is its maximum speed? How long until it stops? What is the box's total displacement?
Force: Friction calculations
Alice is pushing her little brother, Bob, on ice. Alice weights 35 kg35\ kg while her little brother only weights 15 kg15\ kg. The coefficient of kinetic friction between Bob's shoes and ice is 0.10.1and they have acceleration equal to 2 ms22\ \frac{m}{s^2}.
a) Find the force that Alice exert on Bob.
b) Find the coefficient of static friction between Alice's shoes and ice.
If the coefficient of static friction between the block and the ramp is 0.40.4, find the minimum angle such that the block will slide down the slope.
A 5 kg5\ kgblock is being pulled along at table by a cable and is accelerating along the surface at 2[ms2]2\left[\frac{m}{s^2}\right]. The coefficient of kinetic friction between the block and the table is 0.100.10. Draw the
system then find the tension in the cable. Does the force in the cable change if the system is frictionless? Why or why not?
Forces: Friction
A block is sliding on gym floor. The coefficient of static and kinetic friction between the block and the floor are 0.40.4and 0.070.07 respectively. If the block is initially traveling at 3 m/s3\ m/s find the total distance the block must travel to stop. Draw and label a FBD for both the initial state and the final state.
Forces: Friction
A professional mover drags a 20kg mattress across the floor. The mover exerts a force of 50 N at 30° to the horizontal. The coefficient of kinetic friction is 0.100. What is the acceleration of the mattress?
Vehicles must be able to traverse a curve of radius 60.0 m safely at speeds up to 80 km/h. If the average vehicle weighs 1000 kg, what minimum coefficient of friction is required to make this possible?
Force of friction
A 400-gram package lying on a horizontal surface is attached to a horizontal string that passes over a smooth pulley. When a mass of 200 grams is attached to the other end of the string, the package is on the point of moving. Find the coefficient of friction.