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Vehicles must be able to traverse a curve of radius 60.0 m safely at speeds up …

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Wize University Physics Textbook (Master) > Circular Motion

Centripetal Acceleration and Centripetal Force

4 Activities

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

Friction

4 Activities

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?
More Centripetal Acceleration and Centripetal Force Questions:
Two strings on a spinning rod - solving
Practice: Two Strings on Spinning Rod
The 4.00-kg block in the figure 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 the diagram and the tension in the upper string is 80.0 N.
Vertical circular motion
Practice: Vertical String
A box of mass 2.50 kg is attached to a string and whirled in a vertical circle of radius 1.0 m. At the exact top of the path, the tension in the string is 3 times the ball’s weight.
Ball on a string at an angle
Practice: Ball on String at an Angle
A 2.0 kg ball is suspended by a 1.20 m long string. A girl grabs the string and swings it downwards in front of her at a constant speed. The string makes an angle of 35º with the vertical. Determine the speed of the ball.
Because of Earth's rotation about its axis, a point at the poles has no centripetal acceleration. (Assume Earth is a uniform sphere and take g=9.800 ms2. g=9.800\ \frac{m}{s^2}.\ )
A wheel of radius 14.0 m is turning about a horizontal axis through its center. The linear speed of a passenger on the rim is constant and equal to 7.00 m/s.
(a) What are the magnitude and direction of the passenger's acceleration as she passes through the lowest point in her circular motion?
(b) Repeat part (a), but for the highest point instead of the lowest.
Ball on a string at an angle
A 2.0 kg ball is suspended by a 1.20 m long string. A girl grabs the string and swings it downwards in front of her at a constant speed. The string makes an angle of 35º with the vertical. Determine the speed of the ball.
A puck of mass m slides on a frictionless table while attached to a hanging cylinder of mass M by a cord through a hole in a table. What is the angular momentum of the puck?
(Hint: find the speed of the puck by considering uniform circular motion - what is the force providing the centripetal acceleration?)
Practice: Sliding off of a globe
A child is sliding on a spherical pile of snow of radius R. The child is initially at rest at the very top of the hemisphere, but is given a slight push to start sliding down. Neglect friction.
Energy conservation and circular motion
A compressed spring is used to propel a 25-gram ball-bearing along a frictionless horizontal track which contains a circular vertical loop of radius 0.30 m in a vertical plane. The spring obeys Hooke's law and is compressed 20 cm by a force of 5.0 N.
a) What is the speed of the ball-bearing at the top of the loop? Treat the ball bearing as a point mass.
b) What is the minimum spring compression required to have the ball-bearing complete a full loop?
Tension and centripetal force
The 4.00-kg block in the figure 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 the diagram and the tension in the upper string is 80.0 N.
Two strings on a spinning rod - setup, approach
The 4.00-kg block in the figure 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 the diagram and the tension in the upper string is 80.0 N.
Set up the problem (a free-body diagram, find unknown angles and distances, define coordinates) and then go to the next activity. Ask yourself: how do we deal with the rpm quantity in part (b)?
Vertical circular motion
A box of mass 2.50 kg is attached to a string and whirled in a vertical circle of radius 1.0 m. At the exact top of the path, the tension in the string is 3 times the ball’s weight.
For the following systems, draw free-body diagrams and explain what real force(s) is/are providing the centripetal force.
The moon orbiting around the earth
Being in the Gravitron amusement ride (inside, the people are stuck against the walls while the ride spins extremely fast - see picture below)
A small car with mass 0.800 kg travels at constant speed on the inside of a track that is a vertical circle with radius 5.00 m (Fig.). If the normal force exerted by the track on the car when it is at the top of the track (point B) is 6.00 N, what is the normal force on the car when it is at the bottom of the track (point A)
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.)
air puck problem
An air puck of mass m1=0.25 kg{\small m_1=0.25\ kg} is tied to a string and allowed to revolve in a circle of radius R = 1.0 m on a frictionless horizontal table. The other end of string passes through a hole in the center of the table, and a mass of m2=1.0 kg{\small m_2=1.0\ kg} is tied to it (Fig.). The suspended mass remains in equilibrium while the puck on the tabletop revolves.
Ball on a string at an angle
A 2.0 kg ball is suspended by a 1.20 m long string. A girl grabs the string and swings it downwards in front of her at a constant speed. The string makes an angle of 35º with the vertical. Determine the speed of the ball.
Circular Motion
A 20-g marble is free to slide on a frictionless wire loop with radius of 15 cm. The loop starts to rotate about its vertical axis until the bead slides up to θ=60∘ as shown below. What is the angular velocity of the loop at this moment?
A point object travelling in a circle must always have a net force acting on it.
Centripetal force
When an object experiences uniform circular motion, the direction of the net force is
A ball of mass 5 kg and charge Q is performing uniform circular motion on a horizontal surface. The radius of rotation is R=1m and the period of rotation is T=5 s.
If the ball is attached to a spring with equilibrium length of 0.5 m, what is the spring constant?
Assume we put another charge with the same magnitude at the origin for maintaining the circular motion. What is the type and magnitude of the charge?
The 4.00-kg block is Fig. 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 is the diagram 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 revolution per minute at which the lower cord just goes slack. (d) Explain what happens if the number of revolutions per min is less than in part c.
In the 'Giant swing' , the seat is connected to two cables as shown in Fig. , one of which is horizontal.The seat swings in a horizontal circle at a rate of 32.0 rpm (rev/min).If the seat weighs 255 N and an 825 N person is sitting in it, find the tension in each cable.
A boy standing in one spot swings a box on a string in a horizontal circle of radius 2m around him as fast as he can. If the force of tension in the string is 100 N and the mass of the box is 30kg, how fast is the box moving? How many revolutions per minute does it make?
A ball of mass M is released from rest at a vertical height h above the ground. The ball rolls down a frictionless inclined plane and makes it to a loop the loop of radius R.
What is the velocity of the ball as it reaches to the bottom of the incline?
What is the normal force at the bottom?
A 2.0 kg ball is suspended by a 1.20 m long string. A girl grabs the string and swings it downwards in front of her at a constant speed. The string makes an angle of 35º with the vertical. Determine the speed of the ball.
If the angle that the string makes with the vertical increases, what happens to the ball speed?
A 65 kg man is riding a Ferris wheel with radius of 15 m, that moves at 1.5 rpm. Determine the normal force that the man experiences at the top of the ferris wheel and at the bottom.
A boy standing in one spot, swings a box on a string in a horizontal circle with the radius of 2m around him as fast as he can. If the force of tension in the string is 100 N and and the mass of the box is 30kg, how fast is the box moving? How many revolutions per minute does it make?
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!)
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.
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?
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.