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Energy conservation and circular motion

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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

Spring Force

4 Activities

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?



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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.
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?
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?
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 Spring Force Questions:
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?
Vertical spring
The springs AA, BBand CChave the same initial length. If kA=kC=0.5kBk_A=k_C=0.5k_B,
a) Find the values of mBm_B, mCm_C.
b) Rank the period of oscillations.
Problems on Momentum Conservation and Collisions
Practice: Conservation of Momentum with Spring
A 15.0-kg block is attached to a very light horizontal spring with spring constant 500 N/m and is resting on a friction-less horizontal table. It is struck by a 3.00-kg stone traveling horizontally at 8.00 m/s to the right. The stone rebounds at 2.00 m/s horizontally to the left. Find the maximum distance that the block will compress the spring after the collision. Enter the answer with 3 significant digits.
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?
Hooke's Law and Simple Harmonic Motion
A stretchy rope suspended from the ceiling is 59 cm long when a 70 N weight hangs from it, but is 80 cm long when a 205 N weight hangs from it. Determine the spring constant “k” of the rope.
Momentum and spring
A 15.0-kg block is attached to a very light horizontal spring with spring constant 500 N/m and is resting on a friction-less horizontal table. It is struck by a 3.00-kg stone traveling horizontally at 8.00 m/s to the right. The stone rebounds at 2.00 m/s horizontally to the left. Find the maximum distance that the block will compress the spring after the collision.
Practice: Spring constant
A 300-gram ball starts to roll down 4 meters on a 30 degree incline. (That is, the distance it travels along the slope is 4 meters.) The ball then rolls 2 meters on flat surface and hits a plate, connected to a spring. The spring is compressed 25 cm. If the kinetic coefficient of friction of all surfaces is 0.1, what is the spring constant?
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?
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).
A 2 kg block rests on a spring as shown above, when a 3 kg block is dropped from a height of 3 m above it. The spring constant is 28 N/m. Determine:
The system below initially starts from rest, with a spring constant of 28 N/m.
At t = 0, the 3 kg block is removed. If the 2 kg block is not attached to the spring:
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?
Problems on Momentum Conservation and Collisions
A 15.0-kg block is attached to a very light horizontal spring with spring constant 500 N/m and is resting on a friction-less horizontal table. It is struck by a 3.00-kg stone traveling horizontally at 8.00 m/s to the right. The stone rebounds at 2.00 m/s horizontally to the left. Find the maximum distance that the block will compress the spring after the collision. Enter the answer with 3 significant digits.
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?
Hooke's Law and Simple Harmonic Motion
A stretchy rope suspended from the ceiling is 59 cm long when a 70 N weight hangs from it, but is 80 cm long when a 205 N weight hangs from it. Determine the spring constant “k” of the rope.
Vertical spring
The springs AA, BBand CChave the same initial length. If kA=kC=0.5kBk_A=k_C=0.5k_B,
a) Find the values of mBm_B, mCm_C.
b) Rank the period of oscillations.
This question concerns the great garbage patch in the middle of Pacific ocean. Consider the garbage patch to be a perfect cylinder. At this moment 100 seagulls are sitting on the patch. Every time a wave hits the garbage patch the garbage patch bobs up and down 5 times in 7.2 seconds. When the garbage patch is still the 100 seagulls leave. You know notice that the garbage bobs up and down 5 times in 7 seconds.
The garbage patch weighs 1000 kg. (To make calculations simpler this number is much smaller than the real number.)
a) What is the total mass of the 100 seagulls
A 0.15 kg frame, when suspended from a coil spring, stretches the spring 0.070 m.A 0.200-kg lump of putty is dropped from rest onto the frame from a height of 30.0 cm(Fig). Find the maximum distance the frame moves downward from its initial position.