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Two strings on a spinning rod - setup, approach

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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

Tension

3 Activities

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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)?


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.
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 Tension Questions:
Two blocks are connected by a light string which passes over two pulleys as shown. The string and the pulleys are massless and there is no friction. A scale located between two pulleys. The heavier block has a mass of 5kg, and the lighter block has a mess of 3kg. What is the reading on the scale (Pick the closest answer)
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?
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.
Suspended masses
Three masses are suspended from each other as shown. Assume they have equal masses (they are given numbers 1, 2, and 3 for identification purposes only). Which rope has the highest tension? Which has the lowest tension? Why?
Method of sections + example
Determine the forces F1, F2, F3 shown below. The structure is fixed at the left to a wall. All angles are either 45 or 90 degrees. Use positive numbers for members in tension and negative numbers for members in compression.
Practice: Two masses on a pulley
If M = 10kg and m = 5kg, find the net acceleration of the masses. Assume the pulley and strings are frictionless and of negligible mass.
A 5 kg5\ kgblock is being pulled along at table by a cable (horizontally) 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.
a) Sketch the system.
b) Find the tension in the cable.
Consider the truss shown below. (On the left is a sturdy wall.) All triangles are 45-45-90 triangles.
a) Label each member as either being in compression, in tension, or a zero force member.
b) Determine the value of F1, F2, and F3.
A 10 kg mass is hanging from a rope wrapped around a cylindrical pulley. The falling mass causes the pulley to rotate. The mass of the pulley is 3 kg. What is the acceleration of the falling mass, and what is the tension of the rope?
A horizontal rod of length L and mass M has a mass m at one end. It is supported by pivot P on the wall at the left end and a cable at angle θ\theta of at the other end as shown.
a) Find the tension in the cable.
b) If the cable snaps, with what angular velocity will the rod swing down and slam into the wall? (That is, what will the angular velocity be as it collides with the wall?)
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.
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.
Method of joints example
Consider the structure below. The triangles are equilateral. Label the members with letters A through G. A and B are the top two members, from left to right; C, D, E, F are the vertical members, left to right; G is the bottom member.
a) Without doing any calculations, label each member as being either in tension or compression.
b) Determine F1 and F5 in terms of F.
Forces: Torque
A wooden beam of mass 150 kg and length 10m is suspended from a horizontal wall support at the left end and connected by a cable to the same wall at the right end. The cable makes an angle of 45º with the horizontal. A person of mass 42 kg stands on the beam 2.5 m from the left wall. A 25 kg child also rests on the beam, at 7m from the left wall. Calculate (a) the tension in the rope and (b) the magnitude of the force exerted by the wall on the beam.
(Hint for part (b): there are two components. We want the magnitude, but you still need to consider both parts to find the correct magnitude.)
A tent post of length L is held up by two wires connected to the ground. If the tension in the right wire is 30.0 N, what is the tension in the left wire?
A camper hangs a 100kg pack to two separate trees. The two pieces of rope he uses are of different lengths, so the angles of depression (below horizontal) are 30o and 60o. Find the tension in each rope.
A 700kg elevator accelerates upward at 5m/s2, pulled by a cable of negligible mass. Find the tension force in the cable.
Practice: Pulley (no friction)
A giant ice cube of mass 400 kg is on an icy surface (there is no friction). The ice cube is connected by a weightless pulley to a mass that is hanging off the side of the surface below. You do not know the mass of the second object, but you want to measure it.
You release the ice cube from rest and let it slide. It begins to move, accelerating at a constant rate, and you measure that it travels 7.2 cm in 10 seconds. What is the mass of the object?
A camper hangs 100.0kg pack between two trees using two separate ropes of different lengths. One rope hangs at 60.0o below the top of the trees, and the other hangs at 30.0o. Find the tension in each rope.
A 5 kg5\ kgblock is being pulled along at table by a cable and is accelerating along the surface at 2m/s2m/s. 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?
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,
a) Find the acceleration of the system.
b) What is the tension in the string?
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.
(three significant numbers)
Let's say Bob weighs 50kg and Joe weighs 100kg and they are playing a game of tug of war, where the tension in the rope is 50N. Ignore friction to solve for the acceleration of the two men.
Two masses on a pulley
If M = 10.0kg and m = 5.0kg, find the net acceleration of the masses. Assume the pulley and strings are frictionless and of negligible mass. Enter your answer with 2 significant digits, units are m/s2.
Two blocks of mass m1=2kg,m2=4kgm_1 = 2kg, m_2 = 4 kg are connected over a pulley as shown below. The pulley has mass M = 1kg and radius R= 2 cm. What is the acceleration of the blocks and the tension in the rope on either side of the pulley? (HINT: The tension must be different or the pulley would not rotate.)
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 (5.0 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?
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?
A 700kg elevator accelerates upward at 5m/s2, pulled by a cable of negligible mass. Find the tension force in the cable. What happens if the elevator accelerates downward?
A camper hangs a 100-kg pack between two trees using separate ropes of different lengths, as shown in the figure. Find the tension in each of the ropes.
A round spherical steel ball is hanging from ceiling via two ropes as shown below. Ropes are identical and maximum tension they tolerate is 150 Newton. Find maximum weight of the ball that these ropes can handle without breaking.
An object with mass M is hanging from a massless ring that is supported by two identical ropes attached to vertical walls. The ropes can tolerate maximum tension of 1200 N. What is maximum value for M that is allowed without breaking the ropes?
A) 162 kg B) 136 kg C) 112 kg D) 151 kg
Let's say Bob weighs 50kg and Joe weighs 100kg and they are playing a game of tug of war, where the tension in the rope is 50N. Ignore friction to solve for the acceleration of the two men.
Forces: Tension
A 700kg elevator accelerates upward at 5m/s2, pulled by a cable of negligible mass. Find the tension force in the cable.
If M = 10kg and m = 5kg, find the net acceleration of the masses. Assume the pulley and strings are frictionless and of negligible mass.
A camper hangs 100kg pack between two trees using two separate ropes of different lengths. Find the tension in each rope.
Two blocks are connected by a light string which passes over two pulleys as shown. The string and the pulleys are massless and there is no friction. A scale located between two pulleys. The heavier block has a mass of 5kg, and the lighter block has a mess of 3kg. What is the reading on the scale (Pick the closest answer)
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.
A block of mass 4 kg is suspended on two strings between two walls. The angles each string makes below the horizontal is 30°. What is the tension forces in each string? Provide an answer in Newtons and 1 decimal place.
Force of tension
A monkey of mass 10kg climbs up a vertical string suspended from a hook with an acceleration of 2m/s2 . Find tension in the string.