Problem 2 (25 pts) ● A new child's toy is made of a circular hoop of...
Problem 2 (25 pts)
● A new child's toy is made of a circular hoop of radius 25 cm and has a small bead of mass 20 grams attached to the hoop. The bead is free to move around the hoop without any friction.
The hoop is oriented vertically and spins around at 10 revolutions per second about a pole which passes through the center of the circular hoop.
As the hoop is rotating the bead slides up the hoop to an angle of and sits there stationary going around in a circle.
(A) Find the relation of the radius of the circle in which the bead is moving (r) to the radius of the circular hoop (R) in terms of the angle ? (Note: In this step of the problem your solution should only involve the variables R, r, ...no numbers (8 pts)
(B) Find the angle at which the bead is sitting stationary as the hoop is rotating (This should be a numeric solution)? (9 pts)
(C) Is it possible for the bead to sit
stationary at the
center of the hoop ( = 90o), explain your reasoning? (8
pts)
10 rev/sec
Homework Answers
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Problem 2 (25 pts)
● A new child's toy is made of a circular hoop of...
Can someone show me not just the answers, but how it's solved? Problem 2 (25 pts)...
Can someone show me not just the answers, but how it's
solved?
Problem 2 (25 pts) A new child's toy is made of a circular hoop of radius 25 cm and has a small bead of mass 20 grams attached to the hoop. The bead is free to move around the hoop without any friction. The hoop is oriented vertically and spins around at 10 revolutions per second about a pole which passes through the center of the circular hoop....
Problem 5 (15 points) A small bead can slide without friction on a circular hoop that...
Problem 5 (15 points) A small bead can slide without friction on a circular hoop that is a vertical plane and has a radius of 0.100 m. The hoop rotates at a constant rate of 4.00 rev/sec (recall 1 rev = 2π rad) about a vertical diameter as shown in the figure below (a) Find the angle β at which the bead is in vertical equilibrium. (It has a radial acceleration toward the axis.) (b) Is it possible for the...
3. 25 points A uniform hoop of mass M and radius r has a uniform rod...
3. 25 points A uniform hoop of mass M and radius r has a uniform rod of mass m and length r welded to it as illustrated. a) Given that the rod is at an angle θ from the horizontal, and that the hoop is rotating at a rate ω and rolling on the floor without slipping, what is the total Kinetic Energy, and total Potential Energy (use the height of the center of the hoop as your datum)? Hints:...
2. A toy car with a mass of 35g (0.035kg) is moving clockwise around a loop-the-loop (a track in the shape of a circle that causes the toy car to travel along a circular trajectory) with a radius of...
2. A toy car with a mass of 35g (0.035kg) is moving clockwise around a loop-the-loop (a track in the shape of a circle that causes the toy car to travel along a circular trajectory) with a radius of R- 13cm (0.13m) as depicted in the diagram below. At the point shown (the - on the diagram below) its instantaneous speed (the magnitude of its velocity) is 1.5m/s and its speed is increasing at a rate of 7.1m/s2. (a) (4...
3. A very thin circular hoop of mass m and radius r is made to roll,...
3. A very thin circular hoop of mass m and radius r is made to roll, without slipping, down a ramp with an angle of inclination (with respect to the horizontal), as shown in the figure below. See Figure 3. Note: The moment of inertia of the thin circular hoop is given by: I houp = mra Consider a system consisting of a ladder with a painter climbing said ladder. The ladder has a length 1 = 5,00 meters and...
5. A return to the circular disc problem examined in class (Lecture 2): (Despite all of...
5. A return to the circular disc problem examined in class (Lecture 2): (Despite all of the text below you are required to do very little. Please read on.) A thin, circular plate assumed to lie on the ry-plane is rotating about its center O, located at (0, 0), with constant angular speed w. (w > 0 means that the plate is rotating in the counterclockwise direction.) Using the results obtained in class, show that the velocity field of of...
Multiple Choice (select the best answer) (2 pts each 1. Consider a uniform hoop of radius...
Multiple Choice (select the best answer) (2 pts each 1. Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy? A) Translational kinetic energy is larger B) Rotational kinetic energy is larger. C) Both are equal. D) You need to know the speed of the hoop to tell. 2. A disk and a hoop of the same mass and radius are released at the same...
Problem 9 m,r A solid ball of mass m and radius r sits at rest at the top of a hill of height H l...
Problem 9 m,r A solid ball of mass m and radius r sits at rest at the top of a hill of height H leading to a circular loop-the loop. The center of mass of the ball will move in a circle of radius R if it goes around the loop. The moment of inertia of a solid ball is Ibull--mr. (a) Find an expression for the minimum height H for which the ball barely goes around the loop, staying...
Problem 4 [25 pts] Grader & Score Consider two circular disks centered on the origin so...
Problem 4 [25 pts] Grader & Score Consider two circular disks centered on the origin so that when viewed from the side (i.e. the negative y-axis) they appear as bars in the diagram. Each disk has an area R2 and a positive charge Q. The disks are separated by a small distance s R so that the center of the top disk is located at<0,Q,s/2 > and the center of the bottom disk is at < 0,0, -s/2 >. Point...
Can someone show me not just the answers, but how it's
solved?
Problem 2 (25 pts) A new child's toy is made of a circular hoop of radius 25 cm and has a small bead of mass 20 grams attached to the hoop. The bead is free to move around the hoop without any friction. The hoop is oriented vertically and spins around at 10 revolutions per second about a pole which passes through the center of the circular hoop....
Problem 5 (15 points) A small bead can slide without friction on a circular hoop that is a vertical plane and has a radius of 0.100 m. The hoop rotates at a constant rate of 4.00 rev/sec (recall 1 rev = 2π rad) about a vertical diameter as shown in the figure below (a) Find the angle β at which the bead is in vertical equilibrium. (It has a radial acceleration toward the axis.) (b) Is it possible for the...
3. 25 points A uniform hoop of mass M and radius r has a uniform rod of mass m and length r welded to it as illustrated. a) Given that the rod is at an angle θ from the horizontal, and that the hoop is rotating at a rate ω and rolling on the floor without slipping, what is the total Kinetic Energy, and total Potential Energy (use the height of the center of the hoop as your datum)? Hints:...
2. A toy car with a mass of 35g (0.035kg) is moving clockwise around a loop-the-loop (a track in the shape of a circle that causes the toy car to travel along a circular trajectory) with a radius of R- 13cm (0.13m) as depicted in the diagram below. At the point shown (the - on the diagram below) its instantaneous speed (the magnitude of its velocity) is 1.5m/s and its speed is increasing at a rate of 7.1m/s2. (a) (4...
3. A very thin circular hoop of mass m and radius r is made to roll, without slipping, down a ramp with an angle of inclination (with respect to the horizontal), as shown in the figure below. See Figure 3. Note: The moment of inertia of the thin circular hoop is given by: I houp = mra Consider a system consisting of a ladder with a painter climbing said ladder. The ladder has a length 1 = 5,00 meters and...
5. A return to the circular disc problem examined in class (Lecture 2): (Despite all of the text below you are required to do very little. Please read on.) A thin, circular plate assumed to lie on the ry-plane is rotating about its center O, located at (0, 0), with constant angular speed w. (w > 0 means that the plate is rotating in the counterclockwise direction.) Using the results obtained in class, show that the velocity field of of...
Multiple Choice (select the best answer) (2 pts each 1. Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy? A) Translational kinetic energy is larger B) Rotational kinetic energy is larger. C) Both are equal. D) You need to know the speed of the hoop to tell. 2. A disk and a hoop of the same mass and radius are released at the same...
Problem 9 m,r A solid ball of mass m and radius r sits at rest at the top of a hill of height H leading to a circular loop-the loop. The center of mass of the ball will move in a circle of radius R if it goes around the loop. The moment of inertia of a solid ball is Ibull--mr. (a) Find an expression for the minimum height H for which the ball barely goes around the loop, staying...
Problem 4 [25 pts] Grader & Score Consider two circular disks centered on the origin so that when viewed from the side (i.e. the negative y-axis) they appear as bars in the diagram. Each disk has an area R2 and a positive charge Q. The disks are separated by a small distance s R so that the center of the top disk is located at<0,Q,s/2 > and the center of the bottom disk is at < 0,0, -s/2 >. Point...
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