A solid 0.5350 kg ball rolls without slipping down a track toward a vertical loop of radius \( R = 0.6150 \, \text{m} \). What minimum translational speed \( v_{\text{min}} \) must the ball have when it is a height \( H = 0.9631 \, \text{m} \) above the bottom of the loop in order to complete the loop without falling off the track?Assume that the radius of the ball itself is much smaller than the loop radius \( R \). Use \( g = 9.810 \, \text{m/s}^2 \) for the acceleration due to gravity.\[ v_{\text{min}} = \quad \qquad \text{m/s} \]**Diagram Explanation:**The diagram shows a ball starting at the top of a slope, with a vertical loop at the bottom. The loop is illustrated as a circle with a radius \( R \). The ball needs a minimum speed \( v_{\text{min}} \) to complete the loop without falling. Height \( H \) is marked vertically from the bottom of the loop to the ball's starting position. The figure notes that it is not to scale.

Given that - Mass of the solid ball Radius Height Acceleration due to gravity To Find - We have…

A solid 0.5350 kg ball rolls without slipping down a track toward a vertical loop of radius R = 0.6150 m. What minimum translational speed Umin must the ball have when it is a height H = 0.9631 m above the bottom of the loop in order to complete the loop without falling off the track? R Assume that the radius of the ball itself is much smaller than the loop radius R. Use g = 9.810 m/s² for the acceleration due to gravity. Figure is not to scale. m/s Umin =

A solid 0.5350 kg ball rolls without slipping down a track toward a vertical loop of radius R = 0.6150 m. What minimum translational speed Umin must the ball have when it is a height H = 0.9631 m above the bottom of the loop in order to complete the loop without falling off the track? R Assume that the radius of the ball itself is much smaller than the loop radius R. Use g = 9.810 m/s² for the acceleration due to gravity. Figure is not to scale. m/s Umin =

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: A bicyclist starting at rest produces a constant angular acceleration of 1.30 rad per second squared…

A: Given: Angular acceleration, α = 1.30 rad/s radius of wheel, r = 36.0 cm To Find: (a) Bicycle linear…

Q: A uniform disk with a radius R swings without friction about a perpendicular asxis on the rim. If it…

A: Given,Uniform disk of radius R, if we assume disk of mass M having centre of mass lie at centre and…

Q: A thin, hollow sphere of mass 2.20 kg and radius 0.550 m is rolling on a horizontal surface with a…

A: Explanation The hollow sphere is rolling on the horizontal surface. So the sphere has both…

Q: A solid 0.7350 kg ball rolls without slipping down a track toward a vertical loop of radius R =…

Q: A solid 0.6950 kg ball rolls without slipping down a track toward a vertical loop of radius R =…

Q: A vertical wheel with a diameter of 50 cm starts from rest and rotates with a constant angular…

Q: uniform disk with mass 44.0 kg and radius 0.200 m is pivoted at its center about a horizontal,…

Q: The angular velocity of a flywheel with radius 1.0 m varies according to ω(t)=2.0t Plot…

A: It is given that, Angular velocity, ω(t)=2·t Radius of flywheel, r=1.0 m Time period, t=0 s to 3.0…

Q: A person 1.65 m tall swings their leg from the hip at 1.10 radians/s. Calculate the linear…

A: Height of the person, h = 1.65 mAngular speed, ω = 1.1 rad/sThe linear tangential velocity is…

Q: A lawn mower has a flat, rod-shaped steel blade that rotates about its center. The mass of the blade…

A: mass = 0.65 kg Length (L) = 0.55 m

Q: A solid 0.5150 kg ball rolls without slipping down a track toward a vertical loop of radius R =…

Q: id 0.4550 kg ball rolls without slipping down a track toward a vertical loop of radius ?=0.7150 m.…

A: The mass of the solid is m = 0.4550 kg. The ball rolls without slipping down a track toward a…

Q: When climbing into your childhood tree house you realize weight of mass m = 3.0 kg in the middle of…

A: We know that the torque is given as τ= Iα where I is the moment of inertia α is the angular…

Q: A solid ball of mass m = 132 g and radius r = 9.00 cm will roll smoothly without slipping along a…

Q: Flywheels are solid, uniform disks that spin around an axis running through their center of mass and…

A: Write the expression for the kinetic energy of rotation. Here, E represents the energy, R…

Q: A thin circular hoop is released from rest at the top of a plane inclined at 12.1 degrees above the…

A: Given data The inclination of the inclined plane is given as θ=12.1°. The height from where the…

Q: A skater spins about a fixed point on the ice. She begins with her arms extended and an initial…

A: Write a given values of this question. Initial angular velocity is . Final angular velocity is .

Q: A solid 0.5750 kg ball rolls without slipping down a track toward a vertical loop of radius R =…

A: In the Question it is given that A solid 0.5750 kg ball rolls without slipping down a track toward…

Q: a. If the ball is released from rest at a height of 0.61 m above the bottom of the track on the…

Q: A 21 mm diameter glass marble with a mass of 25 g rolls without slipping down a track toward a…

Q: Problem 5: A rigid ring of r = 3.40 m is started in rotational counterclockwise motion at t=0 with…

Q: NE Chapter 10, Problem 062 Z Your answer is partially correct. Try again. In the figure, three 0.07…

Q: A car tire (hoop) has a mass of 35 kg and a radius of 0.43 m. The tire is released from rest at the…

Q: R M A solid sphere of uniform density starts from rest and rolls without slipping down an inclined…

Q: A golfers clubs' linear tangential velocity at contact with the ball on the tee was recorded as 35.6…

Q: Problem 7 : A sphere of radius r0 = 24.0 cm and mass m = 1.20kg starts from rest and rolls without…

A: (given) Radius of sphere (r0) = 24 m Mass of sphere = 1.20 kg Inclined angle=…

Q: Two masses, m = 31.0 kg and mp = 42.0 kg are connected by a rope that hangs over a pulley (as in the…

A: See below

Q: A m = 2kg ring has a radius of r = 0.5m. The moment of inertia of a ring is I = m r². The ring has…

Q: A uniform sphere is placed inside hemispherical bowl of radius R = 75.0 cm. It is released from rest…

Q: A hollow ball of mass m = 2.0 kg and radius r rolls without slipping along a loop-the-loop track,…

Q: 1.1kg bike wheel, is spinning 190rpm clockwise when a student applies a rictional force as shown.…

Concept explainers

Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

Question

A solid 0.5350 kg ball rolls without slipping down a track toward a vertical loop of radius \( R = 0.6150 \, \text{m} \). What minimum translational speed \( v_{\text{min}} \) must the ball have when it is a height \( H = 0.9631 \, \text{m} \) above the bottom of the loop in order to complete the loop without falling off the track?

Assume that the radius of the ball itself is much smaller than the loop radius \( R \). Use \( g = 9.810 \, \text{m/s}^2 \) for the acceleration due to gravity.

\[ v_{\text{min}} = \quad \qquad \text{m/s} \]

**Diagram Explanation:**

The diagram shows a ball starting at the top of a slope, with a vertical loop at the bottom. The loop is illustrated as a circle with a radius \( R \). The ball needs a minimum speed \( v_{\text{min}} \) to complete the loop without falling. Height \( H \) is marked vertically from the bottom of the loop to the ball's starting position. The figure notes that it is not to scale.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

A solid 0.6350 kg ball rolls without slipping down a track toward a vertical loop of radius ?=0.6350 m. What minimum translational speed ?min must the ball have when it is a height ?=0.9944 m above the bottom of the loop in order to complete the loop without falling off the track? Assume that the radius of the ball itself is much smaller than the loop radius ?. Use ?=9.810 m/s^2 for the acceleration due to gravity.
T m A 25.0 kg mass is hung from a rope that is passed over a pulley and held by a man standing on a ramp. The pulley can be treated as a solid disk with a mass of 10.0 kg that has a radius of 0.400 m. The man pulls the rope so that the pulley rotates from rest through an angular displacement of 15.0 rad in 2.00s. A. What is the angular acceleration of the disk? B. What is the tension of the rope as it pulls up on the box? C. What is the force applied by the man on the rope as he pulls the box upward?
A solid 0.7350-kg ball rolls without slipping down a track toward a loop-the-loop of radius R 0.8950 m. What minimum translational speed Vmin must the ball have when it is a height H= 1.402 m above the bottom of the loop, in order to complete the loop without falling off the track? Н Number m/s min figure not to scale
h A solid sphere rolls without slipping down an incline. At the top it is at rest. What is the linear speed at the bottom? Parameters: ] mass = m = 4.3 kg; angle of the incline height of the ramp = h = 1.10 m; horizontal length of the ramp = L = 3.02 m. (in m/s) = 20 degrees; A: 3.356 OB: 3.926 OC: 4.594 OD: 5.375 OE: 6.288 OF: 7.357 OG: 8.608 OH: 1.007x10¹
A ball of radius Ris rolling across a rough surface without slipping. What is the relationship between the angular speed w and the translational speed v? Image size: Select the correct answer Ου-R/ω Ου- 1/ω O v= w Ου-ω/R O V = Rw
A large wind turbine (typical of the size and specifications of a turbine that you see in a modern wind farm) has three blades connected to a central hub. The blades are 50 m long and rotate at 10 rpm. What angular speed ω does this correspond to? What is the speed ν of the tip of a blade? What is the speed of a point 25 m from the hub?
A solid 0.5950 kg ball rolls without slipping down a track toward a vertical loop of radius ?=0.6550 m. What minimum translational speed ?min must the ball have when it is a height ?=1.008 m above the bottom of the loop in order to complete the loop without falling off the track? Assume that the radius of the ball itself is much smaller than the loop radius ?. Use ?=9.810 m/s2 for the acceleration due to gravity.
A solid 0.6150 kg ball rolls without slipping down a track toward a vertical loop of radius ?=0.7350 m. What minimum translational speed ?minvmin must the ball have when it is a height H=1.111 m above the bottom of the loop in order to complete the loop without falling off the track? Assume that the radius of the ball itself is much smaller than the loop radius ?R. Use g=9.810 m/s^2 for the acceleration due to gravity.
W; = 0 %3D Wf initial final A flywheel consists of a thin uniform disk of mass m and radius R, free to rotate about a frictionless central axle. A small weight, also of mass m, is attached to the wheel's rim. The is wheel is held at rest (left), the small weight level with the axle, then released. What is the angular velocity of the wheel when the weight reaches its lowest point? 4g V 3R 8g V 5R 3g V 2R V28R 2gR
W L A rod of length L = 35.0 cm rotates about its end through O with a constant angular acceleration a = 2.23 rad/s², as shown in the figure. At t= 0, the initial tangential speed of a point P on the rod is to 14.4 m/s. Find the final tangential speed v of the point P at t = 5 s. O 21.96 O 18.30 O 27.45 O 15.25 12.20
A long, thin uniform rod of length 1.29m and mass 2.08kg is pivoted about a horizontal, frictionless pin passing through one end. The rod is released from one end in the vertical position. L y Pivot x At the instant the rod is horizontal, find its angular speed. Submit Answer Tries 0/10 At the instant the rod is horizontal, what is its angluar acceleration? Submit Answer Tries 0/10 At the instant the rod is horizontal, what is the magnitude of its x-component of acceleration at its centre of mass? Submit Answer Tries 0/10 At the instant the rod is horizontal, what is the magnitude of its Y-component of acceleration at its centre of mass? Submit Answer Tries 0/10
Plz asap