### Physics Magic Trick Experiment#### Apparatus DescriptionYour physics instructor is designing a magic trick for elementary school children and seeks your assistance. The setup involves a small ball and a cup placed on a board. Here’s how it works:- **Components**: A board of length \( \ell = 1.59 \, \text{m} \), a cup, and a support stick.- **Setup**: The ball is placed such that its center aligns with the upper lip of the cup. The cup is attached to the board.- **Mechanism**: When the support stick is removed, the board rotates around the hinged end, and gravity pulls the ball downward. The goal is for the ball to fall into the cup.#### Experiment DetailsThe critical factor is the angle \( \theta \) of the board:- A larger \( \theta \) gives the ball more time to drop into the cup. - If \( \theta \) is too large, the cup might be too far for the ball to reach.- At \( 90^\circ \), the board wouldn’t rotate, preventing the ball from falling into the cup.#### Questions**(a)** Determine the minimum angle \( \theta \) (in degrees) at which the support wouldn't allow the ball to immediately fall off the board. Input your result:\[ \theta \geq \_\_\_\_^\circ \]**(b)** If you provide the wrong angle suggesting the trick will work, calculate where the cup should be positioned \( r_c \) on the board. (Give the distance \( r_c \) from the hinged end of the board in meters):\[ r_c = \_\_\_\_ \, \text{m} \]By altering \( \theta \) and \( r_c \), this educational demonstration can enhance understanding of rotational dynamics and gravitational effects.

Given,Length of the board, l= 1.59 mConcept:We know the torque is defined as from the rotational…

Your physics instructor loves to put on physics magic shows for elementary school children. He is working on a new trick and has asked his star physics student, for assistance. The figure below shows the apparatus he is designing. Cup Hinged end -Support stick A small ball rests on a support so that the center of the ball is at the same height as the upper lip of a cup of negligible mass that is attached to a uniform board of length = 1.59 m. When the support stick is snatched away, the ball will fall and the board will rotate around the hinged end. As the board hits the table, your instructor wants the ball to fall into the cup. The larger the angle 9, the more ti the elementary school children will have to watch the progress of the trick. But if the angle is too large, the cup may not pull ahead of th ball. For example, in the limiting case of 90°, the board would not fall at all!

Your physics instructor loves to put on physics magic shows for elementary school children. He is working on a new trick and has asked his star physics student, for assistance. The figure below shows the apparatus he is designing. Cup Hinged end -Support stick A small ball rests on a support so that the center of the ball is at the same height as the upper lip of a cup of negligible mass that is attached to a uniform board of length = 1.59 m. When the support stick is snatched away, the ball will fall and the board will rotate around the hinged end. As the board hits the table, your instructor wants the ball to fall into the cup. The larger the angle 9, the more ti the elementary school children will have to watch the progress of the trick. But if the angle is too large, the cup may not pull ahead of th ball. For example, in the limiting case of 90°, the board would not fall at all!

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 80-kg man stands at the left end of a 20-kg, 7.0-m-long uniform wooden plank. The plank is sitting…

Q: A 30.0 kg child sits on one end of a long uniform beam having a mass of 20.0 kg, and a 40.0 kg child…

A: Mass of child 1 = M1 = 30 kgMass of child 2 = M2 = 40 kgMass of beam =M = 20 kgDistance of child 1…

Q: In the figure below, a uniform plank, with a length L of 6.20 m and a weight of 460 N, rests on the…

A: The coefficient of static friction between the plank and the ground. given,angle of…

Q: Problem 4: You have been hired to design a family-friendly see-saw. Your design will feature a…

Q: A board sits in equilibrium. On the left end, there is a wire that supports the board from the…

Q: In the figure, a small 0.123 kg block slides down a frictionless surface through heighth = 0.643 m…

Q: A 40-kg door with a height of 2.0 m and a width of 0.80 m is hinged at the end of the door along its…

Q: A solid 5.3 kg sphere of diameter 13 cm rolls up a ramp that is at 30° relative to the horizontal.…

A: (a) kinetic energy of the sphere at the bottom of the ramp…

Q: When using a ladder, it is important to place it against a wall at a safe angle. A ladder could tip…

A: For safe angle, the ratio of working length to distance away from wall = 4:1 To find; Value of safe…

Q: no ai please

Q: The 1400-kg mass of a car includes four tires, each of mass (including wheels) 33 kg and diameter…

A: Given Data: Mass of the car (M) = 1400 kg.Mass of the wheels (m) = 33 kg.Diameter of the wheels (d)…

Q: A plank of mass 87 kg and length 7.8 m is supported by, but not affixed to, two posts which are…

A: Let N1 and N2 be the normal reactions offered by the postLet Wp be weight of plankLet Wm be the…

Q: A board that is a meter long is held up at the 26.0 cm mark. the board is equilibrium when a 0.26 kg…

Q: In the figure, a small 0.455 kg block slides down a frictionless surface through height h = 1.05 m…

A: Given : Mass of the block, m = 0.455 kg Height at which the Mass started, h = 1.05 m Mass of…

Q: A meter stick balances horizontally on a knife-edge at the 50.0 cm mark. With two 4.16 g coins…

Q: A board sits in equilibrium. On the left end, there is a wire that supports the board from the…

Q: Wire Object 1 3 m Object 2 30° 7 m 1 m A homogeneous, 10 m-long beam has a total weight of 70 N and…

A: Given Data : The weight of the beam is given as W = 70 N. The weight of object 1 is given as W1 = 20…

Q: A wooden plank (3 m long) is supported at each end by two support beams. The plank has a mass of 55…

Q: A plank of mass 87 kg and length 7.8 m is supported by, but not affixed to, two posts which are…

A: Given, A plank of mass 87 kg and length 7.8 m

Q: A crowd of innocent bystanders is under the far end of a beam that is hinged to the building and…

Q: A tire, which is mounted on a car, has a radius of 0.23m0.23m. A nail with a mass of 11.4g11.4g is…

Q: A uniform 10.0 m beam of mass 300 kg extends over a ledge, as in Figure. The beam is not attached…

A: A uniform beam of length and massextends over the ledge. The beam is not attached but rests over the…

Q: A clever witch is social distancing during trick-or-treating by sticking her pumpkin-shaped bucket…

A: (given) Length of a broom stick 1.2 m Mass of a broom stick =1.10 kg Mass of pumpkin = 2.4 kg…

Q: John Acorn- Friday Fliers. Six, 8-foot (2.44 m) long aluminum “paper airplane” forms are placed…

Q: A horizontal meter stick supported at the 50-cm mark has a mass of 0.60 kg hanging from it at the…

A: In order to balance the net torque must be zero due to each forces. Torque = r × F

Q: Question 1 A 55.0 kg child sits 1.80 m to the left of center on a seesaw of length, L-7.00 m, and…

A: Given data: Mass of the first child m1 =1.80 m Length of the seesaw L=7.00m Mass of the sea saw…

Q: Question 18 A bar weighs 2 N and is 5 m in length What is the weight needed (M) to balance the bar?…

A: The weight of the bar is 2 N.The length of the bar is 5 m.The hinged point from the left side the 3…

Q: A bucket crane consists of a uniform boom of mass M = 201 kg and length L = 59.81 ft that pivots at…

Concept explainers

Rotational Equilibrium And Rotational Dynamics

In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics.

Equilibrium of Forces

The tension created on one body during push or pull is known as force.

Question

### Physics Magic Trick Experiment

#### Apparatus Description

Your physics instructor is designing a magic trick for elementary school children and seeks your assistance. The setup involves a small ball and a cup placed on a board. Here’s how it works:

- **Components**: A board of length \( \ell = 1.59 \, \text{m} \), a cup, and a support stick.
- **Setup**: The ball is placed such that its center aligns with the upper lip of the cup. The cup is attached to the board.
- **Mechanism**: When the support stick is removed, the board rotates around the hinged end, and gravity pulls the ball downward. The goal is for the ball to fall into the cup.

#### Experiment Details

The critical factor is the angle \( \theta \) of the board:
- A larger \( \theta \) gives the ball more time to drop into the cup.
- If \( \theta \) is too large, the cup might be too far for the ball to reach.
- At \( 90^\circ \), the board wouldn’t rotate, preventing the ball from falling into the cup.

#### Questions

**(a)** Determine the minimum angle \( \theta \) (in degrees) at which the support wouldn't allow the ball to immediately fall off the board. Input your result:

\[ \theta \geq \_\_\_\_^\circ \]

**(b)** If you provide the wrong angle suggesting the trick will work, calculate where the cup should be positioned \( r_c \) on the board. (Give the distance \( r_c \) from the hinged end of the board in meters):

\[ r_c = \_\_\_\_ \, \text{m} \]

By altering \( \theta \) and \( r_c \), this educational demonstration can enhance understanding of rotational dynamics and gravitational effects.

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: Given information

VIEW

Step 2: Calculating the minimum angle

VIEW

Step 3: Calculating the position of cup

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 6 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 ruler with the length of 100 cm and mass of 100g has the pivot point at 35 Cm. Jason suspends an object at 10 cm mark and the system stayed balanced. What is the object mass in grams?
Progress Your answer is partially correct. In the figure, a small 0.299 kg block slides down a frictionless surface through height h = 1.34 m and then sticks to a uniform vertical rod of mass M = 0.598 kg and length d= 1.79 m. The rod pivots about point O through angle 0 before momentarily stopping. Find 0. A Number i 41.3 Units ° (degrees) eTextbook and Media Hint GO Tutorial Save for Later Assistance Used Assistance Used Attempts: 2 of 5 used Submit Answer
Two solid spheres of radius R and mass m are initially separated by a distance d such that the two centres of mass are separated by d+3R as shown below. The spheres are initially at rest, but the gravitational force accelerates them towards each other until they collide.a) Calculate the initial mechanical energy of the system.b) Calculate the gravitational potential energy of the system at the moment they collide.c) Derive an expression for v. State carefully what physical law you are applying.d) Show that, in the limit d >> R, the velocity v is independent of d.
6. A 1.5 m long board with a mass of 4.2 kg sits on top of a 3.0 m long board with mass of 1.5 kg that is balanced on a pivot, as shown in Figure. What is the distance d? d Figure 1
Question 2: #52 An 80 kg construction worker sits down 2.0 m from the end of a 1450 kg steel beam to eat his lunch, as shown in Figure below. The cable supporting the beam is rated at 15,000 N. Should the worker be worried?
A 70kg adult sits at one end of a 9.0m long board. Their 23kg child sits on the other end. A. Where should the pivot be placed so the board is balanced (as distance from adult). Ignore the boards mass. B. Find the pivot point if the board is uniform and has a mass of 15kg.
Don't Use Chat GPT Will Upvote And Give Handwritten Solution Please
The crew on peg leg Petes' ship have mutinied. Now Pete finds himself walking the plank. The plank is 4.5m long and has a mass of 13kg. 3.6 meters of the plank extend out over the waters. The plank pivots on a small rail at the edge of the ship, this is the only point of the plank in direct contact with the ship. The remaining meter of the plank is held in place over the deck by the metal bar. The bar is .6m from the pivot. If Pete has a mass of 111kg, what is the torque provided by the bar when Pete is at the end of the plank?
A seesaw is a flat board that is balanced on a fulcrum (point of balance). When the weight at either end is equal, the seesaw is balanced and both ends are at the same height. When weight is added to either side, the balance will tilt in that direction. To prevent the balance from tipping, the location of the fulcrum must be moved to accommodate the difference in weights placed on each end. A playground equipment company wants to produce a seesaw that will be perfectly balanced when an adult and a child are on either end. The company estimates that an adult, on average, weighs four times as much as a child. The length of the seesaw is 10 feet. C A { 01 2 3 4 5 6 7 8 9 10