The problem involves a slider, modeled as a particle \( P \) with mass \( m \), moving along a frictionless shaft in the horizontal plane, where there is no gravity. At the indicated instant, the slider's speed is \( v \), and the spring is stretched to a length \( r \), greater than its unstretched length \( l_0 \). The spring forms an angle \( \theta \) as shown, and the spring constant \( k \) is unknown. Given that the angular acceleration \(\ddot{\theta} = 0\) and the radial acceleration \(\dot{r} = 0\) in the polar frame, the task is to determine the necessary spring constant. It also requires determining the normal force at this instant. These should be expressed in terms of one or more of the following variables: \( (v, m, r, l_0, \theta) \).**Hint:** Begin by solving for \(\dot{r}\) and \(\dot{\theta}\) from the velocity kinematics.**Diagram Explanation:**- The diagram illustrates the slider \( P \) moving on a vertical shaft. The slider, connected to a spring, moves in the horizontal plane.- The spring extends to a distance \( r \) from a fixed point \( O \), forming an angle \( \theta \) relative to the horizontal axis.- Motion is indicated by vectors: \( v \) for velocity of the slider and \( \theta \) marking the angular direction formed by the spring. This educational setup involves deriving equations of motion and forces considering the physical constraints and is suitable for studies in mechanics and dynamics.

Given data:No radial acceleration, No angular acceleration,

Consider a slider, modeled as a particle P of mass m, moving along a frictionless shaft. The slider moves in the horizontal plane (there is no gravity). At the instant shown, the speed of the slider is v, and the spring is stretched to length r > lo, where lo is its unstretched length. The spring forms an angle as shown and the spring constant k is unknown. If, at the instant shown, 0 = 0 and i = 0 in the polar frame then what must the spring constant be? Also determine the normal force at this instant. Express both in terms of one or more of the following variables: (v, m,r,lo,0). (Hint: first solve for r and è from the velocity kinematics.)

Consider a slider, modeled as a particle P of mass m, moving along a frictionless shaft. The slider moves in the horizontal plane (there is no gravity). At the instant shown, the speed of the slider is v, and the spring is stretched to length r > lo, where lo is its unstretched length. The spring forms an angle as shown and the spring constant k is unknown. If, at the instant shown, 0 = 0 and i = 0 in the polar frame then what must the spring constant be? Also determine the normal force at this instant. Express both in terms of one or more of the following variables: (v, m,r,lo,0). (Hint: first solve for r and è from the velocity kinematics.)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: The 10 kg block A is on an inclined plane with 0 = 30° as shown in the figure below. The block is…

A: Draw the FBD of the block.

Q: An object of mass 3M, moving in the +x direction at speed Vo, breaks into two pieces of mass M and…

Q: The sphere of mass m1 = 5 kg falls from a height H = 1.4 m onto the homogeneous board of negligible…

A: The block will reach a height of 0.575 m after the collision. See attachment for detailed…

Q: Draw a Free Body Diagram of the particle, clearly indicating all forces acting on the particle, anc…

A: Given: m=1 kgR=1.5 mk=65 N/m

Q: Write all the steps with free body diagrams as well please and thank you

Q: Rod AB is fixed to move horizontally, with end A moving the constant velocity shown in the figure.…

Q: If its angular rate of rotation is constant and equals 6 rad/s, determine the horizontal tangential…

A: Solution: Given Data: m=2 kgr=0.4θθ.=6 rad/sθ=45o To Find: (a) Horizontal tangential force, P? (b)…

Q: An automobile P is traveling along a circular track of radius R=958.4 m. At position "A" on the…

Q: Determine for P in the frame N the position vector, velocity vectory, and acceleration vector NaP.

Q: One ball of mass m 1.4 kg is being swung in the vertical, circular path with radius of r = 2.9 m. At…

A: following acceleration act on the ball centripetal acceleration, ac=v2/ r gravitational acceleration…

Q: A box is released from rest at the top of a ramp at timet = 0. It slides down the ramp and collides…

A: Consider the time interval 0<t<tA. Let W be the weight of box so calculate the weight in the…

Q: A particle P of mass m = 3 kg arrives at point O with a horizontal velocity Up and starts rolling…

A: Given:

Q: k m m = 200g, k = 4.44 N/m, v(0) = 0.1 m/s to the right, x(0) = 0.05m to the left of the equilibrium…

Q: The "flying car" is a ride at an amusement park which consists of a car having wheels that roll…

A: Given Data: Constant speed of the track vt=3 ms The radius of the circular path R=9.8 m The total…

Q: The sphere of mass m1 = 5 kg falls from a height H = 1.4 m onto the homogeneous board of negligible…

A: The objective of the question is to find out how high the body of mass m2 rises after the collision.…

Q: The 2 kg bracelet in the figure is released at point A without initial velocity. The ring moves…

A: we are given; Mass=2kg Spring constant k=600N/m

Q: The spool, which has a mass of 2 kg, slides along the smooth horizontal spiral rod, r= (0.400) m,…

A: The mass of the spool is

Q: Consider the pendulum shown in Figure 1, where a small ball of mass m = 1kg suspended by a massless…

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

The problem involves a slider, modeled as a particle \( P \) with mass \( m \), moving along a frictionless shaft in the horizontal plane, where there is no gravity. At the indicated instant, the slider's speed is \( v \), and the spring is stretched to a length \( r \), greater than its unstretched length \( l_0 \). The spring forms an angle \( \theta \) as shown, and the spring constant \( k \) is unknown. Given that the angular acceleration \(\ddot{\theta} = 0\) and the radial acceleration \(\dot{r} = 0\) in the polar frame, the task is to determine the necessary spring constant. It also requires determining the normal force at this instant. These should be expressed in terms of one or more of the following variables: \( (v, m, r, l_0, \theta) \).

**Hint:** Begin by solving for \(\dot{r}\) and \(\dot{\theta}\) from the velocity kinematics.

**Diagram Explanation:**

- The diagram illustrates the slider \( P \) moving on a vertical shaft. The slider, connected to a spring, moves in the horizontal plane.
- The spring extends to a distance \( r \) from a fixed point \( O \), forming an angle \( \theta \) relative to the horizontal axis.
- Motion is indicated by vectors: \( v \) for velocity of the slider and \( \theta \) marking the angular direction formed by the spring.

This educational setup involves deriving equations of motion and forces considering the physical constraints and is suitable for studies in mechanics and dynamics.

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 data

VIEW

Step 2: Solution

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 5 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, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Give me right solution with clear calculations.
I Suppose an autonomous surface vessel (ASV) traveling with velocity TvG/O= vi₁ begins to make a turn by adjusting the thrust of its left and right thrusters, TA and TB, respectively. The center of mass of the ASV is located at G and the ASV is symmetric about its vertical axis. The ASV also experiences a drag force that is proportional to its speed and opposes its velocity. At the instant shown, the drag force is D = -kvi₁ where k is a drag coefficient. 1. To model the mass moment of inertia, approximate the ASV as consisting of three rigid bodies: a flat plate as a center body of mass 6m and two slender rods housing the propulsion assemblies, each of mass m, at the outboard sides of the vehicle. Determine the mass moment of inertia, IG, about the vertical axis passing through the center of mass G. (Hint: Use the parallel axis theorem.) 2. At the instant shown, determine the inertial acceleration vector ac/o = axi₁ + ayi2 of the center of mass and the angular acceleration a of the…
4. A loading car is at rest on a track forming an angle of 25° with the vertical when a force is applied to the cable attached at C. The gross weight of the car and its load is 5465 lb WG, and it acts at point G. Know the tension in the cable connected at C is 5000 Ib Tc. Neglect friction between the car and the track. Determine how far the car travels in 15 seconds. Model this as a particle at G. 24 in. B 25 in. 30 in. 25 in.
Q3. One ball of mass m = 0.7 kg is being swung in the vertical, circular path with radius of r = 2.3 m. At the instant shown, the ball is moving at a speed of v = 5.8 m/s. Determine the tension force in the cable OA. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper Sl unit. Take g = 9.81 m/s². Your Answer: Answer A 45° units
I Review | Constants Calculate the work done on the block by the spring as the block falls an arbitrary distance z. Express your answer in terms of the variables a, m, x, and the acceleration due to gravity g, if needed. Consider a hanging spring of negligible mass that does not obey Hooke's law. When the spring is pulled downward by a distance r, the spring exerts an upward force of magnitude ar, where a is a positive constant. Initially the hanging spring is relaxed (not extended). We then attach a block of mass m to the spring and release the block. The block stretches the spring as it falls (Figure 1). (a) How fast is the block moving when it has fallen a distance z, ? (b) At what rate does the spring do work on the block at this point? (c) Find • View Available Hint(s) the maximum distance rz that the spring stretches. (d) Will the block remain at the point found in part (c)? W. Vspring = Submit Part D Calculate the work done on the block by any other forces as the block falls an…
A ball with a mass of 55.0 g is thrown as shown. (this is a view from the side) There are only two forces acting on it: gravity and air resistance. The air resistance is in the opposite direction of the velocity and has a magnitude of 0.110 N. Find the acceleration vector of the ball. NOTE 1: Don't forget to draw a free body diagram V = 15.0m S 0 = 30.0°