**Problem Overview:**You apply a horizontal force \( F_{yb} = 43 \, \text{N} \) to a string connected to a block of mass \( m_b = 7.5 \, \text{kg} \), which is also attached to the axle of a solid cylinder with mass \( m_c = 5 \, \text{kg} \) and radius \( r = 0.4 \, \text{m} \). The other end of the string is tied to a spring with spring constant \( k = 135 \, \text{N/m} \). The system is on an inclined plane with an angle \( \theta = 27^\circ \), experiencing friction (with static friction coefficient \( \mu_s = 0.62 \) and kinetic friction coefficient \( \mu_k = 0.39 \)). Initially, everything is at rest, and the spring is unstretched. The block and cylinder move down the incline, with the cylinder rolling without slipping, and the spring stretches.**Diagram Explanation:**The diagram shows an inclined plane with angle \( \theta \) and a block connected to a spring and a solid cylinder. The force \( \vec{F_{yb}} \) is applied horizontally to the system. The spring is compressed against the plane, and \( \vec{k} \) represents the spring force.**Question:**What is the speed of the block and cylinder after moving 64 cm down the plane?**Answer:**The speed is calculated as \( v = 2.18193489018 \, \text{m/s} \).

Name: **Problem Overview:**You apply a horizontal force \( F_{yb} = 43 \, \
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Description: **Problem Overview:**You apply a horizontal force \( F_{yb} = 43 \, \text{N} \) to a string connected to a block of mass \( m_b = 7.5 \, \text{kg} \), which is also attached to the axle of a solid cylinder with mass \( m_c = 5 \, \text{kg} \) and ra

Given data: Horizontal force Fyb = 43 N Block's mass mb = 7.5 kg Cylinder mass mc = 5 kg Radius r = 0.4 m Spring constant k = 135 N/m Angle θ=27o Static frictional constant μs=0.62 Kinetic frictional constant μk=0.39 Displacement of block and cylinder d = 64 cm The expression for the energy due to friction can be given as: Kf=mbgcosθ-Fybsinθμkd =7.5 kg×9.81 m/s2×cos27o-43 N×sin27o0.39×64×10-2m =11.49 J The expression for the translation kinetic energy of both cylinder and block together can be given as; KT=12mb+mcv2 =127.5 kg+5 kgv2 =6.25v2 The expression for the rotational kinetic energy of the cylinder can be given as: KR=12Iω2 =1212mcr2vr2 =14mcv2 Substitute the respective values. KR=145 kgv2 =1.25v2 The change in potential energy for both cylinder and block is, ∆U=-mb+mcgdsinθ =-7.5+59.810.64sin27o =-35.63 J The expression for the spring potential energy can be given as; Us=12kd2 =12135 N/m0.64 m2 =27.65 J According to conservation of energy. Kf+KT+KR+∆U+Us=Fybdcosθ Substitute the respective values. 11.49+6.25v2+1.25v2-35.63+27.65=43 N0.64 mcos27o3.51+7.5v2=24.52v=1.67 m/s

Science

Physics

You pull on a string with a horizontal force of magnitude Fyb = 43 N that is attached to a block of mass mp = 7.5 kg. then to the axle of a solid cylinder of mass me = 5 kg and radius r = 0.4 m, then to a spring of spring constant k = 135 N/m. This is all done on an inclined plane where there is friction (s = 0.62 and μ = 0.39), and the incline angle is = 27 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the spring stretches. k belllllll Speed b 0 yb First, what is the speed of the block and cylinder after you have pulled the block and cylinder 64 cm down the plane? U2.18193489018 m/s

You pull on a string with a horizontal force of magnitude Fyb = 43 N that is attached to a block of mass mp = 7.5 kg. then to the axle of a solid cylinder of mass me = 5 kg and radius r = 0.4 m, then to a spring of spring constant k = 135 N/m. This is all done on an inclined plane where there is friction (s = 0.62 and μ = 0.39), and the incline angle is = 27 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the spring stretches. k belllllll Speed b 0 yb First, what is the speed of the block and cylinder after you have pulled the block and cylinder 64 cm down the plane? U2.18193489018 m/s

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)...

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Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

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Question

**Problem Overview:**

You apply a horizontal force \( F_{yb} = 43 \, \text{N} \) to a string connected to a block of mass \( m_b = 7.5 \, \text{kg} \), which is also attached to the axle of a solid cylinder with mass \( m_c = 5 \, \text{kg} \) and radius \( r = 0.4 \, \text{m} \). The other end of the string is tied to a spring with spring constant \( k = 135 \, \text{N/m} \). The system is on an inclined plane with an angle \( \theta = 27^\circ \), experiencing friction (with static friction coefficient \( \mu_s = 0.62 \) and kinetic friction coefficient \( \mu_k = 0.39 \)). Initially, everything is at rest, and the spring is unstretched. The block and cylinder move down the incline, with the cylinder rolling without slipping, and the spring stretches.

**Diagram Explanation:**

The diagram shows an inclined plane with angle \( \theta \) and a block connected to a spring and a solid cylinder. The force \( \vec{F_{yb}} \) is applied horizontally to the system. The spring is compressed against the plane, and \( \vec{k} \) represents the spring force.

**Question:**

What is the speed of the block and cylinder after moving 64 cm down the plane?

**Answer:**

The speed is calculated as \( v = 2.18193489018 \, \text{m/s} \).

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