Charles Kingsley

Answered

2022-01-04

A slender rod is 80.0 cm long and has mass 0.120 kg. A small 0.0200-kg sphere is welded to one end of the rod, and a small 0.0500-kg sphere is welded to the other end. The rod, pivoting about a stationary, frictionless axis at its center, is held horizontal and released from rest. What is the linear speed of the 0.0500-kg sphere as it passes through its lowest point?

Answer & Explanation

Janet Young

Expert

2022-01-05Added 32 answers

Step 1

$\mathrm{\u25b3}U={m}_{2}g{y}_{2}+{m}_{3}g{y}_{3}=g\times (0.05\times (-0.4)+0.02\times 0.4)=-0.118N.m$

Determine the system's overall potential change. m2 and m3 are the masses at the rod ends. note the rod centre of mass neither gains nor loses potential.

Step 2

$I}_{1}=2\rho {\int}_{0}^{r}{r}^{2}dr=2\times \frac{0.12}{0.8}{\int}_{0}^{0.4}{r}^{2}dr=0.0064kg.{m}^{2$

Determine the rod's moment of inertia.

Step 3

$I}_{2+3}=\sum m{r}^{2}=(0.05+0.02)\times {0.4}^{2}=0.0112kg.{m}^{2$

determine the end masses' moment of inertia

Step 4

$\mathrm{\u25b3}U=K=\frac{1}{2}({I}_{1}+{I}_{2+3}){\omega}^{2}$

compare the system's kinetic energy to the change in potential energy.

Step 5

$=0.118=\frac{1}{2}\times 0.0176{\omega}^{2}$

Calculate velocity at lowest point:

Step 6

$\omega =3.66ra\frac{d}{s};v=r\omega =0.4\times 3.66=1.46\frac{m}{s}$

Debbie Moore

Expert

2022-01-06Added 43 answers

Answer:

Explanation:

Given that,

Slender rod

Length of rod

Mass of slender rod

Sphere Bob at one end

Mass

Sphere Bod at the other end

Mass

Linear speed of mass 2 at the lowest point

We need to calculate the change in potential of the complete system. m2 and m3 are the masses at the rod ends. note the rod centre of mass neither gains nor loses potential.

So, at the lowest point,

Note, at the lowest point, the mass 1 is 40cm (0.4m) form the midpoint, Also, the mass 2 is

Now, the moment of inertia of the rod is given as

calculating of inertia of the end masses.

Now, the Energy of the masses due to angular velocity is given as

Using conservation of energy

The potential energy is equal to the kinetic energy of the system

Then,

0

karton

Expert

2022-01-11Added 439 answers

Step 1

The PE of an object is the amount of energy the object will store because it is at a certain height.

The PE is given as

U=mgh

where m= mass of the object, g= acceleration due to gravity, and h= height.

Step 2

The PE of the system is given by

Again, PE of the system is given by

The linear velocity is given by

Step 3

Hence, the required velocity is 1.462m/s

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