Question

A sphere of radius r=34.5 cm and mass m= 1.80kg starts from rest and rolls without slipping down a 30.0 degree incline that is 10.0 m long. calculate the translational and rotational speed when it reaches the bottom.

Answer #1

**from the given data**

**vertical height, h = 10*sin(30)**

**= 5 m**

**Now Apply conservation of energy**

**final kinetic energy = initial potentail
energy**

**0.5*m*v^2 + 0.5*I*w^2 = m*g*h**

**0.5*m*v^2 + 0.5*(2/5)*m*r^2*w^2 = m*g*h**

**0.5*m*v^2 + 0.2*m*r^2*w^2 = m*g*h**

**0.5*m*v^2 + 0.5*m*v^2 = m*g*h**

**0.7*m*v^2 = m*g*h**

**v = sqrt(g*h/0.7)**

**= sqrt(9.8*5/0.7)**

**= 8.37 m/s
<<<<<<----------Answer**

**rotational speed, w = v/r**

**= 8.37/0.345**

**= 24.3 rad/s
<<<<<<----------Answer**

**angular velocity, w = 4 rev/s**

**= 4*2*pi rad/s (since 1 revolution = 2*pi
radians)**

**= 25.13 rad/s
<<<<<-------Answer**

A sphere of radius r0 = 22.0 cm and mass m = 1.20kg starts from
rest and rolls without slipping down a 34.0 degree incline that is
12.0 m long.
Part A: Calculate its translational speed when it reaches the
bottom. (m/s)
Part B: Calculate its rotational speed when it reaches the
bottom. (rad/s)
Part C: What is the ratio of translational to rotational kinetic
energy at the bottom? (Ktr/Krot)
Part D: Does your answer in part A depend on...

A solid sphere of uniform density starts from rest and rolls
without slipping a distance of d = 4.4 m down a
θ = 22°incline. The sphere has a
mass M = 4.3 kg and a radius R
= 0.28 m.
1)Of the total kinetic energy of the sphere, what fraction is
translational?
KE
tran/KEtotal =
2)What is the translational kinetic energy of the sphere when it
reaches the bottom of the incline?
KE tran =
3)What is the translational speed...

A hollow sphere (mass M, radius R) starts from rest at the top
of a hill of height H. It rolls down the hill without slipping.
Find an expression for the speed of the ball's center of mass once
it reaches the bottom of the hill.

A uniform, solid sphere of radius 3.00 cm and mass 2.00 kg
starts with a purely translational speed of 1.25 m/s at the top of
an inclined plane. The surface of the incline is 1.00 m long, and
is tilted at an angle of 25.0 ∘ with respect to the horizontal.
Assuming the sphere rolls without slipping down the incline,
calculate the sphere's final translational speed v 2 at the bottom
of the ramp.

A uniform solid disk of mass 2.20 kg and diameter 50.0 cm starts
from rest and rolls without slipping down a 30.0 ? incline that is
5.25 m long. g = 9.81 m/s2 .
(a) Calculate the linear speed of the center of the disk when it
reaches the bottom of the incline.
(b) Determine the angular speed of the disk about its center at
the bottom of the incline.
(c) Through what angle (in radians) does this disk turn...

A uniform, solid sphere of radius 5.75 cm 5.75 cm and mass 3.25
kg 3.25 kg starts with a purely translational speed of 1.25 m/s
1.25 m/s at the top of an inclined plane. The surface of the
incline is 2.25 m 2.25 m long, and is tilted at an angle of 29.0 ∘
29.0∘ with respect to the horizontal. Assuming the sphere rolls
without slipping down the incline, calculate the sphere's final
translational speed ? 2 v2 at the...

A sphere of mass M, radius r, and rotational inertia I is
released from rest at the top of an inclined plane of height h as
shown above. (diagram not shown)
If the plane has friction so that the sphere rolls without
slipping, what is the speed vcm of the center of mass at the bottom
of the incline?

A uniform solid disk of mass 3.60 kg and diameter 45.0 cm starts
from rest and rolls without slipping down a 39.0 ? incline that is
6.25 m long. g = 9.81 m/s2 .
(a) Calculate the linear speed of the center of the disk when it
reaches the bottom of the incline.
b) Determine the angular speed of the disk about its center at
the bottom of the incline.
c) Through what angle (in radians) does this disk turn as...

a ball of mass M and radius R start from rest at a height of 5.0
m and rolls down a 20 degree slope as he fig below. what is the
linear speed of the ball when it leaves the incline? assuming that
the ball rolls without slipping B) a disk of M and radius R start
from rest at a height of 5.0 m and rolls down a 20 degree slope as
he fig below. what is the linear...

A Brunswick bowling ball with mass M= 7kg and radius R=0.15m
rolls from rest down a ramp without slipping. The initial height of
the incline is H= 2m. The moment of inertia of the ball is
I=(2/5)MR2
What is the total kinetic energy of the bowling ball at the
bottom of the incline?
684J
342J
235J
137J
If the speed of the bowling ball at the bottom of the incline is
V=5m/s, what is the rotational speed ω at the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 25 minutes ago

asked 46 minutes ago

asked 49 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago