Question

In: Physics

A solid wheel with mass M, radius R, and rotational inertia MR2/2, rolls without sliding on...

A solid wheel with mass M, radius R, and rotational inertia MR2/2, rolls without sliding on a horizontal surface. A horizontal force F is applied to the axle and the center of mass has an acceleration a. The magnitudes of the applied force F and the frictional force f of the surface, respectively, are:

  1. F=Ma,f=0

  2. F=Ma,f=Ma/2

  3. F=2Ma,f=Ma

  4. F=2Ma,f=Ma/2

  5. F =3Ma/2, f =Ma/2

Solutions

Expert Solution

Mass of the wheel = M

Radius of the wheel = R

Rotational inertia = I = MR2/2

Linear acceleration of the center of mass = a

Applied force = F

Thus,

For the linear acceleration,

F = M*a = Mg sin 90 - f    (1)          where Fs is the frictional force

For the angular acceleration,

I = R f                            (2)    where is the angular acceleration of the wheel

Since there is no slip, velocity and acceleration at the point of contact with the surface is zero at any given time. So,

= a / R                       (3)

From equation 2 and 3,

f = I / R

f = I a / R2                    

f= M R2 a / 2 * R2

f = Ma / 2                 (4)

From equation (1),

F = Ma - 0 + f

F = Ma + Ma / 2

F = 3 Ma/2                      (5)

From equation 4 and 5,

magnitude of the applied force F and the frictional force f of the surface are,

F = 3Ma/2 , f = Ma/2

Answer is option 5.


Related Solutions

3) A solid cylinder with mass 4kg and radius r=0.5 m rolls without slipping from a...
3) A solid cylinder with mass 4kg and radius r=0.5 m rolls without slipping from a height of 10 meters on an inclined plane with length 20 meters. a) Find the friction force so that it rolls without slippingb) Calculate the minimum coefficient of rolling friction muc) Calculate its speed as it arrives at the bottom of the inclined plane.
Problem: a unifiorm hoop of mass m and radius r rolls without slipping on a fixed...
Problem: a unifiorm hoop of mass m and radius r rolls without slipping on a fixed cylinder of radius R. if the hoop is stats rolling from rest on top of the bigger cylinder, use the method of Lagrange multipliers to find the point at which the hoop fall off the cylinder. Question: I know how to derive Lagrange equeation. but to use the method of Lagrange multipliers, i have to finde constrain. solution says that f1, f2 are constrain....
A wheel has a mass of 0.5 kg and a radius of 0.25 m. It rolls...
A wheel has a mass of 0.5 kg and a radius of 0.25 m. It rolls such that the center of mass of the wheel has a velocity of 10 m/s. a) Calculate the angular velocity of the wheel. b) Calculate the translational kinetic energy of the wheel. c) Calculate the rotational kinetic energy of the wheel. d) Calculate the total kinetic energy of the wheel by summing the two kinetic energies
A uniform hoop of mass M and radius R rolls down an incline without slipping, starting...
A uniform hoop of mass M and radius R rolls down an incline without slipping, starting from rest. The angle of inclination of the incline is θ. a. After moving a distance L along the incline, what is the angular speed ω of the hoop? b. If the coefficient of static friction between the hoop and the incline is µs = 1/3, what is the greatest possible value of θ such that no slipping occurs between the hoop and the...
A sphere of mass M, radius r, and moment of inertial I = Mr2 (where is...
A sphere of mass M, radius r, and moment of inertial I = Mr2 (where is a dimensionless constant which depends on how the mass is distributed in the sphere) is placed on a track at a height h above the lowest point on the track. The sphere is released, and rolls without slipping. It reaches a horizontal surface which subsequently bends into a vertical loop-the-loop of radius R, as in Fig. 2 below. a) When it reaches the top...
Show that the moment of inertia of a spherical shell of radius R and mass M...
Show that the moment of inertia of a spherical shell of radius R and mass M about an axis through its centre is 2/3 MR2. Show also that the moment of inertia of a uniform solid sphere of radius R and mass M is 2/5MR2. The spheres are allowed to roll (from rest), without slipping a distance L down a plane inclined at a angle θ to the horizontal. Find expressions for the speeds of the spheres at the bottom...
Find the moment of inertia of a circular disk of radius R and mass M that...
Find the moment of inertia of a circular disk of radius R and mass M that rotates on an axis passing through its center. [Answer: ½ MR2] Step 1: Pictorial representation: Sketch a neat picture to represent the situation. Step 2: Physical representation: 1) Cut the disk into many small rings as it has the circular symmetry. 2) Set up your coordinate system and choose its origin at the pivot point (or the axle location) for convenience. Then choose a...
A certain wheel is a uniform disk of radius R = 0.5 m and mass M...
A certain wheel is a uniform disk of radius R = 0.5 m and mass M = 10.0 kg. A constant force of Fapp = 15.0 N is applied to the center of mass of the wheel in the positive x-direction. The wheel rolls along the ground without slipping. (a) Compute the rotational inertia of the wheel about its center of mass. (b) Compute the magnitude and direction of the friction force acting on the wheel from the ground. (c)...
The moment of inertia of a thin ring of mass M and radius R about its...
The moment of inertia of a thin ring of mass M and radius R about its symmetry axis is ICM = MR2 Kira is working the ring-toss booth at a local carnival. While waiting for customers, Kira occupies her time by twirling one of the plastic rings of mass M and radius R about her finger. Model the motion of the plastic ring as a thin ring rotating about a point on its circumference. What is the moment of inertia of...
2. Which has more rotational inertia: A solid, uniform sphere of mass 100kg, or a mostly...
2. Which has more rotational inertia: A solid, uniform sphere of mass 100kg, or a mostly hollow spherical shell of mass 100kg? a.They both have the same rotational inertia b.Solid Sphere c.Hollow Sphere 3.If a bicycle starts from rest and is pedaled normally until the bike is moving at 6 meters per second across level ground, what kinds of energy have its tires been given? (Select all that apply) a.Rotational Kinetic Energy b.Translational Kinetic Energy c.Gravitational Potential Energy d.Elastic Potential...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT