Consider two cylindrical objects of the same mass and radius. Object A is a solid cylinder, whereas object B is a hollow cylinder.
Problem 3: 
Consider two cylindrical objects of the same mass and radius. Object A is a solid cylinder, whereas object B is a hollow cylinder.
Part (a) If these objects roll without slipping down a ramp, which one will reach the bottom of the ramp first?
Part (b) How fast, in meters per second, is object A moving at the end of the ramp if it's mass is 210 g, it's radius 14 cm, and the height of the beginning of the ramp is 13.5 cm?
Part (c) How fast, in meters per second, is object B moving at the end of the ramp if it rolls down the same ramp?
Homework Answers
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Consider two cylindrical objects of the same mass and radius. Object A is a solid cylinder, whereas object B is a hollow cylinder.
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A solid homogeneous cylinder and a thin cylindrical shell each have the same mass and radius. They are both released from rest at the same time and from the same elevation at the top of the same inclined plane. As they roll down the incline, they both roll without slipping. Which object will reach the bottom of the inclined plane first? A solid homogeneous cylinder B they both reach the bottom at the same time C thin cylindrical shell
2. Rolling down the hill (a) A solid cylinder of mass 1.0 kg and radius 10...
2. Rolling down the hill (a) A solid cylinder of mass 1.0 kg and radius 10 cm starts from rest and rolls without slipping down a 1.0 m-high inclined plane. What is the speed of the cylinder when it reaches the bottom of the inclined plane? (b) How about a solid sphere of the same mass and radius? (c) How about a hoop of the same mass and radius? (d) Which of the above objects is moving fastest when it...
Nonuniform cylindrical object. In the figure, a cylindrical object of mass M and radius R rolls...
Nonuniform cylindrical object. In the figure, a cylindrical object of mass M and radius R rolls smoothly from rest down a ramp and onto a horizontal section. From there it rolls off the ramp and onto the floor, landing a horizontal distance d = 0.504 m from the end of the ramp. The initial height of the object is H = 0.88 m; the end of the ramp is at height h = 0.13 m. The object consists of an...
A solid cylinder and a hollow cylinder with the same mass and radius are released at...
A solid cylinder and a hollow cylinder with the same mass and radius are released at the top of a ramp. Which will have the slower speed at the bottom of the ramp and why? using appropriate equations and words
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A hollow sphere and uniform sphere of the same mass m and radius R roll down...
A hollow sphere and uniform sphere of the same mass m and radius R roll down an inclined plane from the same height H without slipping (Figure 9-59). Each is moving horizontally as it leaves the ramp. When the spheres | hit the ground, the range of the hollow sphere is L. Find the range L' of the uniform sphere. FIGURE Uniform Hollow sphere sphere
A solid cylinder and a hollow cylinder with the same mass and radius are released at the top of a ramp. Which will have...
A solid cylinder and a hollow cylinder with the same mass and radius are released at the top of a ramp. Which will have the slower speed at the bottom of the ramp and why?
A solid sphere and a hollow cylinder of the same mass and radius have a rolling...
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2. Rolling down the hill (a) A solid cylinder of mass 1.0 kg and radius 10 cm starts from rest and rolls without slipping down a 1.0 m-high inclined plane. What is the speed of the cylinder when it reaches the bottom of the inclined plane? (b) How about a solid sphere of the same mass and radius? (c) How about a hoop of the same mass and radius? (d) Which of the above objects is moving fastest when it...
Nonuniform cylindrical object. In the figure, a cylindrical object of mass M and radius R rolls smoothly from rest down a ramp and onto a horizontal section. From there it rolls off the ramp and onto the floor, landing a horizontal distance d = 0.504 m from the end of the ramp. The initial height of the object is H = 0.88 m; the end of the ramp is at height h = 0.13 m. The object consists of an...
A hollow sphere and uniform sphere of the same mass m and radius R roll down an inclined plane from the same height H without slipping (Figure 9-59). Each is moving horizontally as it leaves the ramp. When the spheres | hit the ground, the range of the hollow sphere is L. Find the range L' of the uniform sphere. FIGURE Uniform Hollow sphere sphere
A solid sphere and a hollow cylinder of the same mass and radius have a rolling race down an incline as in Example 13.9. They start at rest on an incline at a height habove a horizontal plane. The race then continues along the horizontal plane. The coefficient of rolling friction between each rolling object and the surface is the same. Both have mass M Both have radius R. Write an expression for the distances that each object will roll...
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