A ball of mass m = 2 kg and radius r = 0.2 meters, rolls down a water slide, like shown. The slide curves up at the end and launches the ball into the air. The height is h = 1.5 meters, angle ? = 60°, and the angle ? = 25°.
If the ball starts at rest, and rolls without slipping, find ymax, the height to which the child is launched, in meters. Treat the ball as being launched from a height of 0 (ignore the small increase in height at the end of the slide). You can use the solution to the practice problem, to help you solve this, if you want to.
Homework Answers
1) A solid ball of mass M and radius R rolls without slipping down a hill...
1) A solid ball of mass M and radius R rolls without slipping down a hill with slope tan θ. (That is θ is the angle of the hill relative to the horizontal direction.) What is the static frictional force acting on it? It is possible to solve this question in a fairly simple way using two ingredients: a) As derived in the worksheet when an object of moment of inertia I, mass M and radius R starts at rest...
A ball of mass M and radius R, rolls smootly from rest down a ramp at...
A ball of mass M and radius R, rolls smootly from rest down a ramp at an angle theta. The ball descent a vertical height h to reach the bottom of the ramp. What is the acceleration of the ball?
A ball with a radius r and a mass m starts from rest and then rolls...
A ball with a radius r and a mass m starts from rest and then
rolls without slipping a distance L down a roof sloped at an angle
θ. The ball comes off the roof a height H above the ground. Derive
an expression for the ball’s speed v, just as it leaves the roof,
in terms of g, L, and θ:
A. If the ball is a solid sphere.
B.If the ball is a hollow sphere.
C. For each...
2) A solid uniform ball of mass m and radius r rolls down a hemispherical bowl...
2) A solid uniform ball of mass m and radius r rolls down a hemispherical bowl of radius R, starting from a height h above the bottom of the bowl. The surface on the left half of the bowl has sufficient friction to prevent slipping, and the right side is frictionless. R (a) (5 marks) Determine the angular speed w the ball rotates in terms of e', when it rolls without slipping. (b) (5 marks) Derive an expression for the...
A homogenous sphere of mass M = 1.61 kg and radius R = 12.82 cm starts...
A homogenous sphere of mass M = 1.61 kg and radius R = 12.82 cm starts from rest at the upper end of the track (height H = 1.13 m) shown in the Figure and rolls without slipping until it rolls off the right-hand end (height h = 0.74 m). The track is horizontal at the right-hand end. What is the distance to the right of point A at which the ball strikes the horizontal base line?
A hollow sphere of mass m = 0.35 kg and radius r = 64 cm rolls...
A hollow sphere of mass m = 0.35 kg and radius r = 64 cm rolls along a flat surface at an initial speed of v, and then up a curved ramp with radius of curvature 4.7 m without slipping, until it reaches a maximum angle of 12 degrees around the curve and starts to roll backward. What was the initial speed of the ball in units of meters/second?
A ball of radius r,-0.08 m and mass m =1.5 kg rolls without friction on a...
A ball of radius r,-0.08 m and mass m =1.5 kg rolls without friction on a roller-coaster. From what height should the ball be released so that it completes the loop with radius R - 4.0 m without falling? Consider that height is measured from the track surface to the center of the ball (see figure). Select one: a. h > 10.40 m b.h> 11.25 m c. h > 11.33 m d.h> 12.66 m
* A ball of mass M and radius R has a rotational inertia of · The...
* A ball of mass M and radius R has a rotational inertia of · The ball is released from rest and rolls without slipping down the ramp with no frictional loss of energy. The ball is projected vertically upward off a ramp as shown in the diagram, reaching a maximum height yaz above the point where it leaves the ramp. In terms of h, ymar is
A hollow ball (I=2/3 MR^2) of radius 7 cm and mass of 0.2kg starts from rest...
A hollow ball (I=2/3 MR^2) of radius 7 cm and mass of 0.2kg starts from rest and rolls without slipping down a ramp. After the ball has dropped a vertical distance of 0.3 meters, what is its angular speed? Air resistance and losses due to friction may be neglected.
Problem 4. A solid sphere of mass m and radius r rolls without slipping along the...
Problem 4. A solid sphere of mass m and radius r rolls without slipping along the track shown below. It starts from rest with the lowest point of the sphere at height h 3R above the bottom of the loop of radius R, much larger than r. Point P is on the track and it is R above the bottom of the loop. The moment of inertia of the ball about an axis through its center is I-2/S mr. The...
A ball of mass M and radius R, rolls smootly from rest down a ramp at an angle theta. The ball descent a vertical height h to reach the bottom of the ramp. What is the acceleration of the ball?
A ball with a radius r and a mass m starts from rest and then
rolls without slipping a distance L down a roof sloped at an angle
θ. The ball comes off the roof a height H above the ground. Derive
an expression for the ball’s speed v, just as it leaves the roof,
in terms of g, L, and θ:
A. If the ball is a solid sphere.
B.If the ball is a hollow sphere.
C. For each...
2) A solid uniform ball of mass m and radius r rolls down a hemispherical bowl of radius R, starting from a height h above the bottom of the bowl. The surface on the left half of the bowl has sufficient friction to prevent slipping, and the right side is frictionless. R (a) (5 marks) Determine the angular speed w the ball rotates in terms of e', when it rolls without slipping. (b) (5 marks) Derive an expression for the...
A ball of radius r,-0.08 m and mass m =1.5 kg rolls without friction on a roller-coaster. From what height should the ball be released so that it completes the loop with radius R - 4.0 m without falling? Consider that height is measured from the track surface to the center of the ball (see figure). Select one: a. h > 10.40 m b.h> 11.25 m c. h > 11.33 m d.h> 12.66 m
* A ball of mass M and radius R has a rotational inertia of · The ball is released from rest and rolls without slipping down the ramp with no frictional loss of energy. The ball is projected vertically upward off a ramp as shown in the diagram, reaching a maximum height yaz above the point where it leaves the ramp. In terms of h, ymar is
Problem 4. A solid sphere of mass m and radius r rolls without slipping along the track shown below. It starts from rest with the lowest point of the sphere at height h 3R above the bottom of the loop of radius R, much larger than r. Point P is on the track and it is R above the bottom of the loop. The moment of inertia of the ball about an axis through its center is I-2/S mr. The...
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