A solid ball of mass 0.3 kg and radius 1.1 cm starts from rest then rolls without slipping down a long ramp the makes an angle 22 degrees with the horizontal. At what height above the bottom of the ramp must the ball be released if it is to have a speed of 1.6 m/s at the bottom?
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horizontal. At what height above the bottom of the ramp must the ball be released if it is to have a speed of 1.6 m/s at the bottom?"
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- A hollow cylinder and solid cylinder, with the same radius, are placed at the top of an incline and released at the same time from rest. Which one reaches the bottom first? The hollow cylinder. It depends on their masses. The solid cylinder. They reach the bottom at the same timeSolution (a) Find the angular displacement after 2.00 s, in both radians and revolutions. 1 A0 = w;t + Use Equation 7.8, setting @; 1.60 rad/s, a = 3.50 rad/s2, and t = 2.00 s. 1 Að = (1.60 rad/s) (2.00 s) + (3.50 rad/s²) (2.00 s)² 2 A0 = 10.2 rad Convert radians to revolutions. A0 = (Am rad)(1.00 rev/2r rad) AO = 16.02 X rev Your response differs from the correct answer by more than 100%. (b) What is the angular speed of the wheel at t = 2.00 s? Substitute the same values into Equation 7.7. @ = @; + at = 1.60 rad/s + (3.50 rad/s²)(2.00 s) W = rad/s Remarks The result of part (b) could also be obtained from Equation 7.9 and the results from part (a). - INProblem 9: A solid ball with mass, M=2.5 kg and radius, R=0.2 meter is released from rest from the top of an incline of height, h=3.5 meter. Ignore any energy loss due to friction or air drag. Consider g=9.8 m/s2. (a) The linear speed of the ball at the bottom is ________ (b) The rotational kinetic energy of the ball at the bottom is _________
- A uniform solid disk of radius 3 m and mass 2.0 kg rolls without slipping. to the bottom of an inclined plane. If the angular velocity of the disk is 8 rd/s at the bottom, what is the height of the inclined plane? 22m 19.71m None of the above 6.73m 44.1 m/sIn the figure, three 0.10 kg particles have been glued to a rod of length L = 11 cm and negligible mass and can rotate around a perpendicular axis through point O at one end. How much work is required to change the rotational rate (a) from 0 to 20.0 rad/s, (b) from 20.0 rad/s to 40.0 rad/s, and (c) from 40.0 rad/s to 60.0 rad/s? (d) What is the slope of a plot of the assembly's kinetic energy (in joules) versus the square of its rotation rate (in radians-squared per second-squared)? Axis -P--P-- P- (a) Number i Units (b) Number i Units (c) Number i Units (d) Number i UnitsA uniform solid cylinder is initially at rest at the top of a ramp of height 1.5 m. If the cylinder rolls down this ramp without slipping, what will be its speed at the bottom? Why don't you need to consider the work done by friction? Explain your reasoning in detail.
- A uniform sphere is placed inside hemispherical bowl of radius R = 75.0 cm. It is released from rest at an angle 0 = 40.0°. What is the speed of the sphere at the bottom of the bowl if it rolls without slipping? Ishpere = 2/5 mr². Assume r<A 1.10 kg hoop of radius 0.160 m is released from rest at point A in the figure below, its center of gravity a distance of 1.90 m above the ground. The hoop rolls without slipping to the bottom of an incline and back up to point B where it is launched vertically into the air. The hoop then rises to its maximum height hmay at point C. HINT V = (0 C A 1.90 m hmax В 10.350 m (a) At point B, find the hoop's translational speed vR (in m/s). X m/s (b) At point B, find the hoop's rotational speed w, (in rad/s). X rad/s (c) At point C, find the hoop's rotational speed @. (in rad/s). rad/s (d) At point C, find the maximum height h of the hoop's center of gravity (in m). maxSuppose you had a machine for 100% efficiently transferring kinetic energy of a rotating bicycle pedal to electrical energy. If the mass of a pedal is 200 g, (a) how fast must the pedal be moving to power a 17.00 W LED light? (b) what is the angular speed, in rpm, if the distance from the centre of the crank to the pedal is 16 cm?A solid brass ball of mass 22 g and radius 8.51 mm rolls smoothly along a loop-the-loop track when released from rest from a tall ramp leading to the loop-the-loop. The circular loop has a 17 cm radius. (a) What is the minimum height from which you can release the ball so that it will go around the loop-the-loop without falling off? For part (b), assume that the ball is released from rest at a height of 61.83 cm above the bottom of the loop. (b) What is the magnitude of the horizontal force on ball when it is at a height 17 cm going up the hoop? (c)What is the direction of the net force on the ball at the top of the hoop? Î =Consider a basketball player spinning a ball on the tip of a finger. If a player performs 1.95 J of work to set the ball spinning from rest, at what angular speed ? will the ball rotate? Model a basketball as a thin-walled hollow sphere. For a men's basketball, the ball has a circumference of 0.749 m and a mass of 0.624 kg .A solid ball of mass 0.10 kg and radius 2.8 cm is released from rest on a no-slip surface at a height of 0.75 m above the bottom of the track, as shown. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface. Find: a) the ball's angular speed when it is on the frictionless side of the track and b) the height ball rises on the w = 120 rad/s; h = 0.54 m frictionless side.SEE MORE QUESTIONS