You are building a display for a children's science museum in which a uniform, solid sphere of radius 0.088 m starts at rest at the top of a "hill" and rolls, without slipping, down a track and around a loop-the-loop of radius R = 1.76 m. You have already determined that the ball has to be moving at a speed no less than 4.05 m/s at the top of the loop in order to make it around the loop without falling. Note: You should consider whether the ball will be above or below the track at the top of the loop. What is the minimum height of the "hill" in order to ensure that this happens?

One end of a cord is fixed and a small 0.400-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 1.50 m, as shown in the figure below. When θ = 23.0°, the speed of the object is 5.50 m/s. An object is swinging to the right and upward from the end of a cord attached to a horizontal surface. The cord makes an angle θ with the vertical. An arrow labeled vector v points in the direction of motion. (a) At this instant, find the magnitude of the tension in the string.Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N(b) At this instant, find the tangential and radial components of acceleration. at = Your response differs from the correct answer by more than 100%. m/s2 downward tangent to the circle ac = Your response differs from the correct answer by more…

A wheel with a radius of 0.23 m and a mass of 7.31 kg spins about its axis at 6.53 radians per second. What is the kinetic energy of the wheel in J? Treat the wheel as a cylinder of constant density.

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 =