In the figure here, a solid brass ball of mass 0.214 g will roll smoothly along a loop-the-loop track when released from rest alóng the straight section. The circular loop has radius R= 0.18 m, and the ball has radius r<< R. (a) What is h if the ball is on the verge of leaving the track when it reaches the top of the loop? (b) If the ball is released at heighth = 4R, what is the magnitude of the horizontal force component acting on the ball at point Q? (a) h= i (b) F= i

A mass m=10kg is fastened to a light spring k=380N/m by a light that passes over a pulley. Assume the pulley is a uniform cylinder of mass Mp=5kg and radius R=0.2m and rotates without friction. The mass is released from rest when the spring is unstretched. The spring remains firmly fixed to the floor and to the string. What is the angular velocity of the pulley when the mass has fallen a distance h=0.4m stretching the spring.

The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration KG=0.4 m. The spring's unstretched length is Lo=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is 8-30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is 8=0°. The spring's length at the state 2 is L2=4 m. (1) If the mass center G is set as the origin (datum), the gravitational potential energy at the state 1 is_____ (two decimal places) 1116441 L₂ State 2 State 1

A mass m = 77 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius R = 19.9 m and finally a flat straight section at the same height as the center of the loop (19.9 m off the ground). Since the mass would not make it around the loop if released from the height of the top of the loop (do you know why?) it must be released above the top of the loop-the-loop height. (Assume the mass never leaves the smooth track at any point on its path.) ) What is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? m/s      What height above the ground must the mass begin to make it around the loop-the-loop? m      If the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? m/s      If the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the…

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A bowling ball, whose radius R is 11 cm and whose mass is 7.2 kg. rolls from rest down a plank whose length L is 2.1 m. the plank is inclined at an angle φ of 34 degrees to the horizontal. How fast is the ball moving when it reaches the bottom of the plank?   please can you show the answer in hand written form

The system is released from rest with the spring initially stretched 2.8 in. Calculate the velocity v of the cylinder after it has dropped 1.5 in. The spring has a stiffness of 4.1 lb/in. Neglect the mass of the small pulley. k = 4.1 lb/in 80 lb

A small solid marble of mass 0.1 kg and radius 0.04 m rolls without slipping along the loop-the-loop track shown in the figure below, having been released from rest somewhere on the straight section of track. From what minimum height above the bottom of the track must the marble be released in order that it just stay on the track at the top of the loop (R = 1.4 m)? |h R O 14.8 m 5.71 m 10.7 m O 8.71 m 3.71 m

In the figure below, a solid brass ball of mass m will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular motion has radius R, and the ball has radius r << R. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.) (a) What is h if the ball is on the verge of leaving the track when it reaches the top of the loop? 27R 10 h = (b) If the ball is released at height = 6R, what is the magnitude of the horizontal force component acting on the ball at point Q? 50mg 7 F =

The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration KG=0.4 m. The spring's unstretched length is Lo=1.0 m. The stiffness coefficient of the spring is k-2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is 8-30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is 0=0°. The spring's length at the state 2 is L2=4 m. _(kg-m²) (two decimal (9) The mass moment of inertial about the IC center is IIC=_ places) L₂ State 2 State 1