5. A solid sphere (I = mr²) wwith a mass of 3 kg and a radius of 8 cm is placed at rest on a slope. The ball willroll down the slope and hit a 0.5 m spring that is parallel to the incline of the slope.a.The spring compresses 0.3 m as the ball momentarily comes to rest. What is the spring constant of thespring?4m5m4mееее5mb. What would the initial velocity of the ball have to be in order to compress the spring to the full 0.5 m atthe momentary stop?

Step 1:Given mass m=3 kg, radius r= 0.08 m, height h= 4m a) compression x = 0.3 m, By…

Answered: 5. A solid sphere (I = mr²) w with a…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter7: Conservation Of Energy

Section: Chapter Questions

Problem 17P: A smooth circular hoop with a radius of 0.500 m is placed flat on the floor. A 0.400-kg particle...

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A smooth circular hoop with a radius of 0.500 m is placed flat on the floor. A 0.400-kg particle slides around the inside edge of the hoop. The particle is given an initial speed of 8.00 m/s. After one revolution, its speed has dropped to 6.00 m/s because of friction with the floor. (a) Find the energy transformed from mechanical to internal in the particlehoopfloor system as a result of friction in one revolution. (b) What is the total number of revolutions the particle makes before stopping? Assume the friction force remains constant during the entire motion.
A smaller disk of radius r and mass m is attached rigidly to the face of a second larger disk of radius R and mass M as shown in Figure P15.48. The center of the small disk is located at the edge of the large disk. The large disk is mounted at its center on a frictionless axle. The assembly is rotated through a small angle from its equilibrium position and released. (a) Show that the speed of the center of the small disk as it passes through the equilibrium position is v=2[Rg(1cos)(M/m)+(r/R)2+2]1/2 (b) Show that the period of the motion is v=2[(M/2m)+R2+mr22mgR]1/2 Figure P15.48
1. A pinball machine launch ramp consisting of a spring and a 30° ramp of length L as shown in Fig. 1. (a) from its equilibrium position and is then released at t = 0, the pinball (a sphere of mass m and radius r) reaches the top of the ramp at t = T. Derive the expression for the spring constant k in terms of If the spring is compressed a distance x 30° Fig. 1 m, g,x, and L. [Assume that the friction is sufficient, and the ball begins rolling without slipping immediately after launch.] (b) What is the potential energy of the ball when it is at the midpoint of the ramp? (c) terms of g and L. Derive the expression of the speed of the ball immediately after being launched in
6. You land on a new planet and would like to figure out its freefall acceler- ation, gp. You make a pendulum out of a solid disk as seen below: R/2 Suppose the disk has total mass m = 2 kg and radius R = 0.25 m. Its COM is indicated by the blue "x" on the diagram, a distance of R/2 from the circumference. Ensuring that is very small, you let the pendulum oscillate and measure that its total period is T 1.5 s. What is gp? =
8. The cylinder has a mass of 20 kg and is released from rest when h = 0. Determine its speed when h = 3 m. The springs each have an unstretched length of 2 m. 2 m 2 m wwwww k= 40 N/m k = 40 N/m 9. The collar has a mass of 2 kg and is attached to the light spring, which has a stiffness of 30 N/m and an unstretched length of 1.5 m. The collar is released from rest at A and slides up the smooth rod under the action of the constant 50-N force. Calculate the velocity v of the collar as it passes position B. 1.5 m 30° 50 N k = 30 N/m A 2 m
5. Calculate the kinetic energy of a 4.0 g bullet moving at 1000 m/s. A 1000 J B 2000 J 3000 J D 4000 J 6. A child whose mass m = 20 kg, is running through a tunnel a distance 100 m in 20 s. The kinetic energy of the child is: A 200 I B 250J 400 J D 100J
5. A simple pendulum, 1.00 m in length, is released from rest when the support string is at an angle of 48.0° from the vertical. What is the speed of the suspended mass at the bottom of the swing? (g = 9.80 m/s2 and ignore air resistance) a. 4.43 m/s b. 3.82 m/s c. 6.49 m/s d. 2.55 m/s
3. Under normal conditions a tennis ball has a diameter of 6.6 cm, but when a 90 kg professor stands balanced on two identical tennis balls, each one compresses down to ½ its normal height. Modeling the tennis balls as springs, what is the spring constant of a oo tennis ball in N/m?
5. Calculate the kinetic energy of a 4.0 g bullet moving at 1000 m/s. A 1000 J B 2000 J 3000 J D 4000 J 6. A child whose mass m = 20 kg, is running through a tunnel a distance 100 m in 20 s. The kinetic energy of the child is: A 200 J B 250 J 400 J D 100J
9. A load with m = 105 g is attached to a vertical spring that has been compressed by 15 cm. What is the force constant of the spring? a. 6.86 N/m b. 1.029 N c. 0.105 kg d. 7.72 x 102 J 10. Referring to #9, what is its elastic potential energy? a. 6.86 N/m b. 1.029 N c. 0.105 kg d. 7.72 x 10-2 J 11. Which of the following is statements is true? e. the center of mass of an object must lie within the object f. An incredibly compressed spring g. A tightly stretched rubber band h. None of the above Activate Go to Set
9. A load with m = 105 g is attached to a vertical spring that has been compressed by 15 cm. What is the force constant of the spring? a. 6.86 N/m b. 1.029 N c. 0.105 kg d. 7.72 x 102 J 10. Referring to #9, what is its elastic potential energy? a. 6.86 N/m b. 1.029 N c. 0.105 kg d. 7.72 x 10-2 J 11. Which of the following is statements is true? a. the center of mass of an object must lie within the object b. An incredibly compressed spring c. A tightly stretched rubber band d. None of the above Act Go
3. A block of mass m=1.2 kg is attached to a horizontal spring of force constant k=75 N/m. The block is pushed, and spring is compressed, to the position 10.0 cm to the left of the equilibrium position; then, block is released. A. Neglect friction. Find the speed of the block as it passes through the equilibrium position. B. If the friction is significant and µ = 0.22, what is the speed of the block as it passes through the equilibrium position?

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