Principle of Angular Impulse and Momentum To apply the principle of angular impulse and momentum to find final speed and the time to reach a given speed. As shown, ball B, having a mass of 10.0 kg, is attached to the end of a rod whose mass can be neglected.  Finding the final speed of the ball If the rod is 0.550 m long and subjected to a torque M=(1.95t2+3.75) N⋅m, where t is in seconds, determine the speed of the ball when t=4.80 s. The ball has a speed of v=2.25 m/s when t=0     Finding the time needed to reach a specific speed If the shaft is 0.250 m long, the ball has a speed of v=2.85 m/s when t=0, and the rod is subjected to a torque M=(3.40t+2.15) N⋅m, where t is in seconds, determine the time it will take for the ball to reach a speed of 5.80 m/s.

A W disk = 5 lb disk is travelling around in a circle of radius ₁ with an initial tangential velocity of (UB)₁. The cord is pulled down through the hole at a constant velocity of ur. After a few seconds, the disk has a final speed of Vf. Neglect friction and the size of the ball. F|VI| T2 = t= UT B (VB)₁ T1 MB Values for the figure are given in the following table. Note the figure may not be to scale. Variable Value ft 15 (VB)₁ 5 r₁ ft S 2.5 ft ft S 4.5 12 S Vr a. Determine the tangential component of the velocity of the disk when it reaches its final speed, (V₂)+ b. Determine the radius of the rope from the disk to the hole when the disk reaches its final speed, 12. c. Determine the time required for the disk to reach its final speed, t. Round your final answers to 3 significant digits/figures. ft (V₂)t = S S A ft

SOLVE STEP BY STEP A car m = 200 tons makes the journey shown in the figure, if it moves with an initial speed of 150,000 m/s and the maximum height of the path is 15,000 m and the coefficient of friction is 0.4. Find the work of all the forces that intervene at point a, point b and point c, kinetic energy a, b, c, potential energy a, b, c and the power of the car developed along the trajectory Steps draw the free body diagram, the force diagram and use the appropriate equations to find Kinetic energy at points A, B and C Power energy at points A, B and C Power at points A, B and C ● A B 15000 m C

A 100-kg box is towed to move horizontally from rest by a constant force P=200 N. The kinetic friction is μk =0.1. The angle of the force P is θ=30° with respect to the horizontal direction.  The acceleration due to gravity is g=9.81 m/s2.   (5) Calculate the magnitude of the the friction force F= ___(N)  (two decimal places).

At a certain point in the reentry of the space shuttle into the earth's atmosphere, the total acceleration of the shuttle may be represented by two components. One component is the gravitational acceleration g = 9.56 m/s2 at this altitude. The second component equals 11.25 m/s² due to atmospheric resistance and is directed opposite to the velocity. The shuttle is at an altitude of 47.9 km and has reduced its orbital velocity of 28300 km/h to 14750 km/h in the direction = 1.88°. For this instant, calculate the radius of curvature of the path and the rate i at which the speed is changing. Answers: p= i = i FU km m/s²

5. A 2-kg sphere is attached to a massless rigid rod attached to a fixed pivot point O. The rigid rod and mass rotate in the horizontal plane. A moment is applied to the rod of magnitude M = 0.5t² N. m, where t is in seconds. The length of the rod is 0.5 m. Determine the speed of the sphere after the moment is applied for 5 seconds. M(t)

A 10-lb weight is suspended by a spring that is stretched 2 in. bythe weight. Assume a resistance whose magnitude is 20/√g lbtimes the instantaneous velocity in feet per second. If the weightis pulled down 3 in. below its equilibrium position and released,find the time required to reach the equilibrium position for thefirst time.

Dynamics

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Question 9 A car of mass 1200 kg is travelling west with a velocity of 72 kmh=1. It takes a left turn at 50° and continues with the same speed. It takes 5.5 s to turn the corner. a. Find the change in momentum of the car as it rounds the corner. b. Find the force the road applies to the cars tyres as it turns the corner. c. Find the force the car's tyres apply to the road as it turns the corner.