Dynamics Kinetics of a particle Section 4: TJW Force-mass-acceleration: Example 1

Size: px

Start display at page:

Download "Dynamics Kinetics of a particle Section 4: TJW Force-mass-acceleration: Example 1"

Rudolf Jordan
5 years ago
Views:

1 Section 4: TJW Force-mass-acceleration: Example 1 The beam and attached hoisting mechanism have a combined mass of 1200 kg with center of mass at G. If the inertial acceleration a of a point P on the hoisting cable is 6 m/s 2, calculate the corresponding reaction at the support A.

Section 4: TJW Force-mass-acceleration: Example 2 The truck comes to a stop from an inertial forward speed 70 km/h in a distance of 50 m with uniform deceleration, determine whether or not the crate

2 Section 4: TJW Force-mass-acceleration: Example 2 The truck comes to a stop from an inertial forward speed 70 km/h in a distance of 50 m with uniform deceleration, determine whether or not the crate strikes the wall at the forward end of the flat bed. If the crate does strike the wall, calculate its speed relative to the truck as the impact occurs. Use the friction coefficients μ s = 0.30 and μ k = 0.25.

3 Section 4: TJW Force-mass-acceleration: Example 3 If the 2-kg block passes over the top B of the circular portion of the path with a speed of 3.5 m/s, calculate the magnitude N B of the normal force exerted by the path on the block. Determine the maximum speed v which the block can have at A without losing contact with the path.

4 Section 4: TJW Force-mass-acceleration: Example 4 The slotted arm resolved in the horizontal plane about the fixed vertical axis through point O. The 2- kg slider C is drawn toward O at the constant rate of 50 mm/s by pulling the cord S. At the instant for which r = 225 mm, the arm has a counterclockwise angular velocity ω = 6 rad/s and is slowing down at the rate of 2 rad/s 2. For this instant, determine the tension T in the cord and the magnitude N of the force exerted on the slider by the sides of the smooth radial slot. Indicate which side, A or B, of the slot contacts the slider.

Section 4: TJW Force-mass-acceleration: Example 5 Each tire on the 1350-kg car can support a maximum friction force parallel to the road surface of 2500 N.

5 Section 4: TJW Force-mass-acceleration: Example 5 Each tire on the 1350-kg car can support a maximum friction force parallel to the road surface of 2500 N. This limit is nearly constant over all possible rectilinear and curvilinear car motions and is attainable only if the car does not skid. Under this maximum braking, determine the total stopping distance s if the brakes are first applied at point A when the car speed is 25 m/s and if the car follows the centerline of the road.

6 Section 4: TJW Work and energy: Example 1 The resistance R to penetration x of a 0.25-kg projectile fired with a velocity of 600 m/s into a certain block of fibrous material is shown in the graph. Represent this resistance by the dashed line and compute the velocity v of the projectile for the instant when x = 25 mm if the projectile is brought to rest after a total penetration of 75 mm.

7 Section 4: TJW Work and energy: Example 2 Small metal blocks are discharged with a velocity of 0.45 m/s to a ramp by the upper conveyor shown. If the coefficient of kinetic friction between the blocks and the ramp is 0.30, calculate the angle θ which the ramp must make with the horizontal so that the blocks will transfer without slipping to the lower conveyor moving at the speed of 0.15 m/s.

8 Section 4: TJW Work and energy: Example 3 The 7-kg collar A slides with negligible friction on the fixed vertical shaft. When the collar is released from rest at the bottom position shown, it moves up the shaft under the action of the constant force F = 200 N applied to the cable. Calculate the stiffness k which the spring must have if its maximum compression is to be limited to 75 mm. The position of the small pulley at B is fixed.

9 Section 4: TJW Work and energy: Example 4 Each of the sliders A and B has a mass of 2 kg and moves with negligible friction in its respective guide, with y being in the vertical direction. A 20-N horizontal force is applied to the midpoint of the connecting link of negligible mass, and the assembly is released from rest with θ = 0. Calculate the velocity v A with which A strikes the horizontal guide when θ = 90.

Section 4: TJW Impulse and momentum: Example 1 A tennis player strikes the tennis ball with her racket when the ball is at the uppermost point of its trajectory as shown.

10 Section 4: TJW Impulse and momentum: Example 1 A tennis player strikes the tennis ball with her racket when the ball is at the uppermost point of its trajectory as shown. The horizontal velocity of the ball just before impact with the racket is v 1 = 15 m/s and just after impact its velocity is v 2 = 21 m/s directed at the 15 angle as shown. If the 60-g ball is in contact with the racket for 0.02 s, determine the magnitude of the average for R exerted by the racket on the ball. Also determine the angle β made by R with the horizontal.

11 Section 4: TJW Impulse and momentum: Example 2 The third and fourth stages of a rocket are coasting in space with a velocity of 18,000 km/h when a small explosive charge between the stages separates them. Immediately after separation the fourth stage has increased its velocity to v 4 = 18,060 km/h. What is the corresponding velocity v 3 of the third stage? At separation the third and fourth stages have masses of 400 and 200 kg, respectively.

12 Section 4: TJW Impulse and momentum: Example 3 The 12-Mg truck drives onto the 350-Mg barge from the dock at 20 km/h and brakes to a stop on the deck. The barge is free to move in the water, which offers negligible resistance to motion at low speeds. Calculate the speed of the barge after the truck has come to rest on it.

Section 4: TJW Impulse and momentum: Example 4 The 450-kg ram of a pile driver falls 1.4 m from rest and strikes the top of a 240-kg pile embedded 0.9 m in the ground.

13 Section 4: TJW Impulse and momentum: Example 4 The 450-kg ram of a pile driver falls 1.4 m from rest and strikes the top of a 240-kg pile embedded 0.9 m in the ground. Upon impact the ram is seen to move with the pile with no noticeable rebound. Determine the velocity v of the pile and ram immediately after impact. Can you justify using the principle of conservation of momentum even though the weights act during the impact?

14 Section 4: TJW Impulse and momentum: Example 5 Car B (1500 kg) traveling west at 48 km/h collides with car A (1600 kg) traveling north at 32 km/h as shown. If the two cars become entangled and move together as a unit after the crash, compute the magnitude v of their common velocity immediately after the impact and the angle θ made by the velocity vector with the north direction.

Section 4: TJW Impulse and momentum: Example 6 The only force acting on an earth satellite traveling outside of the earth s atmosphere is the radial

15 Section 4: TJW Impulse and momentum: Example 6 The only force acting on an earth satellite traveling outside of the earth s atmosphere is the radial gravitational attraction. The moment of this force is zero about the earth s center taken as a fixed 2 point. Prove that r θ remains constant for the motion of the satellite.

Section 4: TJW Impulse and momentum: Example 7 The small spheres, which have the masses and initial velocities shown in the figure, strike and become attached to the

16 Section 4: TJW Impulse and momentum: Example 7 The small spheres, which have the masses and initial velocities shown in the figure, strike and become attached to the spiked ends of the rod, which is freely pivoted at O and is initially at rest. Determine the angular velocity ω of the assembly after impact. Neglect the mass of the rod.

Section 4: TJW Impulse and momentum: Example 8 A particle is released on the smooth inside wall of a cylindrical tank at A with a velocity v 0 which makes an angle β with

17 Section 4: TJW Impulse and momentum: Example 8 A particle is released on the smooth inside wall of a cylindrical tank at A with a velocity v 0 which makes an angle β with the horizontal tangent. When the particle reaches a point B a distance h below A, determine the expression for the angle θ made by its velocity with the horizontal tangent at B.

18 Section 4: TJW Impact: Example 1 The ram of a pile driver has a mass of 800 kg and is released from rest 2 m above the top of the kg pile. If the ram rebounds to a height of 0.1 m after impact with the pile, calculate (a) the velocity v of the pile immediately after impact, (b) the coefficient of restitution e, and (c) the percentage loss p of energy due to the impact.

19 Section 4: TJW Impact: Example 2 A ball is projected onto the heavy plate with a velocity of 16 m/s at the 30 angle shown. If the effective coefficient of restitution is 0.5, compute the rebound velocity v and its angle θ. 16 m/s

20 Section 4: TJW Impact: Example 3 Spherical particle 1 has a velocity v 1 = 6 m/s in the direction shown and collides with spherical 2 of equal mass and diameter and initially at rest. If the coefficient of restitution for these conditions is e = 0.6, determine the resulting motion of each particle following impact. Also calculate the percentage loss of energy due to the impact.

3. Kinetics of Particles

3. Kinetics of Particles 3.1 Force, Mass and Acceleration 3.3 Impulse and Momentum 3.4 Impact 1 3.1 Force, Mass and Acceleration We draw two important conclusions from the results of the experiments. First,