Todays Objectives: Students will review: 1. Problems from Chapters 12 and 16

In-Class Activities: Particle and Rigid Body

Kinematics

MT EXAM #1 REVIEW PROBLEMS

Given: Small packages traveling on the conveyor belt fall off into a l meter long loading car. the conveyor is running at a constant speed of vC = 2 m/s.

Find: The smallest and largest distance R at which the end A of the car may be placed from the conveyor so that the packages enter the car.

PROBLEM 1

PROBLEM 1 (continued)

PROBLEM 1 (continued)

PROBLEM 2

Given: Measurements of a shot recorded during a basketball game above show the ball barely missing a defenders (B) hands while passing through the hoop. Find: (1) Assuming the size of the ball can be neglected, the magnitude vA of the balls initial velocity and the height h of the ball as it passes over the defender B. (2) The minimum speed the defender would have had to jump to block the ball if he could raise his hands 9 feet above the floor and jumped 0.5 s after the ball was shot. (3) The relative velocity of the ball to Bs hands.

PROBLEM 2 (continued)

PROBLEM 2 (continued)

PROBLEM 2 (continued)

But what is wrong with this analysis? The minimum initial speed that player B had to jump upward 0.5 seconds after player A shot the ball to block it was determined to be 13.3 ft/s. But as he jumps his speed reduces according to vB = vBo gt = 13.3-(32.2)(0.286) = 4.1 ft/s. Hence, the correct solution is given by:

vBALL - vB = 31.8i 11.0j vBALL - vB = 33.6 ft/s

Fig. (a) Fig. (b)

PROBLEM 3 Given: A man with a 16 m long rope walks backward starting from rest (xA = 0) and accelerates at aA = 0.2 m/s2 to pull a boy up a tree limb as shown. When xA = 0, yB = 8 m. The size of the limb can be neglected.

Find: The speed of the boy at the instant yB = 4 m.

PROBLEM 3 (continued)

PROBLEM 4 Given: Collars A and B are connected to the cord that passes over the small pulley at C as shown. When A is located at D, B is 24 ft to the left of D. At the instant shown A is moving at a constant speed of 24 ft/s to the right. Find: The speed of B when A is 4 ft to the right of D.

PROBLEM 4 (continued)

PROBLEM 5

Given: At a given instant the wheel is rotating with the angular motion shown. Find: The acceleration of the collar at A at this instant.

Two solution approaches are possible!

Using the instantaneous center and scalar approach

PROBLEM 5 (continued)

Using the vector approach

PROBLEM 6 Given: The center O of the gear and the rack move with the velocities and accelerations shown. Find: The angular acceleration of the gear and the acceleration of point B on the gear rim.

(a)

PROBLEM 6 (continued)

(b)

PROBLEM 6 (continued)

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