• Author / Uploaded
• Bharat Sai

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1. The horizontal motion of the plunger and shaft is arrested by the resistance of the attached disk which moves through the oil bath. If the velocity of the plunger is v0 in the position A where x=0 and t=0, and if the deceleration is proportional to v so that a=-kv, derive expressions for the velocity v and position coordinate x in terms of the time t. Also express v in terms of x.

A test projectile is fired horizontally into a viscous liquid with a velocity of v0. The retarding force is proportional to the square of the velocity, so that the acceleration becomes a=kv2. Derive expressions for the distance D traveled in the liquid and the corresponding time t 2.

required to reduce the velocity to v0/2. Neglect any vertical motion.

3. For a certain interval of motion the pin A is forced to move in the fixed parabolic slot by the horizontal slotted arm which is elevated in the y-direction at the constant rate of 3 cm/sec. All measurements are in centimeters and seconds. Calculate the velocity v and acceleration a of pin A when x=6cm.

4. To meet design criteria, small ball bearings must bounce through an opening of limited size at the top of their trajectory when rebounding from a heavy plate as shown. Calculate the angle θ made by the rebound velocity with the horizontal and the velocity v of the balls as they pass through the opening.

5. A jet plane flying at a constant speed v at an altitude h=10km is being tracked by radar located at O directly below the line of flight. If the angle θ is decreasing at the rate of 0.020 rad/s when θ=60o, determine the value of r at this instant and the magnitude of the velocity v of the plane.

6. A locomotive is traveling on the straight and level track with a speed v=90km/h and a deceleration a=0.5m/s2 as shown. Relative to the fixed observer at O, determine the quantities r , r ,

and

at the instant when θ=60o and r=400m.

7. Train A travels with a constant speed vA=120 km/h along the straight and level track. The driver of car B, anticipating the railway grade crossing C, decreases the car speed of 90 km/h at the rate of 3 m/s2. Determine the velocity and acceleration of the train relative to the car.

8. A drop of water falls with no initial speed from point A of a highway overpass. After dropping 6m, it strikes the windshield at point B of a car which is traveling at a speed of 100km/h on the horizontal road. If the windshield is inclined 50o from the vertical as shown, determine the angle θ relative to the normal n to the windshield at which the water drop strikes.