At a construction site a pipe wrench struck the ground

General Physics I

Midterm I

· Solve questions worth of 80 marks.

· Clearly mention question numbers while solving

· Mention the formulas you are using and steps of solution.

· Clear and procedural steps carry

1) Compute your average velocity in the following two cases: (a) You walk 73.2 m at a speed of 1.22 m/s and then run 73.2 m at a speed of 3.05 m/s along a straight track. (b) You walk for 1.00 min at a speed of 1.22 m/s and then run for 1.00 min at 3.05 m/s along a straight track. (c) Graph x versus t for both cases and indicate how the average velocity is found on the graph. (10)

(a) average velocity=s/t=v0+at/2=v0+(v1-v0)/2=(v1+v0)/2=(1.22+3.05)/2=2.135m/s

(b) 2.135m/s

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2) At a construction site a pipe wrench struck the ground with a speed of 24 m/s. (a) From what height was it inadvertently dropped? (b) How long was it falling? (10)

3) Two subway stops are separated by 1100 m. If a subway train accelerates at 1.2 m/s2 from rest through the first half of the distance and decelerates at 1.2 m/s2 through the second half, what are (a) its travel time and (b) its maximum speed? (10)

4) In 1939 or 1940, Emanuel Zacchini took his human- cannonball act to an extreme: After being shot from a cannon, he soared over three Ferris wheels and into a net . Assume that he is launched with a speed of 26.5 m/s and at an angle of 53.0°. (a) Treating him as a particle, calculate his clearance over the first wheel. (b) If he reached maximum height over the middle wheel, by how much did he clear it? (c) How far from the cannon should the net’s center have been positioned (neglect air drag)? (10)

5) A rifle that shoots bullets at 460 m/s is to be aimed at a target 45.7 m away. If the center of the target is level with the rifle, how high above the target must the rifle barrel be pointed so that the bullet hits dead center? (5)

6) Only two horizontal forces act on a 3.0 kg body that can move over a frictionless floor. One force is 9.0 N, acting due east, and the other is 8.0 N, acting 62 north of west. What is the magnitude of the body’s acceleration? (5)

7) A 500 kg rocket sled can be accelerated at a constant rate from rest to 1600 km/h in 1.8 s. What is the magnitude of the required net force? (5)

8) Four penguins that are being playfully pulled along very slippery (frictionless) ice by a curator. The masses of three penguins and the tension in two of the cords are m1 12 kg, m3 15kg,m4 20kg,T2 111N,andT4 222N.Findthepen- guin mass m2 that is not given. (10)

9) A block of mass m1 3.70 kg on a frictionless plane inclined at angle 30.0 is connected by a cord over a massless, frictionless pulley to a second block of mass m2 2.30 kg . What are (a) the magnitude of the acceleration of each block, (b) the direction of the acceleration of the hanging block, and (c) the tension in the cord? (10)

10) Blocks A and B have weights of 44 N and 22 N, respectively. (a) Determine the minimum weight of block C to keep A from sliding if μs between A and the table is 0.20. (b) Block C suddenly is lifted off A. What is the acceleration of block A if μk between A and the table is 0.15? (10)

11) A puck of mass m 1.50 kg slides in a circle of radius r 20.0 cm on a frictionless table while attached to a hanging cylinder of mass M 2.50 kg by means of a cord that extends through a hole in the table (Fig. 6-43). What speed keeps the cylinder at rest? (10)

12) A helicopter lifts a 72 kg astronaut 15 m vertically from the ocean by means of a cable. The acceleration of the astronaut is g/10. How much work is done on the astronaut by (a) the force from the helicopter and (b) the gravitational force on her? Just before she reaches the helicopter, what are her (c) kinetic energy and (d) speed? (10)

13) You drop a 2.00 kg book to a friend who stands on the ground at distance D 10.0 m below. If your friend’s out- stretched hands are at distance d 1.50 m above the ground (Fig. 8-30), (a) how much work Wg does the gravitational force do on the book as it drops to her hands? (b) What is the change U in the gravitational potential energy of the book – Earth system during the drop? If the gravitational potential energy U of that system is taken to be zero at ground level, what is U (c) when the book is re- leased and (d) when it reaches her hands? (10)

14) A bullet of mass 10 g strikes a ballistic pendulum of mass 2.0 kg. The center of mass of the pendulum rises a vertical distance of 12 cm. Assuming that the bullet remains embedded in the pendulum, calculate the bullet’s initial speed. (10)