Past Final Exam

Question 1

A Styrofoam block of volume 1 m^3 is floating is water (density 1 x 10^3 kg/m^3). assuming the block is fully submerged in water, what is the buoyancy force acting on the block?

Answer 1

9.8 kN

Question 2

if h = 1 m, the length of each cable is I = 2m, and the mass is 100 kg, what is the tension T in each cable?

Answer 2

980 N

Question 3

how much additional thermal energy is required to raise the temperature of a 225 g lead ball from 150 degrees Celsius to 25 degrees Celsius? the specific heat of lead is 128 J/kg*K.

Answer 3

288 J

Question 4

find the speed of an ocean wave whose displacement is given by the equation y(x,t) = 3.7 cos(2.2x - 5.6t) where x and y are in meters and t is in seconds

Answer 4

2.5 m/s

Question 5

an object hanging in air weighs 100N. when it is submerged under water, it weighs 50 N. what is the density of the object? assume the density of water is 1020 kg/m^3

Answer 5

2040 kg/m^3

Question 6

a hole of radius 2 mm forms in the bottom of a very large water storage tank that holds water to a depth of 10 m. ignoring viscosity, what is the speed of the water flowing out of the hole?

Answer 6

14 m/s

Question 7

a simple pendulum has a period of T = 1 second. the length of the pendulum is doubled. what is the new period?

Answer 7

sqrt(2)*T

Question 8

a pulley with radius 0.2 m and mass M = 1.5 kg is attached to a falling bucket with mass M = 1.5 kg. what will be the linear acceleration of the falling bucket after it is released? model the pulley as a uniform disk.

Answer 8

6.5 m/s^2

Question 9

a spring with a mass is bumped and undergoes a small oscillation. the mass is 1 kg, and the spring constant is 100 N/m. what is the frequency of the oscillation?

Answer 9

1.59 Hz

Question 10

a 30 m/s wind (air density p = 1.29 kg/m^3) blows over a house. what is the lift force on the 15 x 15 m roof? assume the roof is very thin.

Answer 10

131 kN

Question 11

a 3 kg hollow sphere of radius 5 cm starts from rest and rolls without slipping down a 15 degree incline. if the length of the incline is 100 cm, then the velocity of the center of mass of the hollow sphere at the bottom of the incline is:

Answer 11

1.75 m/s

Question 12

a roller coaster is released at a height h = 50 m. when the roller coaster gets to the ground, what is the speed, assuming all the gravitational potential energy is converted into kinetic energy? ignore friction and air resistance.

Answer 12

31 m/s

Question 13

a submarine is at a depth of 500 m under the water. the force on a circular hatch of 1 m in diameter due to the seawater (density = 1025 kg/m^3) pressure from outside the submarine is:

Answer 13

3.95 x 10^6 N

Question 14

a projectile from the origin with a velocity of 20 m/s at an angle of 45 degrees Celsius above the horizontal. what is the range of the projectile?

Answer 14

41 m

Question 15

a fluid flows at 10 m/s in a horizontal pipe. if the pipe narrows to a third of its original cross sectional area, what is the flow speed in the narrower section? you can model the fluid as ideal and incompressible.

Answer 15

30 m/s

Question 16

a car moving at a steady 10 m/s on a level highway encounters a depression that has a circular cross-section with a radius of 30 m. the car maintains its speed as it drives through the depression. what is the normal force exerted by the seat of the car on a 60 kg passenger when thee car is at the bottom of the depression?

Answer 16

790 N

Question 17

a roller coaster has a vertical loop with radius 9.8 m. what is the minimum speed at which the car must be moving at the top so that the passengers do not lose contact with the seats?

Answer 17

9.8 m/s

Question 18

a race car of mass 740 kg is moving at a speed of 53 m/s. suddenly, the driver brakes and makes the car stop in 4 seconds without any of the tires sliding. the power dissipated by the brakes is:

Answer 18

260 kW

Question 19

a tractor (T) is pulling a trailer (M) with a constant velocity (there is no friction). if the velocity is 20 m/s and M = 200 kg and T = 500 kg, then the force on the trailer due to the tractor is:

Answer 19

0

Question 20

how long does it take to melt a 1 kg block of ice at 0 degrees Celsius with a 200 W stove? assume all the power goes into melting the block. the latent heat of fusion for water at 0 degrees Celsius is 334 J/g

Answer 20

28 min

Question 21

how high would a person who is 100 kg need to climb before gaining 80,000 Joules of potential energy? 80,000 Joules is a typical energy obtained from eating a candy bar

Answer 21

81.6 m

Question 22

the specific heat of gold is determined by heating a 10 g grain at room temperature. it is determined that it takes 15 J to raise the temperature by 12 degrees Celsius. what is the specific heat of the gold grain?

Answer 22

125 J/kg*K

Question 23

Earth mass is M = 5.97 x 10^24 kg and its radius is R = 6370 km. thee International Space Station is orbiting Earth at an altitude of 410 km. how long does it take for the ISS to circle Earth once?

Answer 23

93 min

Question 24

an ideal gas takes up 600 cm^3 of volume at a temperature of 25 degrees Celsius. At what temperature will this same gas occupy 1150 cm^3 if the pressure is held constant?

Answer 24

298 degrees Celsius

Question 25

a merry-go-around of radius 2 m and moment of inertia 100 kg m^2 is initially at rest. a kid of mass 40 kg is running tangentially to the perimeter of the merry-go-round at a speed of 2 m/s, and jumps on. what is the rotational velocity of the merry-go-round with the kid on it?

Answer 25

0.62 rad/s