10) A boy is playing with a ball whose mass is 0.2 kg and a very light (negligib

Question

10) A boy is playing with a ball whose mass is 0.2 kg and a very light (negligible mass) spring. He finds that if he hangs the ball from the spring, it stretches the spring from its unstrained length of 0.8 m to 1.2 m. He also finds that if he swings the spring with the ball attached to its end (such that ball moves on a horizontal circle and the spring stays perfectly horizontal throughout the motion) that the faster he turns, the more the spring gets stretched What is the spring constant of the spring? b. How fast does the boy have to turn (what is the angular velocity) such that the spring stretches to twice its unstrained length? 11) To draw water from a well, a farmer uses a thin-walled cylindrical pipe of mass 2 kg and radius 8 cm as a reel that draws the rope connected to a bucket. The bucket has an inner volume of 0.02 ma, and weighs 9.8 N when empty. The farmer turns the pipe by applying a force perpendicular to the end of a crank arm of length 32 cm What is the magnitude of the force that the famer has to apply to bring a full bucket of water up with constant velocity of 2.0 m/s? 12) You are invited to a pool party with Alice (54kg), Bob (75kg), and Charlie (82kg), but you can't stop thinking about physics. You estimate that the swimming pool has a surface area of 60m and is filled with chlorinated-water such that the depth is 1.8m a) What are the absolute pressures at the surface of the pool and at the bottom of the pool? b) What is the magnitude of the total force on the pool floor? c) Bob and Charlie are arguing over who gets to use an inflatable tube. It has a mass of 1.64 kg when deflated, and when inflated with pressurized air of density 2.0 kg/m3, it has a volume of 0.08 m3. Calculate the mass of the heaviest person that this inflatable tube can support without sinking completely in the pool, and see if you can settle Bob and Charlie's argument. d) Alice and Bob jump in the pool Alice jumps feet first and takes 600 ms seconds) to stop while Bob belly-flops and is stopped in 10 ms. If they have the same speed of 4m/s just before they hit the water, what are the average forces exerted by the water on Alice, and Bob? e) Charlie is showing off with an acrobatic dive. Initially he has an angular velocity of 7 rad/s and no net external torque is acting on him. He then pulls in his arms and legs into a tuck position and his angular velocity increases to 14 rad/s f Charlie's initial moment of inertia is 1.4 kg m what is his final moment of inertia e. in the tuck position)? 13) You set out to make some pasta. You put some room temperature water (76 F) on the stove to heat up, but accidentally forget the pot on the stove and all of the water boils off (evaporates). What is the ratio of the heat required to heat-up the water to its boiling point, compared to the amount of heat required to boil-off all the water after it had reached the boiling point?

Explanation / Answer

10)

The spring constant k can be calculated as follow:

F(hooks) = F(gravity)

kx = mg

k = mg/x

k = 0.2 x 9.8/(1.2 - 0.8) = 4.9 N/m

Hence, K = 4.9 N/m

b)we know that,

w = sqrt (k/m) = sqrt (4.9/0.2) = 4.95 rad/s

Hence, w = 4.95 rad/s

[ if k changes, k = 0.2 x 9.8/0.8 = 2.45 , w = sqrt (2.45/0.2) = 3.5 rad/s]

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