Question

A 2 meter long mass less spring is hanging from the ceiling. You hang a 1...

A 2 meter long mass less spring is hanging from the ceiling. You hang a 1 kg weight to the bottom of the spring. After the weight is attached the spring stretches 5 cm down. You take off the weight and removed the spring from the ceiling and place it on the floor so it is horizontal.

1. There is no friction on the floor. Calculate the maximum compression that the spring reaches at its relaxed position if you fire a 0.5 kg weight at it with a velocity of 20 meters per second.

2. How much would the answer to the first question change if the spring was only stretched 1 cm downward when the 1 kg weight is attached?

3. If the spring from question 2 is compress a distance equal to spring from question 1 and then put the 0.5 kg weight there and released it, what would be the velocity of the mass after it left the spring?

Homework Answers

Answer #1

Vertical force balance gives, kx = mg

=> k = mg/xo = 1 * 9.8 / 0.05 = 196 N/m

1) KE of the 0.5 kg weight is converted to the elastic PE of the spring.

mv2/2 = kxmax2/2

=> xmax = v(m/k)1/2 = 20 * (0.5 / 196)1/2 = 1.01 m

2) knew = 1 * 9.8 / 0.01 = 980 N/m

xmax' = v(m/knew)1/2 = 20 * (0.5 / 980)1/2 = 0.45 m

3) Elastic PE of the spring is converted to the KE of the 00,5 kg weight.

mv2/2 = knewxmax2/2

=> v = xmax (knew/m)1/2 = 1.01 * (980 / 0.5)1/2 = 44.7 m/s

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A 8.0-cm-long spring is attached to the ceiling. When a 2.5 kg mass is hung from...
A 8.0-cm-long spring is attached to the ceiling. When a 2.5 kg mass is hung from it, the spring stretches to a length of 17 cm . 1. What is the spring constant k? 2. How long is the spring when a 3.0 kg mass is suspended from it?
A 10-cm-long spring is attached to the ceiling. When a 2.0 kg mass is hung from...
A 10-cm-long spring is attached to the ceiling. When a 2.0 kg mass is hung from it, the spring stretches to a length of 15 cm.What is the spring constant k? How long is the spring when a 3.9 kg mass is suspended from it?
A spring hanging vertically under its own weight has length 20 cm. When a 6.5 kg...
A spring hanging vertically under its own weight has length 20 cm. When a 6.5 kg mass is attached to the end of it, it stretches vertically so that its new length is 117 cm when hanging at rest. If we remove the 5.8 kg mass, attach a 8.5 kg mass to the end of the spring, and again allow it to hang vertically, how long will the spring be?
A 12 cm long spring is attached to the ceiling. When a 2.4 kg mass is...
A 12 cm long spring is attached to the ceiling. When a 2.4 kg mass is hung from it, the spring stretches to a length of 17 cm. (a) What is the spring constant k? N/m (b) How long is the spring when a 3.2 kg mass is suspended from it? cm
A body weighing 1 [kg] is attached to a spring hanging from the ceiling. The spring...
A body weighing 1 [kg] is attached to a spring hanging from the ceiling. The spring stiffness constant is k = 6k = 6 [N / m]. The medium surrounding the system offers resistance proportional to body speed with a damping constant: µ = 5μ = 5 [N.s / m]. The body's center of mass is initially at a distance of 1 [m] below the equilibrium point, then the body is released by printing an upward velocity of 44 [m...
A spring is hanging vertically from a shelf. When a weight of mass 0.16 kg is...
A spring is hanging vertically from a shelf. When a weight of mass 0.16 kg is hung from the spring, the spring stretches a distance 25 cm. That weight is then removed and a new weight of mass 0.30 kg is hung from the spring. This second weight is then lifted a distance of 1.8 cm and released. The weight oscillates up and down. What is the period of oscillation (in units of seconds)?
A 33.0 cm long spring is hung vertically from a ceiling and stretches to 40.9 cm...
A 33.0 cm long spring is hung vertically from a ceiling and stretches to 40.9 cm when a 7.00 kg mass is hung from its free end. (a) Find the spring constant (in N/m). (b) Find the length of the spring (in cm) if the 7.00 kg weight is replaced with a 175 N weight.
You hang a 400 gram mass on a spring and the spring stretches 16.0 cm. You...
You hang a 400 gram mass on a spring and the spring stretches 16.0 cm. You then pull the mass down an additional 4.0 cm and let it go.    a) Write an equation for the position of the mass as a function of time. b) Where will the mass be located 4.0 seconds later? c) What will its velocity be?
You hang a 175 g mass on a spring and start it oscillating with an amplitude...
You hang a 175 g mass on a spring and start it oscillating with an amplitude of 7 cm and a phase constant of −π/3. a. If the spring stretched 16 cm when you first hang the mass on it, how long will one oscillation take? b. Draw a position vs. time graph for two cycles of motion. Consider the position y = 0 to be the equilibrium position of the mass hanging on the spring. c. Will the velocity...
A 2 foot long spring is suspended from the ceiling. To this spring we attach a...
A 2 foot long spring is suspended from the ceiling. To this spring we attach a 32 lb weight that stretches the spring 1.99 feet into an equilibrium position. At time t = 0 we pull on the string and stretch it another 8 inches before releasing it. The friction in the spring gives rise to a damping force of 1lb with a velocity of 24 inches/second. At what time will the ball be closest to the ceiling? A. t...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT