Question

A 7.8kg mass hanging from a spring scale is slowly lowered onto a vertical spring, as...

uploaded imageA 7.8kg mass hanging from a spring scale is slowly lowered onto a vertical spring, as shown in the figure.
What does the spring scale read just before the mass touches the lower spring?(N)
The scale reads 22N when the lower spring has been compressed by 2.6cm . What is the value of the spring constant for the lower spring? (N/m)

At what compression length will the scale read zero? (cm)

0 0
Add a comment Improve this question Transcribed image text
✔ Recommended Answer
Answer #1
Concepts and reason

The concepts used to solve this problem are Hooke’s law of the motion of a mass which is hung on spring balance that compresses the spring, and net force acting on the lower spring.

First, use the force affecting the spring scale to calculate the spring scale reading, which touches the lower spring.

Then, use the spring scale reading and the new scale reading to find the force of lower spring that pushes upward.

Then apply Hooke’s law to calculate spring constant of the spring compressed by 2.0 cm.

Finally, use the spring constant for the lower spring to calculate the compressed length that will read zero in spring scale.

Fundamentals

When the mass rests on the lower spring, the force acting on the mass is weight.

The expression for the weight of the mass is,

W = mg

Here, W is the weight of the mass, m is the mass hanging in the spring scale, and g is the acceleration due to gravity.

Hooke’s law states that the stretch of the spring from its rest position is proportional to the applied force.

Express the relation using Hooke’s law.

F=-kor

Here, F is the applied force, k is the spring constant, and x is the compressed length.

(a)

The only force affecting the spring scale before the mass touches the vertical spring is the weight of the mass.

Hence, the only force acting on the spring balance is weight of the mass.

W = mg

Substitute 7.8 kg
for m and 9.8m/s2
for g.

W =(7.8kg)(9.8m/s)
= 76.44N
76N

(b)

When the mass is hanging from the spring scale, it reads. When the mass from a spring scale is lowered on to a lower vertical spring, the spring balance reading decreases. This is because the restoring force from the vertical spring pushes the mass from the scale upward.

In equilibrium, the acceleration is zero, so the net force is zero. Thus, the spring force and force due to gravity must balance each other.

Since the spring scale reads , the force of lower spring that pushes upward is,

W=F+W

Here, is the new scale reading and is the restoring force from the lower spring.

is acting in the direction opposite to the weight of the mass hanging from the scale. Thus, F, =-kor

Substitute for.

W=(-kat)+W

Rearrange the equation for spring constant,

W=(-kx)+W
-kor=W-W
k=-W-W

Substitute for , for , and 0.026 m
for .

ku
(22N - 76N
0.026m
= 2076.923 N/m
2100 N/m

(c)

The scale reads zero when the weight of the hanging mass is completely balanced by the restoring force of the lower vertical spring.

The equation for compression length at which the scale read zero is,

W+F1 = 0

Substitute for .

W - x = 0

Rearrange the equation to compressed length at which the spring should be zero,

Substitute for and 2100 N/m
for .

x=
(76)
(2100 N/m)
=-0.03619m (10 cm
3.6 cm

Ans: Part a

Spring scale reads just before the mass touches the lower spring is .

Part b

The spring constant for the lower spring is 2100 N/m
.

Part c

Compressed length at which the spring should be zero is 3.6 cm
.

Add a comment
Know the answer?
Add Answer to:
A 7.8kg mass hanging from a spring scale is slowly lowered onto a vertical spring, as...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Similar Homework Help Questions
  • A 5.0-kg block suspended from a spring scale is slowly lowered onto a vertical spring (Figure...

    A 5.0-kg block suspended from a spring scale is slowly lowered onto a vertical spring (Figure 1) . Part A What does the scale read before the block touches the vertical spring? Part B If the scale reads 34N when the bottom spring is compressed 30 mm, what is k for the bottom spring? Part C How far does the block compress the bottom spring when the scale reads 0? Express your answer with the appropriate units. Enter positive value...

  • A vertical scale on a spring balance reads from 0 to 250 N . The scale has a length of 10.5 cm from the 0 to 250 N readi...

    A vertical scale on a spring balance reads from 0 to 250 N . The scale has a length of 10.5 cm from the 0 to 250 N reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.75 Hz . Ignoring the mass of the spring, what is the mass m of the fish?

  • A 360 g block is dropped onto a relaxed vertical spring that has a spring constant...

    A 360 g block is dropped onto a relaxed vertical spring that has a spring constant of k = 1.3 N/cm (see the figure). The block becomes attached to the spring and compresses the spring 13 cm before momentarily stopping. While the spring is being compressed, what work is done on the block by (a) the gravitational force on it and (b) the spring force? (c) What is the speed of the block just before it hits the spring? (Assume...

  • A 290 g block is dropped onto a relaxed vertical spring that has a spring constant...

    A 290 g block is dropped onto a relaxed vertical spring that has a spring constant of k = 4.7 N/cm (see the figure). The block becomes attached to the spring and compresses the spring 18 cm before momentarily stopping. While the spring is being compressed, what work is done on the block by (a) the gravitational force on it and (b) the spring force? (c) What is the speed of the block just before it hits the spring? (Assume...

  • Constants A vertical scale on a spring balance reads from 0 to 160 N The scale...

    Constants A vertical scale on a spring balance reads from 0 to 160 N The scale has a length of 12.5 cm from the 0 to 160 N reading A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.00 Hz Ex

  • A vertical scale on a spring balance reads from 0 to 180 N. The scale has...

    A vertical scale on a spring balance reads from 0 to 180 N. The scale has a length of 10.5 cm from the 0 to 180 N reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.05 Hz Part A Ignoring the mass of the spring, what is the mass m of the fish? Express your answer in kilograms. View Available Hint(s) O O ? IVAR m= 22.2 | kg Submit Previous Answers...

  • t The Fish Scale Constants ? Part A A vertical scale on a spring balance reads...

    t The Fish Scale Constants ? Part A A vertical scale on a spring balance reads from 0 to 155 N. The scale has a length of 11.5 cm from the 0 to 155 N reading A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2 80 Hz Ignoring the mass of the spring, what is the mass m of the fish? Express your answer in kilograms. View Available Hint(s) kg Submit Previous Answers

  • A 400 g mass is attached to a vertical spring and lowered slowly until it rests...

    A 400 g mass is attached to a vertical spring and lowered slowly until it rests at a new equilibrium position, which is 50 cm below the spring's original equilibrium. The system is then set into simple harmonic motion. What is the period of the motion? $

  • show full working out A vertical scale on a spring balance reads from 0 to 165...

    show full working out A vertical scale on a spring balance reads from 0 to 165 N . The scale has a length of 10.5 cm from the 0 to 165 N reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.35 Hz. Part A Ignoring the mass of the spring, what is the mass m of the fish? Express your answer in kilograms. View Available Hint(s) ΕΠΙ ΑΣΦ ? ma kg

  • A 300 g block is dropped onto a relaxed vertical spring that has a spring constant...

    A 300 g block is dropped onto a relaxed vertical spring that has a spring constant of k = 2.1 N/cm. The block becomes attached to the spring and compresses the spring 12 cm before momentarily stopping. (a) While the spring is being compressed, what work is done on the block by the gravitational force on it? J (b) What work is done on the block by the spring force while the spring is being compressed? J (c) What is...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT