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

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## Question “A 7.8kg mass hanging from a spring scale is slowly lowered onto a vertical spring, as…”

A 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)

## Answer

Hooke’s law of motion of a mass that is suspended on spring balance compresses spring and net force acts on lower spring are the concepts used to solve the problem.

To calculate the spring scale reading, first use the force that affects the spring scale. This will touch the lower spring.

Next, take the spring scale reading along with the new scale reading to determine the force of the lower spring pushing upward.

Hooke’s law is used to calculate the spring constant for the spring that has been compressed by 2.0 cm.

To calculate the compressed length, you can use the spring constant of the lower spring. This will give you zero in spring scale.

The force acting upon the mass when it rests on the lower spring is weight.

The weight of the mass can be expressed as:

*W* refers to the mass of the object, *M* refers to the spring-scale mass and *G* the acceleration caused by gravity.

Hooke’s law says that the force applied to a spring is proportional in its stretch from its rest position.

Hooke’s law is used to express the relationship.

*F* here is the applied force. *K* is a spring constant. *x* the compressed length.

(a)

The weight of the mass is the only factor that affects the spring scale before it touches the vertical spring.

The only force that affects the spring balance is the weight of the mass.

Substitute HTMLmedia_tag_3$ to *m*, and HTMLmedia_tag_4$ to *g*.

(b)

is the reading of the spring balance when the mass hangs from it. The spring balance reading will decrease if the spring scale’s mass is lower than the vertical spring. The restoring force of the vertical spring pushes up the mass from the scale.

The acceleration in equilibrium is zero so the net force of zero. Therefore, the spring force must be balanced with gravity’s force.

The spring scale is

. This means that the lower spring pushing upwards is .

refers to the new scale reading, and //media_tag_10$ the restoring force of the lower spring.

acts in the opposite direction to the mass on the scale. Thus,

Substitute HTMLmedia_tag_13$ with HTMLmedia_tag_14$.

Change the equation to make spring constant.

Substitute

to

;

to

; and

to

(c)

When the hanging mass’s weight is fully balanced by the restoring force from the lower vertical spring, the scale reads zero.

The equation for compression length at zero scale reading is

Substitute HTMLmedia_tag_25$ to

.

Adjust the equation so that the spring is at a compressed length of zero.

Substitute HTMLmedia_tag_29$ to

or HTMLmedia_tag_31$ to

Ans: Part A

The spring scale is read just before the mass touches lower spring is

.

Part b

The spring constant for lower springs is

.

Part c

is the compressed length at which spring should be null.

## Conclusion

Above is the solution for “**A 7.8kg mass hanging from a spring scale is slowly lowered onto a vertical spring, as…**“. We hope that you find a good answer and gain the knowledge about this topic of **science**.