# A mass m = 16 kg rests on a fr

A mass m = 16 kg rests on a frictionless table and acceleratedby a spring with spring constant k = 4739 N/m. The floor isfrictionless except for a rough patch. For this rough path, thecoefficient of friction is μk = 0.45. The mass leavesthe spring at a speed v = 2.9 m/s.

1)How much work is done by the spring as it accelerates themass?

2)How far was the spring stretched from its unstrechedlength?

3)The mass is measured to leave the rough spot with a finalspeed vf = 1.7 m/s. How much work is done by friction asthe mass crosses the rough spot?

4)What is the length of the rough spot?

5)In a new scenario, the block only makes it (exactly) half-waythrough the rough spot. How far was the spring compressed from itsunstretched length?

6)in this new scenario, what would the coefficient of frictionof the rough patch need to be changed to in order for the block tojust barely make it through the rough patch?

1) The work done by the spring is converted into kinetic energyof the body as there is no friction. The kinetic energy of theblock when it leaves the spring is 1/2 m v2

W = 1/2 x 16 x 2.92 = 67.28 J

2) Intial elastic energy stored in the spring is converted intokinetic energy of the block, Hence

1/2 k x2 = 1/2 m v2 =>  x2 = m v2 / k = 16 x 2.92 /4739 = 0.0284; then x = 0.17 m

The compression in the spring is 0.17m

3) The speed of the body before rough spot is 2.9 m/s and itsspeed after rough spot is 1.7 m/s. The decrease in kinetic energyis due to workdone by frictional force.

Hence Wf = KEf – KEi = 1/2 m Vf2 – 1/2 m Vi2 = 1/2 m (Vf2 – Vi2)= 1/2 x 16 x (1.72 – 2.92)

The work done by friction is Wf = – 44.16 J

4) Wf = mg x S   => 44.16 = 0.45 x 16 x 9.8 x S => S =0.626 m = 62.6 cm

The length of the rough patch is 0.626m

5) If the body travels only half of the rough patch then thework done by the spring is equal to work done against thefrictional force. Let y is new compression in spring.

1/2 k y2 = mg x S/2 =>  y2 = mg x S / k = 0.45 x 16 x 9.8 x 0.626 / 4739 = 0.0093

The new compression in the spring is y = 0.096 m = 9.6cm

6) The body crosses the rough patch in this new scenario if thecoefficient of kinetic friction is half of its original value. Thenew coefficient of kinetic friction is 0.225.

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!"
Calculate the price
Pages (550 words)
\$0.00
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with brilliantassignmenthelp.com
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
Testimonials
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
11,595
Customer reviews in total
96%
Current satisfaction rate
3 pages
Average paper length
37%
Customers referred by a friend
Use a coupon FIRST15 and enjoy expert help with any task at the most affordable price.
Claim my 15% OFF Order in Chat