Spring Swing
Can someone help me with this oscillating spring question?
A 380 g wood block is firmly attached to a very light horizontal spring. The block can slide along a table where the coefficient of friction is 0.30. A force of 32N compresses the spring 20 cm. If the spring is released from this position, how far beyond its equilibrium position will it stretch on its first swing?Can someone help me with this oscillating spring question?
No damping force means this is algebraic physics (as opposed to differential).
Without friction and dampening, a perfect spring would oscillate for forever and the mass would move from -20cm to +20cm (compression to extension). We need to calculate how much the friction force takes away from this theoretical maximum of +20cm.
The spring equation is F = -kx
With 32N & -20cm we calculate k = 160N/m
Now we have to compensate for the friction, friction is a force that opposes the motion of the object in magnitude proportional to the normal force.
The normal force is Fn = m * g (mass * force of gravity)
Fn = 380g * 9.8m/s² = 3.724 kg*m/s² = 3.724 N
The frictional force is Ff = - Fn * μ
μ is the coefficient of friction.
Ff = - 3.724 N * 0.30 = -1.1172 N
Now substitute the modified force into the spring equation:
(F + Ff) = -k x
(32N - 1.1172N) = 160N * x
x = 0.193018 m = 19.3 cm
The "big leaps" for this problem is realizing the theoretical maximum is +20cm and that we have to figure out how much less this is due to a force (the friction force).
That means what we need is an equation involving force and distance for a spring, which is F = -k x.
If we can figure out k and F we'll know x.
 |
 Spring Swings Deluxe Fun Ride Zip Line 70 Foot Cable Trolley Set SAME DAY SHIP $98.99 Time Remaining: 1d 17h Buy It Now for only: $98.99 |
 Deluxe Fun Ride Zip Line Backyard Trolley by Spring Swings $25.00 (1 Bid) Time Remaining: 2d 4h 52m |
 New Fun Spring Swings Twizzler Fun Ride $47.99 Time Remaining: 3d 12h 50m Buy It Now for only: $47.99 |
 New Spring Swings Fun Ride Original Zip Line $69.99 Time Remaining: 3d 13h 6m Buy It Now for only: $69.99 |
 Outdoor Spring Swing Disc Swing $69.00 Time Remaining: 5d 2h 48m Buy It Now for only: $69.00 |
 Spring Swings Fun Ride Classic Zip Line NEW $59.99 Time Remaining: 5d 4h 1m Buy It Now for only: $59.99 |
 Spring Swing Fun Ride Super Z Ultimate Zip Line 90 Foot Cable Trolley Set NEW $148.49 Time Remaining: 5d 11h 12m Buy It Now for only: $148.49 |
 SWING SEAT SPRING SWING DISC PLAYGROUND SET TOY FORT CHILDREN OUTDOORS FUN 0119 $107.99 Time Remaining: 6d 4h 28m Buy It Now for only: $107.99 |
 SPRING CLIP Outdoor Playset Swing Set $3.00 Time Remaining: 6d 5h 14m Buy It Now for only: $3.00 |
 SWING SEAT 3 8 x 3 1 2 SPRING CLIPS PAIR SWING SET HARDWARE HANGER CHAIN 0079 $6.47 Time Remaining: 6d 6h 50m Buy It Now for only: $6.47 |
 Spring Swings Original Fun Ride Zip Line Trolley 35ft $49.49 Time Remaining: 6d 8h 16m Buy It Now for only: $49.49 |
 Spring Swings Super Z Fun Ride Zip Line Trolley 90ft $148.49 Time Remaining: 6d 8h 29m Buy It Now for only: $148.49 |
 Spring Swing set Twizzler Fun Ride playground playset $35.99 Time Remaining: 6d 8h 47m Buy It Now for only: $35.99 |
 New Spring Swings Fun Ride Deluxe Trolley Ride Fun In Motion $49.99 Time Remaining: 6d 11h 9m |
 Twizzler II Spring Swings More $36.99 Time Remaining: 6d 21h 38m Buy It Now for only: $36.99 |
 SWING SEAT 5 16 SPRING CLIPS PAIR PLAYGROUND HARDWARE HANGER SEAT CHAIN 0136 $8.37 Time Remaining: 7d 6h 28m Buy It Now for only: $8.37 |
 Jumping Rodeo Bull Swing Spring Suspended $199.00 Time Remaining: 9d 16h 22m Buy It Now for only: $199.00 |
 Spring Snap Hooks 1 pair Swingset Spring Clips Playground Swings Trapeze $4.25 Time Remaining: 10d 11h 42m Buy It Now for only: $4.25 |
 Fun Ride Super Z Spring Swings More $149.99 Time Remaining: 11d 13h 36m Buy It Now for only: $149.99 |
 Fun Ride Classic Trolley Ride Spring Swings More $49.99 Time Remaining: 11d 13h 36m Buy It Now for only: $49.99 |
 Spring Swings Disc Seat Swing $70.18 Time Remaining: 11d 18h 43m Buy It Now for only: $70.18 |
 Spring Swings Deluxe Fun Ride Colors May Vary New Swings Sets Gym Play Outdoor $109.61 Time Remaining: 12d 4h 21m Buy It Now for only: $109.61 |
 Spring Swings Twizzler Fun Ride New Swings Sets Gym Play Outdoor Sports Games $49.18 Time Remaining: 12d 4h 21m Buy It Now for only: $49.18 |
 Spring Swings Fun Ride Original Zip Line New Swings Sets Gym Play Outdoor Sports $64.04 Time Remaining: 12d 4h 21m Buy It Now for only: $64.04 |
 Spring Swings Super Z Fun Ride New Swings Sets Gym Play Outdoor Sports Games $172.71 Time Remaining: 12d 4h 21m Buy It Now for only: $172.71 |
 SPRING SWING w DISC NEW in Box $64.99 Time Remaining: 12d 5h 32m Buy It Now for only: $64.99 |
 Swingset Spring Clip Snap Hook for Swingset 1 Pair Swing Set Accessories $3.00 Time Remaining: 13d 12h 35m Buy It Now for only: $3.00 |
 Spring Swings ORIGINAL Fun Ride Zip Line Trolley 35ft playground playset toy NEW $49.49 Time Remaining: 13d 14h 3m Buy It Now for only: $49.49 |
 Tree Swing Bounce Childrens Disc Springs Toddler 3 8 $59.99 Time Remaining: 15d 8h 28m Buy It Now for only: $59.99 |
 Spring Swing Disc Seat Single Bounce Adapter $79.99 Time Remaining: 17d 19h 38m Buy It Now for only: $79.99 |
 Jumping Pony Spring Suspended Horse Swing $179.00 Time Remaining: 21d 2h 59m Buy It Now for only: $179.00 |
 Spring Swings Fun Ride Classic Zip Line For Kids NEW $61.95 Time Remaining: 24d 11h 8m Buy It Now for only: $61.95 |
 Spring Swings Deluxe Fun Ride Zip Line Up to 225 Lbs $117.99 Time Remaining: 25d 9h 33m Buy It Now for only: $117.99 |
 Spring Swings DELUXE Fun Ride Zip Line playground playset wire Trolley 70ft NEW $98.99 Time Remaining: 25d 11h 42m Buy It Now for only: $98.99 |
 Spring Swings SUPER Z Fun Ride Zip Line Trolley playground swingset playset 90ft $148.49 Time Remaining: 25d 11h 46m Buy It Now for only: $148.49 |
 Spring Swings Twizzler Fun Ride NEW NIB $43.95 Time Remaining: 25d 13h 10m Buy It Now for only: $43.95 |
 SWINGSET SPRING CLIP CHAIN NOT QUICK LINK SEAT SLIDE PARTS SWING SET HARDWARE $1.50 Time Remaining: 25d 13h 50m Buy It Now for only: $1.50 |
 2pcs Multifunction NEW Swing Set Steel Spring Clicp Chain Swing Links L size $4.99 Time Remaining: 25d 15h 45m Buy It Now for only: $4.99 |
 Spring Swings Fun Ride Original Zip Line $61.66 Time Remaining: 25d 18h 43m Buy It Now for only: $61.66 |
 NEW SPRING SWINGS TWIZZLER FUN RIDE $47.99 Time Remaining: 26d 19h 3m Buy It Now for only: $47.99 |
 Spring Swings Kids Twist Spin T Swing Twizzler Fun Ride $44.74 Time Remaining: 28d 10h 29m Buy It Now for only: $44.74 |
 3 8 x 3 1 2 SPRING CLIPS PAIR SWING SET HARDWARE HANGER SEAT CHAIN PLAY 0079 $6.47 Time Remaining: 29d 17h 40m Buy It Now for only: $6.47 |