Question
Asked Oct 17, 2019

A block of mass m = 2.00 kg is attached to a spring of force constant k = 405 N/m as shown in the figure below. The block is pulled to a position xi = 4.95 cm to the right of equilibrium and released from rest.

(a) Find the speed the block has as it passes through equilibrium if the horizontal surface is frictionless.

(b) Find the speed the block has as it passes through equilibrium (for the first time) if the coefficient of friction between block and surface is μk = 0.350.

k
www.w
m
xx
x0
help_outline

Image Transcriptionclose

k www.w m xx x0

fullscreen
check_circle

Expert Answer

Step 1

Given:

Mass of the block = 2.00 kg

Force constant = 405 N/m

Distance travelled by the block = 4.95 cm

Coefficient of friction, μk = 0.350

 

Step 2

For frictionless surface,

Speed of the block as it passes through equilibrium can be calculated as;

K.E. of the block = P.E. energy of the block

 

where
m mass of the block
k force constant
distance travelled by the block
x
v = velocity of the block
т
plug in the values
405x(4.95x10)
2
v 70.43x10m/s
v 0.7043 m/s
help_outline

Image Transcriptionclose

where m mass of the block k force constant distance travelled by the block x v = velocity of the block т plug in the values 405x(4.95x10) 2 v 70.43x10m/s v 0.7043 m/s

fullscreen
Step 3

Speed of the block as it passes through equilibrium and μk is the coeff...

where,
m =mass of the block
k =force constant
x distance travelled by the block
v=velocity of the block
&Coefficient of friction
g acceleration due to gravity
kc2-2umgx
тm
kc-2umgx
т
plug in the values
405x (4.95 x10-2x 0.350 x 2x 9.8 x 4.95 x 10
v =
2
1-0.68
2
0.32
v =0.16
v 0.4 m/s
help_outline

Image Transcriptionclose

where, m =mass of the block k =force constant x distance travelled by the block v=velocity of the block &Coefficient of friction g acceleration due to gravity kc2-2umgx тm kc-2umgx т plug in the values 405x (4.95 x10-2x 0.350 x 2x 9.8 x 4.95 x 10 v = 2 1-0.68 2 0.32 v =0.16 v 0.4 m/s

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Science

Physics

Friction

Related Physics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: how to solve for mass and tension using the equation T=mg given the weight and angles

A: The expression for tension on a single strand is

question_answer

Q: A 10 μF capacitor initially charged to 25 μC is discharged through a 1.4 kΩ resistor.   Part A ...

A: Given:Initial charge on the capacitor, Qο = 25µCFinal charge on the capacitor, Q = 10 µCResistance, ...

question_answer

Q: Two ice skaters, with masses of 40.0 kg and 75.0 kg , are at the center of a 60.0 m -diameter circul...

A: Given that the masses of the skaters are m1=40.0kg, and m2=75.0kg, and the diameter of the circular ...

question_answer

Q: A 0.400-kg particle has a speed of 1.50 m/s at point A and kinetic energy of 7.60 J at point B. (a) ...

A: Let the mass of the particle be denoted as mKinetic energy at point A and B be denoted as (K.E)A  an...

question_answer

Q: 5)A bucket filled with water has a mass of 23.0 kg and is attached to a rope that is wound around a ...

A: The free body diagram is

question_answer

Q: 5. A steam catapult launches a jet aircraft from the aircraft car￾rier John C. Stennis, giving it a ...

A: Sub part (a)Kinematics equation,

question_answer

Q: A 60.0-kg person rides in an elevator while standing on a scale. The scale reads 400 N. What is the ...

A: Given,

question_answer

Q: Suppose that R = 4 kΩ and C = 5 μF. What is the time constant for the discharge of the capacitors in...

A: Given,

question_answer

Q: An asteroid can be modeled as a right circular cylinder of radius 150 m and length 500 m with unifor...

A: Given,