A 1.50 kg mass slides to the right on a surface having a coefficient of kinetic

Question

A 1.50 kg mass slides to the right on a surface having a coefficient of kinetic friction 0.250. The object has a speed of vi = 2.70 m/s when it makes contact with a light spring that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d. The object is then forced toward the left by the spring and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring.

(a) Find the distance of compression d.


(b) Find the speed v at the unstretched position when the object is moving to the left.


(c) Find the distance D where the object comes to rest.

Please state answer with units, as well as making sure that the answer is correct. double check work

Explanation / Answer

a)

here conserving energy between 1 and 2

E1 + W12 = 0.5 * m * v^2 - u * m * g * d = E2 = 0.5 * k * d^2

0 = k*d^2 / m + 2 * u * g * d - v^2

d = (-2 * u * g + sqrt( (2 * u *g)^2 - (4 * k/m) * -v^2 )) / (2*k/m)

d = ( -2 * 0.25 * 9.8 + sqrt( ( 2 * 0.25 * 9.8)^2 + ( 4 * 50 / 1.5) * 2.7^2 )) / ( 2 * 50 / 1.5)

d = 0.3998 m

b)

conserving energy between 2 and 3

E2 + W23 = 0.5 * k * d^2 - u * m * g * d = E2 = 0.5 * m * v^2

v = sqrt( (k * d^2 / m ) - 2 * u * g * d )

v = sqrt( ( (50 * 0.3998^2 / 1.5) - 2 * 0.25 * 9.8 * 0.3998 )

v = 1.835 m/s

c)

conserving energy 3 and 4

E3 + W34 = 0.5 * m * v^2 - u*m*g*D = E4 = 0 J

D = v^2 / (2*u*g)

D = 1.835^2 / ( 2 * 0.25 * 9.8)

D = 0.687 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.