A block of mass 1.4 kg is attached to a horizontal spring that has a force const

Question

A block of mass 1.4 kg is attached to a horizontal spring that has a force constant 900 N/m as shown in the figure below. The spring is compressed 2.0 cm and is then released from rest.

(a) A constant friction force of 3.6 N retards the block's motion from the moment it is released. Using an energy approach, find the position x of the block at which its speed is a maximum.


(b) Explore the effect of an increased friction force of 13.5 N. At what position of the block does its maximum speed occur in this situation?

Explanation / Answer

Initial Energy
E = 1/2 k d²

At maximum speed
E' = 1/2 k x² + 1/2 m v²

W = E
F (d - x) = 1/2 k d² - (1/2 k x² + 1/2 m v²)
v² = k d² / m - k x² / m - 2F (d - x) / m

differentiate and vmax if dv/dx = 0
2v dv/dx = - 2 k x / m + 2F / m = 0
F = k x
x = F / k

a)
x = 3.6 / 900 = 4x10-3 m = 0.4 cm

b)
x = 13.5 / 900 = 0.015 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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