A spring with a spring constant of 500N/m is used to propel a .45kg mass up an i

Question

A spring with a spring constant of 500N/m is used to propel a .45kg mass up an inclined plane. The spring is compressed 30 cm from its equilibrium position and launches the mass from rest across a horizontal surface and onto the plane. The plane has a length l=3m and is inclined at 29degrees. Both the plane and the horizontal surface have a coefficient of kinetic friction with the mass of .35. When the spring is compressed, the mass is at distance d=1.4m from the bottom of the plane.

A. What is the speed of the mass as it reaches the bottom of the plane?

B. What is the speed of the mass as it reaches the top of the plane?

C. What is the total work done by friction from the beginning to the end of the mass's motion?

Explanation / Answer

Initial PE of the spring = 0.5 k x^2 [x = 0.30 m.]

0.5 k x^2 = 0.5 m u^2 + work against frictional force

0.5 k x^2 = 0.5 m u^2 + mu m g * s

(k/m) x^2 = u^2 + 2 mu g*s

u^2 = (k/m) x^2 - 2 mu g * s

u^2 = (500 / 0.45) 0.30^2 - 2 * 0.35 * 9.8 * 1.4

u = 9.51 m/s

-------------------------------------------------------

Frictional force up the plane = -mu m g cos theta

Deceleration = -mu g cos theta + g sin theta

Distance moved along the plane = l

v^2 = u^2 - 2 as

v^2 = u^2 - 2(mu g cos theta + g sin theta ) l

v^2 = 9.51^2 - 2 * 9.8 ( 0.35 cos 29 + sin 29) * 3

v = 6.63 m/s

--------------------------------------------------------

Work done by friction from the beginning to the end of the mass

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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