Question

Question 5: A 2 kg package is pushed along a horizontal su the horizontal surface, the package travels a distance of 3.0 m along a ramp: horizontal At the top of the ramp is a loading dock Packages reaching the end assume al surfaces encounter a spring with a Spring constant of 1400 NmFor this problem frictionless sa kinetic energy of 40 J. After 9 a ramp, inclined at 30° to the ges reaching the end of the loading dock A Does the package make it to the spring at the end of the loading dock? Support your answer mathematically PE = mgh JE - 403 7.918.15 - PE = 29.4J

A. Does the package make it to the spring at the end of the loading dock?
B. If it does, what is the Maximum compression of the spring?

Answer 1

here,

mass of package , m = 2 kg

initial kinetic energy ,KE0 = 40 J

s = 3 m

theta = 30 degree

a)

the minimum mechanical energy required , ME = m * g * s * sin(theta)

ME = 2 * 9.81 * 3 * sin(30) J = 29.43 J

as ME < KE

the block will reach at the end of loading rock

b)

let the compression in the spring be x

using conservation of mechanical energy

KE - ME = 0.5 * K * x^2

40 - 29.43 = 0.5 * 1400 * x^2

solving for x

x = 0.12 m

the compression in the spring is 0.12 m