Question

1.

At a mail sorting facility, a spring is used to launch packages up an inclined plane 3.0 m long inclined at 18°. The coefficient of friction between the package and the plane is 0.25. Packages under 1.0 kg make it to the top of the incline and qualify for the lowest postage rate. Heavier packages must be removed from the ramp, and are subject to greater postage

a . Calculate the work done by all forces on a 1.0 kg package which just makes it to the top of the ramp.

b. Calculate the amount the spring was compressed before releasing the package if the spring constant is 3.00 kN/m.

c.How high up the ramp would a 2.0 kg package travel before stopping

2.A proton (m = 1.00 amu) travelling 1.0 km/s collides elastically with a stationary carbon atom (m = 12.0 amu). If the proton rebounds

in a direction that is 90° from its original direction, then what is the speed of the proton, the speed of the carbon, and the direction of the carbon after the collision (direction relative to the original direction of the proton)?

Answer 1

Given,

L = 3 m ; theta = 18 deg ; u = 0.25 ;

a)Work done by gravity

Wg = m g h

Wg = m g L sin(theta)

Wg = 1 x 9.8 x 3 x sin18 = 9.1 J

Wg = 9.1 J

by friction

Wf = u m g cos(theta) L

Wf = 0.25 x 1 x 9.8 x cos18 x 3 = 6.9 J

Wf = 6.9 J

work done by the spring force

Ws = Wg + Wf = 9.1 + 6.9 = 16 J

Ws = 16 J

Work done by the normal force = 0 J

b)Wspring = 1/2 k x^2

1/2 k x^2 = 16

x = sqrt (2 x 16/3000) = 0.103 m

Hence. x = 0.103 m

c)Ws = PE + Wf

1/2 k x^2 = m g L sin(theta) + u m g L cos(theta)

L (2 x 9.8 x sin18 + 0.25 x 2 x 9.8 x cos18) = 0.5 x 3000 x 0.103^2

L = 16/10.72 = 1.49 m = 1.5 m

Hence, l = 1.5 m

(kindly put other question separately for detailed solution , we do one at a time.)