Question

3. The net force acting on a 2.0-kg particle as it is pushed along a horizontal floor (considered along the positive x-axis) varies as shown on the given chart. The velocity of the object at x = 1 m is 3.0 m/s. (a) Find the total work done on the crate along F (N) the floor from x-0 to x-3 m. (b) Estimate the final velocity of the particle at x 3 m. 0 r (m) [(a) -2J; (b) 1.73 m/s]

Answer 1

here,

mass , m = 2 kg

at x1 = 1 m and v1 = 3 m/s

a)

the total work done on the crate along the floor , Wt = area under the curve

Wt = (4 * 1) + ( -4) * ( 2 - 1 ) + 0.5 * ( 3 - 2) * (-4)

Wt = - 2 J

b)

let the final velocity at x = 3 m be v

using work energy theorm

work done between x=1 m to x=3 m = kinetic energy gained

( -4) * ( 2 - 1 ) + 0.5 * ( 3 - 2) * (-4) = 0.5 * 2 * (v^2 - 3^2)

solving for v

v = 1.73 m/s

the speed at x=3 m is 1.73 m/s