Question #1c2bd

1 Answer
Matt ยท Stefan V.
Apr 27, 2016

"4.4 J"

Explanation:

Before the force is applied we know

"momentum" = "mass" times "velocity" = "10 kg m/s"

Since mass in the above is "5 kg", then velocity = "2 ms"^(-1)

We can now work out kinetic energy, KE:

KE=1/2mv^2=1/2*5*2^2="10 J"

The force of "0.2 N" is now applied in the direction of travel for 10 seconds. Newton's second law can be expressed as "the force applied equals the rate of change of momentum". OR

F=(mv-"mu")/t=m * (v-u)/t

Where v is the final velocity after applying force, and u is the initial velocity ( "2 ms"^(-1) in this case from above)

So

0.2 = 5 * ((v-2))/10

rearranging helps us find v

2 = 5 * (v-2)

2/5 = v-2

v = 12/5" ms"^(-1)

Hence final kinetic energy, KE, is

KE = 1/2mv^2 = 1/2 * 5 * (12/5)^2 = "14.4 J"

So the overall change in KE is

Delta_"KE" = 14.4 - 10 = "4.4 J"

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