Question

Question #1c2bd

Answer 1

`"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"`