Question #993d6

1 Answer
Apr 8, 2017

15 is 3
16 is 4
17 is 4
18 is 4

Explanation:

Each in turn

Qu 15 . If we use the formula v2=u2+2as
Then since v, final velocity, is nil we can simplify to:
u2=2as

Using Newton's 2nd law ,F=ma, we can substitute for a
u2=2(Fm)s
The negative values indicates that the force is decelerating and acts in the opposite direction to u.

Since we want to consider distance, s, we can rearrange:
s=u2m2F

For the 4kg mass travelling at 2m/s
s=2242F=162F

For the 1kg mass travelling at 4m/s
s=4212F=162F

Since F is the same, we can see that they take the same distance to stop.

We could also have used energy arguments that kinetic energy must equal work done to bring to a stop:
Hence 12mv2=F.s
Since the KE of the objects is the same, the distance moved by the braking force would be the same

Qu16
We need to consider work done against gravity (since there is no friction to do work against). The distance moved in the vertical direction is given by 0.5sin300=0.25m

The weight is 10N (1kg×10ms2)
So work done against gravity is:
WD=F.s=10×0.25=2.5J

Qu 17 Both people are at the same height so have the same GPE (U) since this is a function of the height above the ground

Qu18

The rollercoaster has GPE and Kinetic energy

=mgh+12mv2
=(80×10×200)+(1.2×80×202)
=176,000J=17.6×104J