You are here
A 10.0 kg block is moving on horizontal floor with negligible friction. As shown in Fig. 7.37, a variable force is applied on the block in its direction of motion from its position at 0 m till 4 m. If the block had a kinetic energy of 180 J when it was at 0 m, find the block's speed (i) at 0 m, and (ii) at 4 m. Does the block have negative acceleration in any portion of its motion?
Show Answer
(i) At 0 m:
1
2
mv
2
= 180
⇒ v
2
=
360
10
= 36
⇒ v
= 6
m s
-1
.
Work by the force = area under Fig. 7.37
=
1
2
(1)(50) + (2)(50) +
1
2
(1)(50)
= 25 + 100 + 25
= 150
J
.
(ii) KE at 4 m
= 180 + 150
= 330
J
⇒ v
2
=
660
10
= 66
⇒ v
=
66
≈ 8.1
m s
-1
.
The applied force stays in the direction of motion (always positive) throughout, so the block keeps speeding up — it has no negative acceleration in any portion.
= 150 J
= 1 2 (10)v 2
⇒ v
= 6 m s -1
= 66 ≈ 8.1 m s -1
