Question

6.
A block of mass m is placed over the rough
horizontal surface of a truck of friction co-efficient
u = 0.5 as shown -
L = 2m
m
If the truck suddenly starts accelerating towards
right with acceleration of 6 m/s2, find the time after
which the block falls off the truck ? (g = 10 m/s2)
(1) 1 sec
(2) 2 sec
(3) 0.5 sec
(4) block will never fall​

Answer 1

Answer: after 2 seconds

Explanation:

If acceleration of the truck a0≤μg , the truck and the block move together.

(i) a0=2m/s2, acceleration of the block =a0

f=2a0=2×2=4N

(ii) a0=4m/s2

f=2a0=2×4=8N

(iii) a0=6m/s2>μg , the block will move in the backward direction with respect to the truck

N0=20N

fmax=μN=0.5×20=10N

(b) a0=8m/s2>μg , the block will move in the backward direction w.r.t. the truck

10=2a⇒a=5m/s2

Acceleration of the block w.r.t. the truck is in the backward direction.

a1=a0−a=8−5=3m/s2

s=12a1t2⇒6=12×3×t2⇒t=2s

The block will fall off the truck in 2s. Distance travelled by the truck in this time.

s'=12a0t2=12×8×22=16m