Question

At the moment t=0 the force F=at is applied to a small
body of mass m resting on a smooth horizontal plane
(a is constant).
The permanent direction of this force forms an angle
a with the horizontal (as shown in the figure). Find :
F
c.
m
(a) the velocity of the body at the moment of its
breaking off the plane;
(b) the distance traversed by the body up to this
moment.

Answer 1

Answer:

→ let small body of mass m and indicate x-axis along

the horizontal plane and y-axis, perpendicular to it.

Let block breaks of the plate at t = to i.e. N- 0.

So, N=mg−ato sinα=0

or t

0

=

asinα

mg

...(1)

From in =max, for the body under integration

m

dt

dV

x

=atcosα ; Integrating within the limit for v/t

m∫

0

v

dvx=acosα∫

0

tdt (using eq (1))

So, v=

dt

ds

=

2m

acosα

t

2

...(2)

Integrating ,Eq

n

(2) for s(t)

s=

2m

acosα

3

t

3

...(3)

using the values of t=t

0

from Eq (1) into Eqs (2) and (3)

v=

2asinα

mg

2

cosα

and s=

6a

2

sin

3

α

m

2

g

2

cosα