A block of mass 2.0 kg kept at rest on an inclined place of inclination $37^{\circ}$ is pulled up the plane by applying a constant force of 20 N parallel to the incline. The force acts for on second. (a) Show that the work done by the applied force does not exceed 40 J. (b) Find the work done by the force of gravity in that one second if the work done by the applied force is 40 J.(c) Find the kinetic energy of the block at the instant the force ceases to act. Take g= $10 m / s^{2}$ .

Open in App

Solution

$(a) m = 2 k g, θ = 37^{\circ}, F = 20 N$

From the free body diagram,

$F = (2 g s i n θ) + m a$

$\Rightarrow a = \frac{20 - 20 s i n θ}{2} = 4 m / s e c^{2}$

$s = u t + \frac{1}{2} a t^{2} = 2 m$

$(u = 0, t = 1 s, a = 1.66)$

So, work done, $W = F S = 20 \times 2 = 40 J$

$(b) I f W = 40 J$

$S = \frac{W}{F} = \frac{40}{20} = 2 m$

$h = 2 s i n 37^{\circ} = 1.2 m$

So,work done $W = - m g h$

$(c) v = u + a t$

$= 4 \times 1 = 4 m . s e c$

So, $K . E, = \frac{1}{2} m v^{2}$

$= \frac{1}{2} \times 2 \times 16 = 16 J$

Suggest Corrections

Similar questions

A block of mass 2.0 kg is pushed down an inclined place of inclination $37^{\circ}$ with a force of 20 N acting parallel to the incline. It is found that the block moves on the incline with an acceleration of 10 $m / s^{2}$ . If the block started from rest, find the work done (a) by the applied force in the first second, (b) by the weight of the block in the first second and (c) by the frictional force acting on the block in the first second. Take g= $10 m / s^{2}$ .

A block of mass 2.0 kg is pushed down an inclined plane of inclination $37^{\circ}$ with a force of 20 N acting parallel to the incline. It is found that the block moves on the incline with an acceleration of $10 m / s^{2}$ . If the block started from rest, find the work done $(W_{F})$ by the applied force, work done $(W_{g})$ by the weight of the block and work done $(W_{f})$ by the frictional force acting on the block in the 1st second. Take $g = 10 m / s^{2}$ .

Q. A block of mass

2.0 k g

is pushed down an inclined plane of inclination

37^{o}

with a force of

20 N

acting parallel to the incline. It is found that the block moves on the incline with an acceleration of

10 m / s^{2}

. If the block started from rest, find the work done (a) by the applied force in the first second

A block of ice mass 2.0 kg is pushed down an inclined plane of inclination $37^{\circ}$ with a force of 20 N acting parallel to the incline. It is found that the block moves on the incline with an acceleration of $10 m / s^{2}$ If the block started from rest, find the work done $(W_{f})$ by the applied force in the first second, $W_{g}$ by the weight of the block in the first second and $(W_{f})$ by the frictional force acting on the block in the first second. Take $g = 10 m / s^{2}$

Q. A block of mass 2 kg is pulled upwards by a force

F = 40 N

as shown in figure. Block is displaced by

2 m

. Find work done by the applied force and also due to the force of gravity on the block. (Take

g = 10 m / s^{2}

)

Join BYJU'S Learning Program

(a)m=2kg,θ=37∘,F=20N From the free body diagram, F=(2g sin θ)+ma ⇒a=20−20sin θ2=4m/sec2 s=ut+12at2=2m (u=0,t=1s,a=1.66) So, work done,W=FS=20×2=40J (b)IfW=40J S=WF=4020=2m h=2sin37∘=1.2m So,work done W=−mgh (c)v=u+at =4×1=4m.sec So, K.E,=12mv2 =12×2×16=16J