A block of mass 1kg is pushed up a surface inclined to horizontal at an angle of $30^{\circ}$ by a force of 10N parallel to the inclined surface $[f i g u r e]$ . The coefficient of friction between block and the incline is 0.1. If the block is pushed up by 10 m along the incline, calculate
(a) work done against gravity
(b) work done against force of friction
(c) increase in potential energy
(d) increase in kinetic energy
(e) work done by applied force.

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In figure, f is the force of friction acting down the incline.
Here, $m = 1 k g, θ = 30^{\circ}$
$F = 10 N, μ = 0.1, s = 10 m$ . (a) Work done against gravity
$W_{g} = m g sin θ \times s = 1 \times 10 {sin 30}^{\circ} \times 10 = \frac{100}{2} = 50 J$
(b) Work done against friction
$W_{f} = f \times s = μ R \times s = μ m g cos θ \times s$
$= 0.1 \times 1 \times 10 {cos 30}^{\circ} \times 10 = 10 \times 0.866 = 8.66 J$
(c) Increase in P.E. $= m g h = m g (s sin θ) = 1 \times 10 \times 10 {sin 30}^{\circ} = 50 J$
(d) Increase in K.E. $= Δ K = ?$
Acceleration of block up the incline
$a = \frac{F - (m g sin θ + μ m g cos θ)}{m} = \frac{10 - (1 \times 10 \times \frac{1}{2} + 0.1 \times 10 \times 0.866)}{1} = 4.13 m / s^{2}$
From $υ^{2} - u^{2} = 2 a s$
$Δ K = \frac{1}{2} m (υ^{2} - u^{2}) = \frac{1}{2} m \times 2 a s = m a s = 1 \times 4.13 \times 10 = 41.3 J$

Updated on:21/07/2023

Class 11 PHYSICS WORK, ENERGY AND POWER

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A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of $30^{\circ}$ by a force of 10 N parallel to the inclined surface as shown in the figure.
The coefficient of friction between block and the incline is 0.1. If the block is pushed up by 10 m along the incline, then the work against gravity is (Take $g = 10 m s^{- 2}$ )

A10 J
B50 J
C100 J
D150 J
Question 1 - Select One
In the arrangement shown in figure coefficient of friction between $5 k g$ block and incline plane is $μ = 0.5$ . Friction force acting on the $5 k g$ block is

A $20 N$
B $15 N$
C $10 N$
D $5 N$
Question 1 - Select One
A block of mass $m = 4 k g$ is placed oner a rough inclined plane as shown in figure. The coefficient of friction between the block and the plane is $μ = 0.5$ . A force $F = 10 N$ is applied on the block at an angle of $30^{\circ}$ .

Astatic in nature in the direction up the plane and have the value $30.2 N$
Bstatic in nature in the direction down the plane and have the value $30.2 N$
Ckinetic in nature in the direction up the plane and have the value $30.2 N$
DNone of these
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A block of mass $2 k g$ is pushed down an inclined plane of angle $37^{\circ}$ above horizontal with a force parallel to inclined plane. The coefficient of friction is (3)/(4). The block moves $10 m$ in $2$ seconds starting form rest. The magnitude of the force is
A $10 N$
B $12 N$
C $24 N$
D $34 N$
Question 1 - Select One
A block of mass 10kg is pushed up on a smooth incline plane of inclination $30^{\circ}$ , so that it has acceleration $2 m / s^{2}$ . The applied force is
A50 N
B60 N
C70 N
D80 N
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A block of mass m is lying on an inclined plane. The coefficient of friction between the plane and the block is $μ$ . The force $(F_{1})$ required to move the block up the inclined plane will be:-
A $m g sin θ + μ m g cos θ$
B $m g cos θ - μ m g sin θ$
C $m g sin θ - μ m g cos θ$
D $m g cos θ + μ m g sin θ$

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