A wooden block of mass M resting on a rough horizontal surface is pulled with a force F at an angle with the horizontal. If μ is the coefficient of kinetic friction between the block and the surface, then acceleration of the block is

Question

A wooden block of mass M resting on a rough horizontal surface is pulled with a force F at an angle with the horizontal. If μ is the coefficient of kinetic friction between the block and the surface, then acceleration of the block is (A)  (F/M)( cos φ +μ sin φ )-μ g  (B)  F sin (φ /M)  (C)  μ F cos φ  (D)  μ Fsin φ

Tardigrade Admin · Accepted Answer

R=Mg-F sin φ f=μ R=μ =(Mg-F sin φ ) F= cos φ -f=Ma a=(1/M)[F cos φ -f] a=(1/M)[F cos φ -μ (Mg-F sin φ )] =(F/M)cosφ -μ g+(μ F/M) sin φ =(F/M)[ cos φ +μ sin φ ]-μ g

Q. A wooden block of mass $M$ resting on a rough horizontal surface is pulled with a force $F$ at an angle with the horizontal. If $μ$ is the coefficient of kinetic friction between the block and the surface, then acceleration of the block is

$\frac{F}{M} (cos ϕ + μ sin ϕ) - μg$

$F sin \frac{ϕ}{M}$

$μ F cos ϕ$

$μ F s in ϕ$

$R = M g - F sin ϕ$ $f = μ R = μ = (M g - F sin ϕ)$
$F = cos ϕ - f = M a$ $a = \frac{1}{M} [F cos ϕ - f]$ $a = \frac{1}{M} [F cos ϕ - μ (M g - F sin ϕ)]$
$= \frac{F}{M} cos ϕ - μg + \frac{μ F}{M} sin ϕ$
$= \frac{F}{M} [cos ϕ + μ sin ϕ] - μg$

Q. A wooden block of mass M resting on a rough horizontal surface is pulled with a force F at an angle with the horizontal. If μ is the coefficient of kinetic friction between the block and the surface, then acceleration of the block is

MF​(cosϕ+μsinϕ)−μg

FsinMϕ​

μFcosϕ

μFsinϕ