Picture a cart with an inclined top surface see diagram- Assume -30-0o-At what rate must the cart accelerate to the slide to keep a frictionless block on it from sliding off-

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Standard XII

Physics

Pure Rolling

Picture a car...

Question

Picture a cart with an inclined top surface (see diagram). Assume $θ = {30.0}^{o}$ .
At what rate must the cart accelerate to the slide to keep a frictionless block on it from sliding off?

4.9 m / s^{2}

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5.7 m / s^{2}

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8.5 m / s^{2}

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17.0 m / s^{2}

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Solution

The correct option is C $5.7 m / s^{2}$
The component of gravitational force on the block along the inclined plane must be balanced by the pseudo inertial force's component along the incline acting the block.
Thus $m g s i n θ = m a c o s θ$
$⟹ a = g t a n θ$
$= 5.7 m / s^{2}$

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Picture a cart with an inclined top surface (see diagram). Assume θ=30.0o.At what rate must the cart accelerate to the slide to keep a frictionless block on it from sliding off?

The correct option is C 5.7m/s2The component of gravitational force on the block along the inclined plane must be balanced by the pseudo inertial force's component along the incline acting the block.Thus mgsinθ=macosθ⟹a=gtanθ=5.7m/s2

Picture a cart with an inclined top surface (see diagram). Assume $θ = {30.0}^{o}$ .
At what rate must the cart accelerate to the slide to keep a frictionless block on it from sliding off?

The correct option is C $5.7 m / s^{2}$
The component of gravitational force on the block along the inclined plane must be balanced by the pseudo inertial force's component along the incline acting the block.
Thus $m g s i n θ = m a c o s θ$
$⟹ a = g t a n θ$
$= 5.7 m / s^{2}$