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A cart on frictionless rollers approaches a smooth, curved slope h = 0.45 meters high. What minimum speed v is required for the cart to reach the top of the slope?

A Cart On Frictionless Rollers Approaches A Smooth Curved Slope H 045 Meters High What Minimum Speed V Is Required For The Cart To Reach The Top Of The Slope class=

Sagot :

Given data

*The given height is h = 0.45 m

*The value of the acceleration due to gravity is g = 9.8 m/s^2

The formula for the minimum speed (v) required for the cart to reach the top of the slope is given by the conservation of energy as

[tex]\begin{gathered} U_k=U_p \\ \frac{1}{2}mv^2=mgh \\ v=\sqrt[]{2gh} \end{gathered}[/tex]

Substitute the known values in the above expression as

[tex]\begin{gathered} v=\sqrt[]{2\times9.8\times0.45} \\ =2.96\text{ m/s} \end{gathered}[/tex]

Hence, the minimum speed (v) required for the cart to reach the top of the slope is v = 2.96 m/s

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