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Question

# A uniform sphere of mass 2.50 kg and radius 15.0 cm is released from rest at the top of an incline that is 5.25 m long and makes an angle of $35^{\circ}$ with the horizontal. Assuming it rolls without slipping, (a) determine its total kinetic energy at the bottom of the incline. (b) Determine its rotational kinetic energy at the bottom of the incline. (c) What type of friction, static or kinetic, is acting on the surface of the sphere? Explain. (d) Determine the force of friction in part (d).

Solution

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Given:

• Mass of the sphere: $m = 2.5 \mathrm{~kg}$;
• Radius of the sphere: $r = 15 \mathrm{~cm}$;
• Initial velocity of the bowling ball: $v_0 = 0 \mathrm{\frac{~m}{~s}}$;
• Angle of inclination: $\theta = 35°$;
• Length of an incline: $s = 5.25 \mathrm{~m}$;

Required: a) The total kinetic energy $K$ of the sphere at the bottom of the incline; b) The rotational kinetic energy $K_r$ of the sphere at the bottom of the incline; c) Type of the friction; d) Force of friction $f$;

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