When a 4.00 kg object is hung vertically on a certain light spring that obeys Hooke’s Law, the spring stretches 2.50 cm. If the 4.00 kg object is removed, (a) how far will the spring stretch if a 1.50 kg block is hung on it, and (b) how much work must an external agent do to stretch the same spring 4.00 cm from its unstretched position?
1. When a 4.00 kg object is hung vertically on a certain light spring that obeys Hooke’s Law, the spring stretches 2.50 cm. If the 4.00 kg object is removed, (a) how far will the spring stretch if a 1.50 kg block is hung on it, and (b) how much work must an external agent do to stretch the
same spring 4.00 cm from its unstretched position?
2. A 100-g bullet is fired from a rifle having a barrel 0.600m long. Assuming the origin is placed where the bullet begins to move, the force exerted by the expanding gas on the bullet is (15,000 + 10.000x − 25,000x2)N, where x is in meters. (a) Determine the work done by the gas
on the bullet as the bullet travels the length of the barrel. (b) If the barrel is 1.000m long, how much work is done, and how does this value compare to the work calculated in part (a)? What is the percent increase or decrease?
3. A small particle of mass m is pulled o the top of a frictionless half-cylinder (of radius R) by a cord that passes over the top of the cylinder. (a) If the particle moves at a constant speed, show that F = mg cos θ. (Note: If the particle moves at constant speed, the component of its acceleration tangent to the cylinder must be zero at all times.) (b) By directly integrating W =∫ F⃗ ∙ dr⃗, find the work done in moving the particle at constant speed from the bottom to the top of the half cylinder.
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