Integration

Integration

1. A bucket has an empty weight of 23N . It is filled with sand of weight 80N and attached to a rope of weight 5.1N/m . Then it is lifted from the floor at a constant rate to a height 32 meters above the floor. While in flight, the bucket leaks sand grains at a constant rate, and by the time it reaches the top no sand is left in the bucket. Find the work done by lifting the sand alone.

2. The electric current (in mA) in a computer circuit as a function of time is i=0.3−0.2t. What total charge passes a point in the circuit in 0.050 s?

3. The voltage across an 8.50 nF capacitor in an FM receiver circuit is initially zero. Find the voltage after 2.00 μs if a current i=0.042t (in mA) charges the capacitor.

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