Question

Suddenly a worker picks up the bag of gravel. Use energy conservation to find the speed of the bucket after it has descended 1.80 m from rest. (You can check your answer by solving this problem using Newton's laws.)

Answer 1

To find the speed of the bucket after it has descended 1.80 m from rest, we can use the principle of energy conservation. The speed of the bucket is 5.94 m/s.

Step-by-step explanation:

To find the speed of the bucket after it has descended 1.80 m from rest, we can use the principle of energy conservation. The initial potential energy of the bucket is mg(h1), where m is the mass of the bucket, g is the acceleration due to gravity, and h1 is the initial height of the bucket. The final kinetic energy of the bucket is (1/2)mv^2, where v is the final velocity of the bucket. Since no energy is lost due to friction or air resistance, we can equate the initial potential energy to the final kinetic energy.

mg(h1) = (1/2)mv^2.

Simplifying the equation, we can cancel out the mass of the bucket:

gh1 = (1/2)v^2.

Now, we can solve for v:

v = sqrt(2gh1).

Substituting the given values, we have:

v = sqrt(2 * 9.8 * 1.80)

= sqrt(35.28)

= 5.94 m/s.