a. The potential energy (PE) of an object can be calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the ground.

In this case, the mass (m) of the sack of grain is 98 kg, the acceleration due to gravity (g) is approximately 9.8 m/s², and the height (h) is 15 m.

So, the potential energy of the sack of grain is PE = 98 kg * 9.8 m/s² * 15 m = 14,364 Joules.

b. The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. Therefore, the potential energy the sack had at the top of the elevator is converted into kinetic energy as it falls. So, the kinetic energy (KE) of the sack just before it hits the ground is equal to the potential energy it had at the top of the elevator, which is 14,364 Joules.

c. The kinetic energy of an object can also be calculated using the formula KE = 0.5 * m * v², where m is the mass of the object and v is its velocity. We can rearrange this formula to solve for v: v = sqrt((2 * KE) / m).

Substituting the known values, we get v = sqrt((2 * 14,364 Joules) / 98 kg) = 17.1 m/s.

So, the impact speed of the sack of grain is 17.1 m/s.

Question

a. The potential energy (PE) of an object can be calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the ground.

In this case, the mass (m) of the sack of grain is 98 kg, the acceleration due to gravity (g) is approximately 9.8 m/s², and the height (h) is 15 m.

So, the potential energy of the sack of grain is PE = 98 kg * 9.8 m/s² * 15 m = 14,364 Joules.

b. The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. Therefore, the potential energy the sack had at the top of the elevator is converted into kinetic energy as it falls. So, the kinetic energy (KE) of the sack just before it hits the ground is equal to the potential energy it had at the top of the elevator, which is 14,364 Joules.

c. The kinetic energy of an object can also be calculated using the formula KE = 0.5 * m * v², where m is the mass of the object and v is its velocity. We can rearrange this formula to solve for v: v = sqrt((2 * KE) / m).

Substituting the known values, we get v = sqrt((2 * 14,364 Joules) / 98 kg) = 17.1 m/s.

So, the impact speed of the sack of grain is 17.1 m/s.

Knowee AI · Accepted Answer

a. The potential energy (PE) of an object can be calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the ground.

In this case, the mass (m) of the sack of grain is 98 kg, the acceleration due to gravity (g) is approximately 9.8 m/s², and the height (h) is 15 m.

So, the potential energy of the sack of grain is PE = 98 kg * 9.8 m/s² * 15 m = 14,364 Joules.

b. The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. Therefore, the potential energy the sack had at the top of the elevator is converted into kinetic energy as it falls. So, the kinetic energy (KE) of the sack just before it hits the ground is equal to the potential energy it had at the top of the elevator, which is 14,364 Joules.

c. The kinetic energy of an object can also be calculated using the formula KE = 0.5 * m * v², where m is the mass of the object and v is its velocity. We can rearrange this formula to solve for v: v = sqrt((2 * KE) / m).

Substituting the known values, we get v = sqrt((2 * 14,364 Joules) / 98 kg) = 17.1 m/s.

So, the impact speed of the sack of grain is 17.1 m/s.

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