As a rock of mass 4 kg drops from the edge of a...

As a rock of mass 4 kg drops from the edge of a 40-meter-high cliff, it experiences air resistance, whose average strength during the descent is 20 N. At what speed will the rock hit the ground? (A) 10 $\mathrm{m} / \mathrm{s}$ (B) 12 $\mathrm{m} / \mathrm{s}$ (C) 16 $\mathrm{m} / \mathrm{s}$ (D) 20 $\mathrm{m} / \mathrm{s}$

As a rock of mass 4 kg drops from the edge of a 40-meter-high cliff, it experiences air resistance, whose average strength during the descent is 20 N. At what speed will the rock hit the ground?
(A) 10 $\mathrm{m} / \mathrm{s}$
(B) 12 $\mathrm{m} / \mathrm{s}$
(C) 16 $\mathrm{m} / \mathrm{s}$
(D) 20 $\mathrm{m} / \mathrm{s}$

Key Concepts

Gravitational Potential Energy

Gravitational potential energy represents the energy held by an object because of its position in a gravitational field. It is calculated as the product of mass, gravitational acceleration, and height, and serves as the initial energy available to be converted into other forms during the object's descent.

Work Done by Non-Conservative Forces

When forces like air resistance act on a moving object, they perform work that is not stored as mechanical energy but rather dissipated, often as thermal energy. This concept modifies the traditional conservation of energy by accounting for energy loss from the system, which directly affects the final kinetic energy and resulting velocity.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. In problems involving falling objects, the gravitational potential energy is converted into kinetic energy plus any energy lost due to factors like air resistance, determining the speed at impact.

Conservation of Energy (with energy losses)

The principle of energy conservation states that the total energy in a closed system remains constant. In scenarios with non-conservative forces such as air resistance, the energy transformation involves a reduction in the energy available for kinetic energy, as some energy is lost to work done against the resistive force, influencing the final speed of the object.

Transcript

00:03 Hi, let's look at what conditions we've known from the question.

00:07 The mass of the rock is 4 kilogram, and the height of the cliff is 40 meters.

00:14 And the average air resistance, which i would use small f to represent, is 20 neutens.

00:22 And the question is to find the final speed of the rock when it hit the ground.

00:29 And we should also notice that there is a hidden condition that the initial speed of the rock is zero meter per second because it says that it drops from the cliff.

00:46 Okay.

00:47 So in order to find out the final spate, we could apply the work energy theory, which is the total work acted.

00:59 Down on an object is equal to the change in the kinetic energy.

01:07 And in order to find out the total work, let's do a free body diagram on this rock.

01:14 I'll draw a green rock and i'll draw the gravity, oops, i draw the gravity of this rock, which is pointing downward.

01:24 And the gravity equals to the mass of this rock times the gravity constant, which is 10 newton per kilogram.

01:35 So we can calculate the gravity by timing the 4 kilogram with the gravity constant 10 newton per kilogram, which is 40 neutrons like this.

01:50 And the other force acting on this object is the friction, the air resistance pointing upward, and the magnitude of the friction is 20 neutrons.

02:08 That's all the forces acting on this rock.

02:12 And we can see that the net force acting on this rock is the.

02:20 Gravity minus the air resistance, which is 40 minus 20 and equals 20 neutrons.

02:30 And the direction of the net force is pointing downward.

02:41 So these two diagrams are basically the same thing...

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