Both kinetic and gravitational potential energy can become zero at infinite distance from the Earth.
Consider an object of mass m projected from the surface of the Earth with a velocity v.
The total energy of the body on the surface of the Earth is the sum of its kinetic energy and gravitational potential energy .
here, M is the mass of the Earth, R is the radius of Earth and G is the universal gravitational constant.
The gravitational potential energy of the object is negative since it is in an attractive field, which is the gravitational field of the Earth.
The energy of the object on the surface of the earth is given by,
As the object rises upwards, it experiences deceleration due to the gravitational force of the Earth. Its velocity decreases and hence its kinetic energy decreases.
The decrease in kinetic energy is manifested as an equal increase in potential energy. The potential energy becomes less and less negative as more and more kinetic energy is converted into potential energy.
At a height h from the surface of the Earth, the energy of the object is given by,
The velocity is less than v.
When h =∞, the gravitational potential energy increases from a negative value to zero.
If the velocity of projection is adjusted in such a manner that the velocity decreases to zero at infinite distance from the earth, the object's kinetic energy also becomes equal to zero.
Thus, it is possible for both kinetic and potential energies to be zero at infinite distance from the Earth. In this case, kinetic energy decreases from a positive value to zero and the gravitational potential energy increases from a negative value to zero.
Answer:
The torque about the origin is 5.0 N.
Explanation:
To calculate the torque (τ) about the origin, you need to know both the force (F) and the position vector (r) from the origin to the point where the force is applied. The formula for torque is:
τ = r × F
Where:
- τ is the torque vector.
- r is the position vector.
- F is the force vector.
In this case, you're given the force vector F = 5.0 y N, where "y" represents the unit vector in the y-direction.
Assuming that the particle is located at a position where the position vector r is given as (x, y), you need to express the position vector in terms of unit vectors. Since the force is applied along the y-axis, you can write the position vector as:
r = x i + y j
Now, you can calculate the torque:
τ = r × F
τ = (x i + y j) × (5.0 y N)
When you take the cross product, the component of the position vector along the direction of the force will contribute to the torque. In this case, only the y-component of the position vector (y j) is along the direction of the force (5.0 y N).
So, the torque about the origin is:
τ = y (5.0 y N)
Now, you can calculate the magnitude of the torque:
|τ| = |y (5.0 y N)| = 5.0 |y|^2 N
The magnitude of the unit vector "y" is 1, so:
|τ| = 5.0 N
The torque about the origin is 5.0 N.
Answer:
Elements of weather
Explanation:
Weather can be defined as the atmospheric conditions of a particular area over a short period of time.
Air pressure, humidity, clouds and temperature are all called elements of weather. The other elements of weather are;
- Wind
- Precipitation.
Air pressure, humidity, clouds, and temperature are all part of weather and climate studies. They represent the weight of air above a point on the earth's surface, the amount of water vapor in the atmosphere, collections of airborne water droplets or ice crystals, and the heat energy in the atmosphere, respectively.
Air pressure, humidity, clouds, and temperature are all components of weather and climate studies, key elements of geography and meteorology. Air pressure is the force exerted by the weight of air above any given point on Earth's surface. Humidity refers to the amount of water vapor in the atmosphere. Clouds are collections of water droplets or ice crystals that form in the Earth's atmosphere when water vapor condenses. Temperature is a measure of the amount of heat energy in the atmosphere, usually expressed in degrees Celsius or Fahrenheit. The combination of all these factors form different weather patterns and influence the Earth's overall climate.
Learn more about Weather and Climate Components here:
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b. a stopwatch that stops immediately when the stop button is clicked
c. a balance that always reads .01 g
d. measuring your height in your bare feet
B. 0 m/s^2
C. -9.81 m/s^2
D. It is not constant.
Answer: B.
Explanation:
When we talk about projectile motion, we have to deal with parabolic motion, which has two components: vertical and horizontal.
In the case of Earth, the acceleration is due gravity, which is constant and directed downwards (vertically) and have a value of .
Now, in the case of the horizontal component, the acceleration will always be zero.
This is because we are dealing with parabolic movement, the x-component of the velocity remains the same (hence, there is no acceleration), while the y-component always change because it is affected by the acceleration due gravity that acts verticaly.