Work, Energy and Simple Machines - Mechanical Energy

An object of mass $15\text{ kg}$ is moving with a uniform velocity of $4\text{ m/s}$. What is the kinetic energy possessed by the object?

Given: mass $m = 15\text{ kg}$, velocity $v = 4\text{ m/s}$. Using the formula $E_k = \frac{1}{2}mv^2$, we get $E_k = \frac{1}{2} \times 15 \times 4^2 = \frac{1}{2} \times 15 \times 16 = 15 \times 8 = 120\text{ J}$.

Kinetic energy is calculated by taking half the product of the mass and the square of the velocity.

Find the energy possessed by an object of mass $10\text{ kg}$ when it is at a height of $6\text{ m}$ above the ground. (Take $g = 9.8\text{ m/s}^2$)

Given: $m = 10\text{ kg}$, $g = 9.8\text{ m/s}^2$, $h = 6\text{ m}$. Potential Energy $E_p = mgh = 10 \times 9.8 \times 6 = 98 \times 6 = 588\text{ J}$.

The gravitational potential energy depends on the mass, the acceleration due to gravity, and the vertical height above the reference level.

A bag of wheat weighs $200\text{ kg}$. To what height should it be raised so that its potential energy may be $9800\text{ J}$? (Take $g = 9.8\text{ m/s}^2$)

Given: $E_p = 9800\text{ J}$, $m = 200\text{ kg}$, $g = 9.8\text{ m/s}^2$. We use $h = \frac{E_p}{mg} = \frac{9800}{200 \times 9.8} = \frac{9800}{1960} = 5\text{ m}$.

By rearranging the potential energy formula, we can solve for height.

A block of wood has a total mechanical energy of $1500\text{ J}$. If its kinetic energy is $850\text{ J}$, calculate its potential energy using vertical subtraction.

Total Mechanical Energy ($ME$) = $1500\text{ J}$. Kinetic Energy ($E_k$) = $850\text{ J}$. Potential Energy ($E_p$) = $ME - E_k$.

The Potential Energy is $650\text{ J}$.

Since $ME = E_k + E_p$, we find the unknown potential energy by subtracting the kinetic energy from the total mechanical energy.