Work and Energy — Important Questions

Gravitational potential energy

Step 1: Potential energy is the energy stored in an object due to its position or configuration. Step 2: Gravitational potential energy specifically refers to energy stored due to an object's height above the ground. Step 3: The book is at a height of 3 meters, so it has gravitational potential energy that could be converted to kinetic energy if it falls. Step 4: It doesn't have kinetic energy since it's not moving. Step 5: Chemical and electrical energy are not relevant to this situation involving height and gravity.

It becomes four times

Step 1: Kinetic energy formula is KE = ½mv², where velocity is squared. Step 2: If initial velocity is v, then initial KE = ½mv². Step 3: When velocity is doubled to 2v, new KE = ½m(2v)² = ½m × 4v² = 4 × (½mv²). Step 4: This shows the new kinetic energy is 4 times the original kinetic energy. Step 5: The squaring of velocity in the formula is why doubling velocity quadruples the kinetic energy, not just doubles it.

Joule

Step 1: Work is defined as force multiplied by displacement (W = F × s). Step 2: The SI unit of force is Newton (N) and the SI unit of displacement is meter (m). Step 3: Therefore, the unit of work is N⋅m, which is defined as one Joule (J). Step 4: Newton is the unit of force, not work. Watt is the unit of power (rate of doing work). Step 5: Meter is a unit of length/displacement, not work. Only Joule correctly represents the unit of work and energy.

500 J

Step 1: Use the gravitational potential energy formula PE = mgh, where m is mass, g is acceleration due to gravity, and h is height. Step 2: Given values are mass (m) = 5 kg, height (h) = 10 m, and g = 10 m/s². Step 3: Substitute into the formula: PE = 5 kg × 10 m/s² × 10 m. Step 4: Calculate: PE = 5 × 10 × 10 = 500 J. Step 5: The other options result from calculation errors like missing one of the multiplication factors.