Energy, Work and Power: Physics 0625 (Cambridge O Level / IGCSE)

A warehouse worker pushes a loaded trolley across a level floor with a steady horizontal force of $45\text{ N}$. The trolley moves a distance of $12\text{ m}$ in the direction of the force. How much work is done on the trolley?

A child sits at the top of a straight playground slide and pushes off, starting from rest.

(a) State the energy store that decreases and the energy store that increases as the child slides down. [2]

(b) The slide is not perfectly smooth. As the child slides down, some energy is transferred to the internal (thermal) energy store of the slide and the child's clothing. State the process by which this energy transfer takes place. [1]

(c) At the top of the slide, the child has $300\text{ J}$ stored in the gravitational potential energy store. By the time the child reaches the bottom, $210\text{ J}$ has been transferred to the kinetic energy store. Using the principle of conservation of energy, calculate the energy transferred to the internal (thermal) energy store. [2]

A student releases a toy cart of mass $0.80\text{ kg}$ from rest at the top of a smooth track. The cart rolls down through a vertical height of $1.25\text{ m}$ before reaching a horizontal section at the bottom. Friction and air resistance are negligible. Take gravitational field strength $g = 10\text{ N/kg}$.

(a) Calculate the loss in gravitational potential energy of the cart as it descends the $1.25\text{ m}$. [2]

(b) State the name of the energy store that this lost gravitational potential energy is transferred to as the cart speeds up. [1]

(c) Using the principle of conservation of energy, calculate the speed of the cart at the bottom of the track. [3]

An electric motor lifts a crate of mass $40\text{ kg}$ vertically through a height of $6.0\text{ m}$ at a constant speed, taking $15\text{ s}$ to complete the lift. During this time, the motor is supplied with $3200\text{ J}$ of electrical energy. Take gravitational field strength $g = 10\text{ N/kg}$.

(a) Calculate the useful work done in lifting the crate. [2]

(b) Calculate the efficiency of the motor during this lift, giving your answer as a percentage. [2]

(c) Calculate the useful output power of the motor during the lift. [2]

(d) State the form that most of the wasted energy takes as it dissipates from the motor system. [1]

A weightlifter raises a barbell, transferring $750\text{ J}$ of energy to the gravitational potential energy store of the barbell in $2.5\text{ s}$. What is the useful power developed by the weightlifter during the lift?

A librarian lifts a box of books of mass $6.0\text{ kg}$ from the floor onto a shelf, raising it through a height of $1.5\text{ m}$. Take gravitational field strength $g = 10\text{ N/kg}$. What is the increase in the gravitational potential energy store of the box of books?

A cyclist and her bicycle have a combined mass of $60\text{ kg}$.

(a) Calculate the kinetic energy store of the cyclist and bicycle when travelling at a speed of $8.0\text{ m/s}$. [2]

(b) The cyclist speeds up to $16\text{ m/s}$, which is double her original speed. Calculate the new kinetic energy store of the cyclist and bicycle. [2]

(c) By comparing your answers to (a) and (b), state and explain the effect on the kinetic energy of doubling the speed of an object. [2]

A wooden sledge loaded with firewood has a total mass of $20\text{ kg}$. It is released from rest at the top of a snow-covered slope and slides down to the bottom, descending through a vertical height of $7.5\text{ m}$ while travelling a distance of $50\text{ m}$ along the slope. As it slides, friction between the sledge and the snow acts as a constant resistive force of $10\text{ N}$ along the direction of motion. Take gravitational field strength $g = 10\text{ N/kg}$.

(a) Calculate the loss in gravitational potential energy of the sledge and its load as it descends the slope. [2]

(b) Calculate the work done against friction as the sledge travels the $50\text{ m}$ along the slope. [2]

(c) Using the principle of conservation of energy, calculate the speed of the sledge at the bottom of the slope. [3]

A builder's hoist lifts a bag of cement of mass $40\text{ kg}$ vertically through a height of $15\text{ m}$ in a time of $10\text{ s}$. Take gravitational field strength $g = 10\text{ N/kg}$. What is the useful power output of the hoist during the lift?

A student of mass $60\text{ kg}$ climbs a flight of stairs of total vertical height $4.5\text{ m}$ in a time of $12\text{ s}$. Take gravitational field strength $g = 10\text{ N/kg}$.

(a) Calculate the useful work done by the student in raising her own body up the stairs. [2]

(b) Calculate the useful power developed by the student while climbing the stairs. [2]

(c) The student's muscles are only $25\%$ efficient at converting chemical energy into this useful mechanical work; the rest is wasted. Calculate the total chemical energy transferred from the student's internal chemical energy store during the climb. [2]

(d) State the main form in which the wasted energy is transferred away from the student's body. [1]