Worksheet: Conservation of Energy
In this worksheet, we will practice calculating the change in the kinetic energy or gravitational potential energy of an object when work is done on it.
Ignoring details associated with friction, extra forces exerted by arm and leg muscles, and other factors, we can consider a pole vault as the conversion of an athlete’s running kinetic energy to gravitational potential energy. If an athlete is to lift his body 4.8 m during a vault, what speed must he have when he plants his pole?
When the force acting on an object is parallel to the direction of the motion of the center of mass, the mechanical energy . When the force acting on an object is antiparallel to the direction of the center of mass, the mechanical energy .
- Astays the same, decreases
- Bincreases, increases
- Cdecreases, increases
- Dincreases, decreases
- Edecreases, decreases
An out-of-condition professor does J of useful work while metabolizing 600 kcal of food energy. Use a value of J/kcal for the number of joules per kilocalorie.
What is the efficiency of the professor?
If a well-conditioned athlete did the same work with an efficiency of 20%, how many food calories would she use?
A small object is placed at the top of a frictionless incline. The object slides downward along the incline onto a rough horizontal surface, where it comes to rest in 5.0 s after traveling 60 m.
What is the speed of the object at the bottom of the incline?
What is the object’s acceleration along the horizontal surface?
What is the height of the incline?
A girl and a skateboard have a total mass of 47 kg. The girl rides the skateboard at a horizontal speed of 13 m/s toward a ramp that is inclined at above the horizontal. The girl travels 12.5 m upward along the ramp before coming to rest. What is the magnitude of the net frictional force that acted on the skateboard along the ramp?
A 7.0-kg box slides along a frictionless floor at 1.7 m/s. The box collides with a spring of negligible mass that compresses by 23 cm before the box comes to a halt.
How much kinetic energy does the box have before it collides with the spring?
Calculate the work done by the spring.
Determine the spring constant of the spring.
The force on a particle with a mass of 1.25 kg varies with displacement according to N. A frictional force also acts on the particle. The particle moves between the position m and m. At m the particle is at rest, and at m the particle moves in the negative -direction at 7.4 m/s. How much work is done on the particle by the frictional force between m and m?
Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of with the horizontal (see the figure). He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate and on his body to get up the ramp.
A projectile of mass 1.35 kg is fired with a speed of 32 m/s at an angle above the horizontal.
Assuming that the point from which the projectile is launched to be the point of zero gravitational potential, calculate the total energy of the projectile at the instant that it is launched.
Calculate the kinetic energy of the projectile when it has its maximum vertically upward displacement.
Calculate the gravitational potential energy of the projectile when it has its maximum vertically upward displacement.
Calculate the magnitude of the projectile’s maximum vertical upward displacement.
A block with a mass of 0.25 kg moves upward along a plane that is inclined at above the horizontal. The coefficient of friction between the block and the plane is 0.37. The block starts moving at a point P on the plane. The block’s initial velocity is 7.2 m/s.
How far does the block along the plane and away from P before becoming instantaneously at rest?
The block reaches a point at which it stops and changes direction, and then starts to slide down the incline. When the block returns to P sliding downward, what is its speed?
A car’s bumper is designed to withstand a 4.0-km/h collision with an immovable object without damage to the body of the car. The bumper cushions the shock by absorbing the force over a distance. Calculate the magnitude of the average force on a bumper that collapses 0.200 m while bringing a car of mass 900 kg to rest from an initial speed of 1.1 m/s.
A shopper applies a force below the positive -direction to move a grocery cart a distance of 20.0 m at constant speed. A 35.0-N force of friction is applied against the cart’s motion.
What is the work done on the cart by friction?
What is the work done on the cart by the gravitational force?
What is the work done on the cart by the shopper?
Find the force the shopper exerts, using energy considerations.
What is the total work done on the cart?
A wagon sits at the top of a hill. The wagon is given a push that increases its speed negligibly, but is just sufficient to set the wagon in motion down a straight slope. The wagon rolls 53.9 m down the slope, which is inclined below the horizontal, and reaches the bottom of the hill. If friction is negligible, what speed is the wagon moving when it reaches the bottom of the hill?
A boxer is hit in the face by a boxing glove covering his opponent’s fist. The arm and glove of the boxer’s opponent have a 6.23-kg-mass and are moving at a speed of 11.2 m/s before striking the boxer’s face. After the impact, the face, glove, and the arm are all at rest. The impact of glove on face produces a total compression of 8.25 cm.
Calculate the average force exerted by the boxing glove on the boxer’s face during the punch.
Calculate the average force exerted by a bare fist on the boxer’s face during the punch, assuming that the punch thrown is identical to the gloved punch but causes only 2.15 cm compression.
Suppose that in one year the total energy requirement of human society is J. If the energy released by the explosion of a 9-megaton thermonuclear weapon is J, and all the energy so released could be converted to useful forms of energy, how many such explosions would be required per year to meet the world’s energy needs?
A horizontally directed force of 27 N is applied to keep a 6.2-kg-mass box moving at a constant speed upward along a frictionless incline. The box moves through an upward vertical height change of 2.7 m.
What is the work done on the box by the force of gravity during the motion of the box? Assume that movement vertically upward corresponds to positive displacement
What is the work done on the box by the normal force during the motion of the box? Assume that movement vertically upward corresponds to positive vertical displacement and that horizontal movement in the direction of the applied force corresponds to positive horizontal displacement.
What is the work done on the box by the horizontally directed force during the motion of the box? Assume that movement vertically upward corresponds to positive vertical displacement and that horizontal movement in the direction of the applied force corresponds to positive horizontal displacement.
A T-shirt cannon launches a shirt at 4.20 m/s at an angle above the horizontal from a platform 3.00 m vertically above the ground. A T-shirt is caught by someone whose hands are 0.515 m vertically above ground level and by someone else whose hands are 3.25 m vertically above ground level. What is the difference between the speeds of the two T-Shirts when they were caught?
A 750-kg-mass car at the bottom of a hill has an initial speed of km/h and rolls upward along the hill. The hill is sloped at above the horizontal and is a rough surface. The vertically upward displacement of the car when it came to rest on the hill is 22.0 m.
If friction was negligible, what would be the vertically upward displacement of the car when it came to rest on the hill?
How much of the car’s kinetic energy was dissipated while climbing the hill?
What is the average force of friction exerted by the hill’s surface on the car?
A hiker being chased by a bear runs to the edge of a cliff and jumps off.
The hiker is running horizontally at 4.5 m/s when he reaches the cliff edge. The hiker’s speed when he hits the ground is 16 m/s. What vertical downward distance did the hiker fall?
If the hiker stepped forward off the cliff edge with negligible horizontal velocity, what speed would they hit the ground at?
The reservoir of the Hoover Dam has an active capacity (the amount of water that can be used for generating electricity) of L. The average height of the water in the reservoir (from the level of the water beyond the dam) is 90 m. The density of water is kg/m3.
How much gravitational potential energy is stored in the reservoir when it is full?
- A J
- B J
- C J
- D J
- E J
If L of water exits the dam at a speed of 3.00 m/s, how much energy is generated by the dam? Assume that the change in the water level of the reservoir is negligible and that the generators are efficient.
- A J
- B J
- C J
- D J
- E J
If the water exits the dam through a cylindrical pipe with a diameter of 3.00 m, what is the power generated by the dam?