If the human body could convert a candy bar directly into work, how high could a 76 kg man climb a ladder if he were fueled by one bar (=1100 kJ)?
If the man then jumped off the ladder, what will be his speed when he reaches the bottom?
A projectile is fired at an upward angle of 48.0° from the top of a 130-m-high cliff with a speed of 180 m/s. What will be its speed when it strikes the ground below? (Use conservation of energy. Neglect air resistance.)
A bicyclist coasts down a 6.5 degree hill at a steady speed of 4.5 m/s. Assuming a total mass of 75 kg (bicycle plus rider), what must be the cyclists power output to climb the same hill at the same speed?
The position of a 260 g object is given (in meters) by x = 5.0t3 - 8.0t2 - 45t, where t is in seconds.
(a) Determine the net rate of work done on this object at t =2.1 s.
(b) Determine the net rate of work done on this object at t = 4.1 s.
(c) What is the average net power input during the interval from t = 0 to t = 2.1 s?
(d) What is the average net power input during the interval from t =2.1 s to t=4.1 s?
During a workout, football players ran up the stadium stairs in 80 s. The stairs are 83 m long and inclined at an angle of 31 degrees. If a player has a mass of 87 kg, estimate his average power output on the way up. Ignore friction and air resistance.
You drop a ball from a height of 2.1 m, and it bounces back to a height of 1.3 m.
(a) What fraction of its initial energy is lost during the bounce?
(b) What is the balls speed just before the bounce?
(c) Where did the energy go?
(d) What is the balls speed just after the bounce?
What should be the spring constant k of a spring designed to bring a 1300 kg car to rest from a speed of 90 km/h so that the occupants undergo a maximum acceleration of 5.5 g?
Two masses are connected by a string as shown in the figure. mA = 3.6 kg rests on a frictionless inclined plane, while mB = 4.6 kg is initially held at a height of h = 0.75 m above the floor.
(a) If mB is allowed to fall, what will be the resulting acceleration of the masses?
(b) If the masses were initially at rest, use the kinematic equations to find their velocity just before mB hits the floor.
(c) Use conservation of energy to find the velocity of the masses just before mB hits the floor.
A sled is initially given a shove up a frictionless 23.0° incline. It reaches a maximum vertical height 1.27 m higher than where it started. What was its initial speed?
A 1300 kg car moving on a horizontal surface has speed = 80 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.3 m. What is the spring stiffness constant of the spring?
A 1.75 m tall person lifts a 1.65 kg book off the ground so it is 2.15 m above the ground.
(a) What is the potential energy of the book relative to the ground?
(b) What is the potential energy of the book relative to the top of the persons head
(c) How is the work done by the person related to the answers in parts A and B?
A 6.0 kg monkey swings from one branch to another 1.5 m higher. What is the change in gravitational potential energy?
A spring has a spring constant k of 82.0 N/m. How much must this spring be compressed to store 40.0 J of potential energy?
A 6.10 kg block is pushed 9.30 m up a smooth 38.0 inclined plane by a horizontal force of 76.0 N . If the initial speed of the block is 3.30 m/s up the plane, calculate the:
(a) initial kinetic energy of the block
(b) work done by the 76.0 N force
(c) work done by gravity
(d) work done by the normal force
(e) final kinetic energy of the block
A 51.0 kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 240 N . For the first 11.5 m the floor is frictionless, and for the next 11.5 m the coefficient of friction is 0.19. What is the final speed of the crate after being pulled these 23.0 m?
A 4.5 kg object moving in two dimensions initially has a velocity v1 = (11.5 i + 20.5 j) m/s. A net force F then acts on the object for 2.0 s, after which the objects velocity is v2 = (15.5 i + 30.5 j) m/s. Determine the work done by F on the object.
A 145 g baseball traveling 33 m/s moves a fielders glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glove?
How much work must be done to stop a 1300 kg car traveling at 90 km/h?
A 3.0-m-long steel chain is stretched out along the top level of a horizontal scaffold at a construction site, in such a way that 2.0 m of the chain remains on the top level and 1.0 m hangs vertically, the figure. At this point, the force on the hanging segment is sufficient to pull the entire chain over the edge. Once the chain is moving, the kinetic friction is so small that it can be neglected. How much work is performed on the chain by the force of gravity as the chain falls from the point where 2.0 m remains on the scaffold to the point where the entire chain has left the scaffold? (Assume that the chain has a linear weight density of 18 N/m .)
The force needed to hold a particular spring compressed an amount from its normal length is given by F = kx + ax3 + bx4. How much work must be done to compress it by an amount, starting from x = 0?
If it requires 5.5 J of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additional 4.1 cm?
A box of mass 5.5 kg is accelerated from rest by a force across a floor at a rate of 2.6 m/s2 for 5.6 s .
Find the net work done on the box.
A 76.0-kg firefighter climbs a flight of stairs 21.0 m high. How much work is required?
Use the work–energy theorem to solve each of these
(a) A skier moving at 5.01 m/s encounters a long, rough, horizontal patch of snow having a coefficient of kinetic friction of 0.220 with her skis. How far does she travel on this patch before stopping?
(b) Suppose the rough patch in part A was only 2.91 m long. How fast would the skier be moving when she reached the end of the patch?
(c) At the base of a frictionless icy hill that rises at 25.0 above the horizontal, a toboggan has a speed of 12.1 toward the hill. How high vertically above the base will it go before stopping?