Use work and energy principles to calculate a speed or a height or an energy value. Most problems are highly scaffolded.
The Top Thrill Dragster stratacoaster at Cedar Point Amusement Park in Ohio uses a hydraulic launching system to accelerate riders from 0 to 52.3 m/s in 4.5 seconds before climbing a completely vertical 421-foot hill.
Jerome (mass=95 kg) visits the park with his church youth group. He boards his car, straps himself in and prepares for the thrill of the day. What is Jerome's kinetic energy before the acceleration period?
Initial KE
Joules
The 4.5-second acceleration period begins to accelerate Jerome along the level track. What is Jerome's kinetic energy at the end of this acceleration period?
KE
Once the launch is over, Jerome begins screaming up the 421-foot, completely vertical section of the track. Determine Jerome's potential energy at the top of the vertical section. (GIVEN: 1.00 m = 3.28 ft)
PE at peak
Determine Jerome's kinetic energy at the top of the vertical section.
KE at peak
Determine Jerome's speed at the top of the vertical section.
Speed at peak
m/s
Paige is the tallest player on South's Varsity volleyball team. She is in spiking position when Julia gives her the perfect set. The 0.230-kg volleyball is 2.42 meters above the ground and has a speed of 1.00 m/s. Paige spikes the ball, doing 9.47 Joules of work on it.
Determine the potential energy of the ball before Paige spikes it.
PE
Determine the kinetic energy of the ball before Paige spikes it.
Determine the total mechanical energy of the ball before Paige spikes it.
Total ME
Determine the total mechanical energy of the ball upon hitting the floor on the opponent's side of the net.
Total ME at floor
Determine the speed of the ball upon hitting the floor on the opponent's side of the net.
Speed
According to ABC's Wide World of Sports show, there is the "Thrill of victory and the agony of defeat". On March 21 of 1970, Vinko Bogataj was the Yugoslavian entrant into the World Championships held in former West Germany. By his third and final jump of the day, heavy and persistent snow produced dangerous conditions along the slope. Midway through the run, Bogataj recognized the danger and attempted to make adjustments in order to terminate his jump. Instead, he lost his balanced and tumbled and flipped off the slope into the dense crowd. For nearly 30 years thereafter, footage of the event was included in the introduction of ABC's infamous sports show and Vinco has become known as "The agony of defeat" icon.
Determine the speed of 79-kg Vinco after skiing down the hill to a height which is 49 meters below the starting location.
After descending the 49 meters, Vinko tumbled off the track and descended another 13 meters down the ski hill before finally stopping. Determine the change in potential energy of Vinko from the top of the hill to the point at which he stops. (+ would be a gain and - would be a loss)
∆PE
Determine the amount of cumulative work done upon Vinko's body as he crashes to a halt. (Consider whether the work is + or -)
Work done
In April of 1976, Chicago Cub slugger Dave Kingman hit a home run which cleared the Wrigley Field fence and hit a house located 530 feet (162 m) from home plate. Suppose that the 0.140-kg baseball left Kingman's bat at 47.8 m/s and that it lost 11.6% of its original energy by the time it cleared the stadium wall at a height of 21.3 meters above the height at which the bat contacted the ball. Determine the speed of the ball as it passed above the wall.
Connor (m=66.1 kg) is competing in the state diving championship. He leaves the springboard from a height of 3.15 meters above the water surface with a speed of 4.94 m/s in the upward direction.
Determine Connor's speed when he strikes the water.
Speed at impact
Connor's body plunges to a depth of 2.55 meters below the water surface before stopping. Determine the average force of water resistance experienced by his body.
Average force
Newtons
Suzie Lavtaski is moving with a kinetic energy of 7800 Joules and at an elevation relative to the bottom of the ski slope that provides her with a potential energy of 11000 Joules. If Suzie has a kinetic energy of 21980 Joules at the bottom of the slope, then what quantity of mechanical energy did she gain through the use of her poles? Neglect the effect of resistive forces.
Gain of ME
In another episode of Don't Do This At Home, a 61.9-kg man steps off a 1.34-m high bench and lands with his knees and ankles locked. The only cushion for his fall is the 0.59-cm give in the pads of his shoes. Calculate the average force exerted upon his body by the ground as he abruptly stops.
Monte works at the local grain elevator during the summer months. He uses the lift to hoist a 131.8-Newton sack of grain to a storage area 20.5 meters above the ground.
What is the potential energy of the sack when in the storage room?
How much work was done in lifting the sack to this height?
If the sack were to fall back down to the elevator floor, how much kinetic energy would it have just prior to landing?
Thinking about Physics (as she usually does), Latasha does the following experiment. She gets her bike moving at 15.8 m/s as she approaches the paved hill at Flick Park. She quits pedaling and allows her 81.6-kg bike (her mass included) coast to a stop as it rises up the hill.
What is the kinetic energy of Latasha and her bike at the bottom of the hill?
Assuming negligible resistance forces, what potential energy will Latasha and her bike have when it finally stops?
To what height will Latasha and the bike rise before stopping?
Height
meters
In another episode of Destroyed in Seconds, a 20.2-kg rock teeters on the edge of a 98.5-meter high cliff. A gentle nudge causes it to fall to the ground below. Assume negligible air resistance.
Determine the potential energy of the rock on the top of the cliff.
Rock PE
Determine the kinetic energy of the rock just before striking the ground.
Rock KE
Determine the speed at which the rock strikes the ground.