The following problems span the entire Work, Energy, and Power unit and serve as a review of the mathematics of the unit.
Josie is playing in the family room, exerting a 12.8 Newton force on a toy box to move it 1.98 meters across the room. How much work does Josie do on the box?
Work done
Newton-meters
Hans Full is pulling on a rope to drag his backpack to school across the ice. He pulls upwards and rightwards with a force of 25.6 Newtons at an angle of 37.7˚ above the horizontal to drag his backpack a horizontal distance of 123.5 meters to the right. Determine the work (in Joules) done upon the backpack.
While training for breeding season, a 382-gram male squirrel does 30 pushups in a minute, displacing its center of mass by a distance of 7.64 cm for each pushup. Determine the total work done on the squirrel while moving upward (30 times).
A machine does 662 Newton-meters of work on a 60-kg mass in 15.3 seconds. What is the power put out by this machine?
Power
Watts
A lift machine raises a 642 Newton box from the ground to a height of 16.0 meters in 10.0 seconds. What is power required of the motor to do this task?
Power required
A 0.260-kg ball possesses a kinetic energy of 50.9 Joules. Calculate the speed of the ball.
Speed
m/s
An object has a kinetic energy of 26.8 Joules. If the object's speed is tripled, then its new kinetic energy will be ____ J.
KE
Joules
An object has a kinetic energy of 20.8 Joules. An object with three times the mass moving at the same speed will have a kinetic energy of ____ J.
In an effort to impress Mr. Hass during PE class, Avery quickly elevates his 62.7-kg body up the rope to a height of 4.35 meters above his starting point. What is Avery's change in potential energy?
PE
The diagram at the right shows six positions of a 0.30-kg ball bouncing across a 3.4-meter-high physics room. Information regarding the vertical position is shown. Assume that the floor is the reference level for zero potential energy.
Determine the gravitational potential energy of the 0.30-kg ball at position A:
Determine the gravitational potential energy of the 0.30-kg ball at position B:
Determine the gravitational potential energy of the 0.30-kg ball at position C:
Determine the gravitational potential energy of the 0.30-kg ball at position D:
Determine the gravitational potential energy of the 0.30-kg ball at position E:
Determine the gravitational potential energy of the 0.30-kg ball at position F:
Lee Ben Fardest, esteemed American ski jumper, has a mass of 71.5 kg. He is moving with a speed of 19.4 m/s at a height of 41.6 meters above the ground. Determine the total mechanical energy of Lee Ben Fardest.
Total ME
Chloe leads South’s varsity softball team in hitting. In a game against New Greer Academy this past weekend, Chloe slugged the 177-gram softball so hard that it cleared the outfield fence and landed on Lake Avenue. At one point in its trajectory, the ball was 18.7 meters above the ground and moving with a speed of 29.1 m/s. Determine the total mechanical energy of the softball.
Ben Laborin is pushing a 23.4-kg cart through the hallways with a speed of 2.62 m/s. He momentarily pulls back on the cart with 49.7 N of force to slow it to 1.01 m/s.
Calculate the initial kinetic energy of the cart.
Initial KE
Calculate the final kinetic energy of the cart (after slowing down).
Final KE
Calculate the the change in kinetic energy of the cart. (Include the appropriate + or – sign.)
Change in KE
Calculate the distance over which the backward force was applied to the cart during the slowing down period.
Distance
meters
A car is moving across a level highway with a kinetic energy of 1.463 x 105 Joules. The brakes are applied and the wheels become locked as the 910-kg car slows to a stop over 8.59 seconds. Determine the work done upon the car. Enter the appropriate + or – sign.
Lizzie is one of South's best skaters. She has a mass of 43.9 kg is moving at 7.03 m/s. She then effortlessly glides to a stop overt a distance of 22.4 meters. How much work is done by friction to bring Lizzie to a stop? Include the appropriate + or – sign.
Suzie Lavtaski (m=50 kg) is skiing at Bluebird Mountain. She is moving at 18 m/s across the crest of a ski hill located 37 meters above ground level at the end of the run.
Determine Suzie's kinetic energy.
Determine Suzie's potential energy relative to the height of the ground at the end of the run.
Determine Suzie's total mechanical energy at the crest of the hill.
If no energy is lost or gained between the top of the hill and her initial arrival at the end of the run, then what will be Suzie's total mechanical energy at the end of the run?
Determine Suzie's speed as she arrives at the end of the run and prior to braking to a stop.
Final speed
Claire deAisles exerts a 8.2-Newton rightward force upon an 83.0-Newton grocery cart to move it 4.93 meters down the frozen food aisle at Hy-Vee. If resistance forces are neglected, what would be the final speed of the cart?
Pauline is pulling her 7.2-kg sled across a frozen pond. She gives the sled a quick tug to set it in motion at 4.0 m/s. The coefficient of friction on the sled and the ice is 0.23. Use the work-energy theorem to determine the distance that it moves before coming to rest.
According to the most careful measurements, it is found that a 0.379-mg flea can jump to a maximum height of about 2.06 cm. Find the speed with which the flea takes off in order to accomplish this amazing feat.
Paige is the tallest player on South's Varsity volleyball team. She is in spiking position when Julia gives her the perfect set. The 0.226-kg volleyball is 2.57 meters above the ground and has a speed of 1.04 m/s. Paige spikes the ball, doing 9.06 Joules of work on it.
Determine the potential energy of the ball before Paige spikes it.
Determine the kinetic energy of the ball before Paige spikes it.
Determine the total mechanical energy of the ball before Paige spikes it.
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.
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 71-kg Vinco after skiing down the hill to a height which is 45 meters below the starting location.
After descending the 45 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 -)
Monte works at the local grain elevator during the summer months. He uses the lift to hoist a 120.6-Newton sack of grain to a storage area 29.2 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?