Work and Power Problems
Activity 1: Number the steps to reflect the order they should be in.
Problem 1: Bud, a large man of mass 130kg, stands on a pogo stick. How much work is done as Bud compresses the spring of the pogo stick 0.50m?
Plugging in to find weight:Fg=(130kg)(9.8m/s2)=1274N.
To do so, we must use the formula for work:
W=Fd.
Thus, the man does 637J of work to compress the spring.
We want to determine the work done by a 130kg man who is compressing the spring in a pogo stick 0.50m.
Plugging in to get work:
W=(1274N)(0.5m)=637J.
We see that in order to calculate work, we must know the force. In this case, the force acting on the spring is the weight of the man, which we can calculate using the formula:
Fg=mg.
Problem 2: In a weightlifting competition, Sergei lifted 205kg to a height of 2.0m in 11s and Stefan lifted 203kg to a height of 2.3m in 9s. Which competitor exerted more power in his lift?
And to find Stefan’s power we follow the same process:Fg=203kg(9.8m/s2)=1989.4N,
W=Fd=1989.4N2.3m=4575.62J,
P=Wt=4575.62J9s=508.4W.
So, to find Sergei’s power we calculate the weight he lifted, then the work he did to lift it and finally his power:
Fg=205kg(9.8m/s2)=2009N,
W=Fd=2009N2.0m=4018J,
P=Wt=4018J11s=365.3W.
Thus we have found that Stefan exerted more power, as he exerted 508.4 Watts of power where Sergei only exerted 365.3 Watts of power.
We want to determine which lifter was more powerful, so we need to determine the amount of power exerted by each man.
To complicate things a little further, we must also first determine the force each man had to apply to lift the weights using the formula for weight:
Fg=mg.
We know that Sergei lifted 205kg to a height of 2.0m in 11s and Stefan lifted 203kg to a height of 2.3 m in 9s.
To find power, we use the formula:
P=Wt.
In order to use this formula, we must first determine the work done by each man using the formula:
W=Fd.
Activity 2: Work each problem out, showing all your work. Write formal solutions for numbers 3 & 4.
1. On his way off to college, Russell drags his suitcase 15.0m from the door of his house to the car at a constant speed with a horizontal force of 95.0 N. A) How much work does Russell do to overcome the force of friction? B) If the floor has just been waxed, does he have to do more work or less work to move the suitcase? Explain.
2. Katie, a 30.0kg child, climbs a tree to rescue her cat who is afraid to jump 8.0m to the ground. How much work does Katie do in order to reach the cat?
3. Marissa does 3.2J of work to lower a shade in her bedroom a distance of 0.8m. How much force must Marissa exert on the window shade?
4. Atlas and Hercules, two carnival sideshow strong men, each lift 200kg barbells 2.0m off the ground. Atlas lifts his barbells in 1.00s and Hercules lifts his in 3.00s. A) Which strong man does more work? B) Calculate the power exerted by each strong man.
5. After finishing her physics homework, Sherita pulls her 50.0kg body out of the living room chair and climbs up the 5.0m high flight of stairs to her bedroom. A) How much work does Sherita do in ascending the stairs? B) On Monday, tired from the weekend, Sherita climbs the stairs slowly, taking 10.0s to get to the top. On Tuesday, in a hurry because her favorite show is about to start, she runs up the stairs in 3.0s. How much power does Sherita exert on each night?