Nt1310 Unit 5 Lab Report

Solve each of the following problems. Show your solution.
1. A hydraulic lift office chair has its seat attached to a piston with an area of 11.2 cm2. The chair is raised by exerting force on another piston, with an area of 4.12 cm2. If a person sitting on the chair exerts a downward force of 219 N, what force needs to be exerted on the small piston to lift the seat?

Answer: a= 11.2 cm2 A= 4.12 cm2 f= 219 N F= 80.56 N

F= fA / a ; (219 N) (4.12 cm2 ) / 11.2 cm2 = 80.56 N

F/ f = 80.56 N/ 219 N = 0.37
A/ a = 4.12 cm2 / 11.2 cm2 = 0.37

2. In changing a tire, a hydraulic jack lifts 7468 N on its large piston, which has an area of 28.27 cm2. How much force must be exerted
on the small piston if it has an area of 1.325 cm2?

Answer: a= 1.325 cm2
A= 28.27 cm2

F= 7468 N

f= 350.02 N

Solution:

f= Fa / A ; (746 N)(1.325 cm2 ) / 28.27 cm2 = 350.02 N

F/ f= 7468 N / 350.02 = 21.34

A/ a= 28.27 cm2 / 1.325 cm2 = 21.34

3.
An engine shop uses a lift to raise a 1784 N engine. The lift has a large piston with an area of 76.32 cm2. To raise the lift, force is exerted on a small piston with an area of 12.56 cm2. What force must be exerted to raise the lift?

Answer: F= 1784 N

A= 76.32
cm2

a= 12.56 cm2

f= 293.59 N

Solution:

f= Fa / A ; (1784 N)(12.56 cm2 ) / 76.32 cm2 = 293.59 N

F/ f= 1784 N / 293.54 N = 6.08

A/ a= 76.32 cm2 / 12.56 cm2 = 6.08

3.
In a newly designed car with a hydraulic braking system, a force of 85 N is applied to one of the master cylinders, which has an area of 8.1 cm2. The master cylinder is connected to one brake piston, which exerts a force of 296 N. What is the area of the brake piston?
Answer: f= 85 N

A= 8.1 cm2

F= 296 N

A= 28.21 cm2

Solution:

A= Fa/ f ; (296 N)(8.1 cm2 ) / 85 N = 28.21 cm2

F/ f = 296 N / 85 N = 3.49

A/ a = 28.21 cm2 / 8.1 cm2 = 3.49

4. A mechanic uses a hydraulic car jack to lift the front end of a car to change the oil. The jack she uses exerts 8915 N of force from the larger piston. To pump the jack, she exerts 444 N of force on the small piston, which has an area of 3.14 cm2. What is the area of the large piston?

Answer: A= 63.05 cm2

a= 3.14 cm2

F= 8915 N

f= 444 N

Solution:

A= Fa/ f ; (8915 N)(3.14 cm2 ) / 444 N = 63.05
cm2

F/ f = 8915 N / 444 N = 20.08

A/a = 63.05 cm2 / 3.14 cm2 = 20.08

6. A student in the lunchroom blows into his straw with a force of 0.26 N. The column of air pushing the liquid in the glass has an area of 0.21 cm2. If the liquid in the glass pushes upward with a force of 79 N, what is the area of the liquid at the surface of the glass?

Answer: f=0.26 N

a= 0.21 cm2

F= 79 N

A= 63.81 cm2

Solution:

A= Fa/ f ; (79 N)(0.21 cm2 ) / 0.26 N = 63.81 cm2

F/ f = 79 N / 0.26 N = 303.85

A/ a= 63.81 cm2 / 0.21 cm2 = 303.86