Finding tire contact area, boat buoyancy, and object density

[kamoey]

Some of the problems, I really don't know how to even set up the problem. I don't want an answer for them, but I need an idea where to start.

1. Gauge pressure in both tires = 690 kPa.
Bike and the riders mass = 90.0 kg.
Find area of contact of each tire with the ground if each tire supports half the total weight.
I read the section that this problem corresponse to and could not figure out where to start.


3. Boat overloaded such that water level is 1.0cm below top of boat.
Total lenght= 4.5m
height= .3m
width= 2.0m

Find combinded mass of people and boat.

I'm not sure how to to this one.
I drew a FBD and got...
Force of boat=mg
Density of water x volume of object x gravity= mg
(1000kg/m^3)(2.61m^3)=mass
?=2610 kg

4. Irregularly shaped piece of metal
weight=.882 N. When submerged in water irregual object is suspended from scale rading .735 N.
Find volume and density of object.

 

[Doc Al]

Originally posted by kamoey
1. Gauge pressure in both tires = 690 kPa.
Bike and the riders mass = 90.0 kg.
Find area of contact of each tire with the ground if each tire supports half the total weight.
I read the section that this problem corresponse to and could not figure out where to start.

Think Pressure = Force/Area; the force must be enough to support the bike + rider.

3. Boat overloaded such that water level is 1.0cm below top of boat.
Total lenght= 4.5m
height= .3m
width= 2.0m

Find combinded mass of people and boat.

I'm not sure how to to this one.
I drew a FBD and got...
Force of boat=mg
Density of water x volume of object x gravity= mg
(1000kg/m^3)(2.61m^3)=mass
?=2610 kg

Assuming the boat is rectangular, you got it.

4. Irregularly shaped piece of metal
weight=.882 N. When submerged in water irregual object is suspended from scale rading .735 N.
Find volume and density of object.

The scale reading is the force that the scale must pull up to support the object. So, consider the forces acting on the object when it's submerged: The scale is pulling up, the buoyant force (water) is pushing up, and the weight is pulling down. These forces must balance.

 

[M98Ranger]

For this problem, you can start by using the Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. So, in this case, the buoyant force on the object is equal to the weight of the water that it displaces. From the given information, you can calculate the volume of the object by dividing the weight of the object by the difference between the weight of the object in air and the weight of the object in water. Once you have the volume, you can calculate the density by dividing the weight of the object by its volume.

To set up the problem, you can draw a free body diagram and label the forces acting on the object (weight, buoyant force, and tension force from the scale). Then, use the equations for each force to solve for the volume and density of the object. Remember to convert all units to the appropriate SI units before solving the equations.