Question

The questions below refer to an empty paint can with a lid. The sides, bottom, and lid are all made with the same metal of the same thickness. The paint can is 24 cm tall, and it’s diameter is 16 cm. The mass of the empty can is 400 grams.

1.) What is the mass of the cylindrical sides of the paint can? (In units of grams)

a. none of the above

b.) 300

c.) 100

d.) cannot be determined from the given information

e.) 400

2.) Spinning about its axis of symmetry, what is the moment of inertia of the entire paint can (sides, lid, and bottom)? (in units of kg x m^2)

a.) less that 0.0005

b.) 0.0022

c.) 0.0013

d.) more than 0.003

e.) 0.00064

Now, the paint can is placed on its side and begins rolling straight down an incline. The angle of the incline is 14.2°. The coefficient of static friction between the can and the incline is 0.8, the coefficient of kinetic friction is 0.6.

3.) What can the linear acceleration of the center of mass of the can rolling down the incline be equal to? (Select all that apply)

a.) net force divided by the mass

b.) (9.8m/s^2)sinø

c.) the angular acceleration times the radius

4.) Compared to the paint can sliding down the same incline on a frictionless surface, the acceleration of the can rolling down the incline is:

a.) greater

b.) the same

c.) less

Answer 1

given

paint can height, h = 24 cm

diameter, d = 16 cm

mass of empty can = 400 grams

sides and bottom and lid are made of asme material f same thickness

1. mas sof cylinderical sides of paint can = area of cylinderical sides of paint can * mass of paint can / area of poaint can

hence

ms = pi*d*h*m/(pi*d*h + 2*pi*d^2/4)

ms = h*m/(h + d/2) = 2hm/(2h + d) = 300 g

hence option b) 300

2. moment of inertial of entire paint can = I

I = 2*0.5*(400 - 300)*(d/2)^2/2 + 300*d^2/4

I = 3200 + 19200 = 22400 g cm^2 = 0.00224 kg m^2

hence option b) 0.0022

3. given angle of incline, theta = 14.2 deg

coefficient of static friction, us = 0.8

coefficienti of kinetic friction, uk = 0.6

linear acecleration of the center of mass can be

angular acceleration*radius (for rolling case)

net force/mass (for any case)

hence option a) and c) both are true with option a) more true than option c)

4. compared to the can sliding doen on fricitonless place, when rolling down in presence of friciton, the acceleration of the can is lowes in presence of friciotn

hence

option c) less