Question

A green drum with a moment of inertia of 19.24kgm^2 and radius 0.95m rotates freely about...

A green drum with a moment of inertia of 19.24kgm^2 and radius 0.95m rotates freely about a vertical axis. A rope is wound around it and strung over a red wheel with a moment of inertia of 16.11kgm2 and radius 0.71m that rotates freely about a horizontal axis. The rope is then attached to a cube dangling below with a mass of 13.47kg. The cube falls 1.8m1.8m from rest. Take the acceleration of gravity to be 9.81ms^2. Assume that the rope does not slip and has negligible mass. What is its velocity at that point?

(a) what is the acceleration?

(b) what is the tension in the string right above the cube?

Homework Answers

Answer #1

let I1 = 19.24 kg.m^2, R1 = 0.95 m

I2 = 16.11 kg.m^2, R2 = 0.71 m

m = 13.47 kg

h = 1.8 m

a) Apply conservation of energy

loss of potential energy = gain in kinetic energy of wheels and cube

m*g*h = (1/2)*m*v^2 + (1/2)*I1*w1^2 + (1/2)*I2*w2^2

m*g*h = (1/2)*m*v^2 + (1/2)*I1*(v/R1)^2 + (1/2)*I2*(v/R2)^2

13.47*9.81*1.8 = (1/2)*13.47*v^2 + (1/2)*19.24*(v/0.95)^2 + (1/2)*16.11*(v/0.71)^2

==> v = 2.67 m/s

now use,

v^2 - vo^2 = 2*a*d

a = (v^2 - vo^2)/(2*d)

= (2.67^2 - 0^2)/(2*1.8)

= 1.98 m/s^2 <<<<<<<<---------------Answer

B) Tension in the string, T = m*(g - a)

= 13.47*(9.81 - 1.98)

= 105 N <<<<<<<<---------------Answer

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A cylindrical drum of mass M, radius R and moment of inertia Icm can rotate about...
A cylindrical drum of mass M, radius R and moment of inertia Icm can rotate about its central axis. A Mass m is suspended from a light rope that has previously been wound around the drum. The mass is frees from the rest at a height h on the floor, unwinding the rope when falling. a) Ignoring the friction, use the Newton's second law to calculate the tension in the string while m is falling. b) Ignoring the friction, uses...
A wheel has a horizontal axis and a moment of inertia I = 220.0 kg۰m2. A...
A wheel has a horizontal axis and a moment of inertia I = 220.0 kg۰m2. A rope is wrapped around the rim of the wheel, R = 0.230 m, and the free end of the rope has a 4.00 kg mass attached to it. The system is released from rest. Draw free-body diagrams for both the wheel and the 4.00 kg mass. Determine the angular acceleration α of the wheel.
A block of mass m = 2.5 kg is attached to a string that is wrapped...
A block of mass m = 2.5 kg is attached to a string that is wrapped around the circumference of a wheel of radius R = 8.8 cm . The wheel rotates freely about its axis and the string wraps around its circumference without slipping. Initially the wheel rotates with an angular speed ω, causing the block to rise with a linear speed v = 0.42 m/s A) Find the moment of inertia of the wheel if the block rises...
A block of mass m = 1.8 kg is attached to a string that is wrapped...
A block of mass m = 1.8 kg is attached to a string that is wrapped around the circumference of a wheel of radius R = 7.6 cm . The wheel rotates freely about its axis and the string wraps around its circumference without slipping. Initially the wheel rotates with an angular speed ω, causing the block to rise with a linear speed v = 0.30 m/s Find the moment of inertia of the wheel if the block rises to...
A freewheel is a wheel with a hub which can rotate freely in one direction, but...
A freewheel is a wheel with a hub which can rotate freely in one direction, but must rotate with a gear in the other. The gear can be thought of as "floating" in one direction and "catching" in the other. One example that most are familiar with is a bicycle wheel, though many other mechanical devices use freewheels, such as wind turbines, hydraulic turbines, grandfather clocks, and other gravity-powered objects. A freewheel with negligible mass spokes has a mass of...
A light-weight potter’s wheel, having a moment of inertia of 24 kg*m^2, is spinning freely at...
A light-weight potter’s wheel, having a moment of inertia of 24 kg*m^2, is spinning freely at 40 rpm. The potter drops a small but dense lump of clay onto the wheel, where it sticks a distance 1.2m from the rotational axis. The subsequent angular speed of the wheel and clay is 32 rpm. The axis of the wheel is vertically directed, and the wheel is initially spinning in the counter-clockwise direction when looking down on the wheel from above. After...
A merry-go-round with a moment of inertia equal to 1250kg?m2 and a radius of 2.5 m...
A merry-go-round with a moment of inertia equal to 1250kg?m2 and a radius of 2.5 m rotates with negligible friction at 1.70 rad/s. A child initially standing still next to the merry-go-round jumps onto the edge of the platform straight toward the axis of rotation, causing the platform to slow to 1.35 rad/s.What is her mass?
1. Find the moment of inertia of a stick of length 4 m and mass 10...
1. Find the moment of inertia of a stick of length 4 m and mass 10 kg that is rotated about an axis that is 30 % from the left end of the stick. Hint do the integration of r^2 dm 2. A 123 kg merry go round with a 5 m radius rotates on a vertical axis. If I push at the edge with a force of 188 N, find the angular acceleration. The moment of inertia of disk...
A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg?m2 is rotating freely...
A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg?m2 is rotating freely with an angular speed of 3.0 rad/s. Two people, each having a mass of 60 kg are standing right outside the edge of the merry-go-round. One person radially steps on the edge merry-go-round with negligible speed and the angular speed changes to ?1. A few seconds later, the second person radially steps on the merry-go-round with negligible speed but at distance of 4.0 m...
A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg?m2 is rotating freely...
A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg?m2 is rotating freely with an angular speed of 3.0 rad/s. Two people, each having a mass of 60 kg are standing right outside the edge of the merry-go-round. One person radially steps on the edge merry-go-round with negligible speed and the angular speed changes to ?1. A few seconds later, the second person radially steps on the merry-go-round with negligible speed but at distance of 4.0 m...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT