Calculating Gate's Torque, KE & Angle When Bull Rushes Out

In summary, the farmer applies a torque of 300 Nm to the gate to prevent the bull from escaping. After 3 seconds, the gate has rotated 1.35 radians and has a rotational kinetic energy of 405 J. However, the gate will not be completely closed in time as it would need to rotate pi/2 radians to close.
  • #1
tachu101
74
0

Homework Statement


A gate to a bullpen is open at a right angle to the fence and the bull is rushing toward the opening to get out. The farmer estimates that the bull will reach the opening in 3 sec. so he pushes at the end of the gate (always at a right angle) with a force of 100N. The moment of inertia of the gate about the hinge is 1,000 kg m^2 and the gate length is 3.

a. What is the magnitude of the torque applied by the farmer.
b. What is the rotational kinetic energy of the gate after 3 seconds
c. Through what angle will the gate have rotated after 3 sec.
d. Will the gate be closed.

Homework Equations



Torque, KE roational, Angular Kinematics

The Attempt at a Solution



a. Torque= rFsin(theata) = (3)(100)sin90= 300Nm
b. KE= (1/2)(I)(w^2) = (1/2)(1000)(?)
c. angle= at^2/2?
d. ?
 
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  • #2
Part a is correct; for parts b, c, and d, you first need the equation (derived from Newton's 2nd law) that allows you to calculate the angular acceleration caused by a net torque.
 
  • #3
If I use torque=Ia and solve for a I will get a=torque/I = (300)/(1000) = .3 rad/sec^2 as the angular acceleration. For the w value after 3 sec it would be .9rad/sec? So I could then do the KE= (1/2)(I)(w^2) = (1/2)(1000)(.9^2) = 405 Then for part c could I use Theta= at^2/2 and get (.3)(3^2)/2 = 1.35 radians. Is any of this right? What would I do for the last part?
 
  • #4
tachu101 said:
If I use torque=Ia and solve for a I will get a=torque/I = (300)/(1000) = .3 rad/sec^2 as the angular acceleration. For the w value after 3 sec it would be .9rad/sec? So I could then do the KE= (1/2)(I)(w^2) = (1/2)(1000)(.9^2) = 405 Then for part c could I use Theta= at^2/2 and get (.3)(3^2)/2 = 1.35 radians. Is any of this right? What would I do for the last part?
Yes, excellent. Don't forget the units for energy, 405 __? For the last part, you know that the gate has rotated 1.35 radians. How many radians would it need to rotate to a completely closed position, given that it started out at a right angle to the fence?
 
  • #5
pi/2 would be the angle needed to close the gate, but 1.35 is less than pi/2, so it would not be closed in time.
 
  • #6
tachu101 said:
pi/2 would be the angle needed to close the gate, but 1.35 is less than pi/2, so it would not be closed in time.
Correct. Now don't forget the units for the kinetic energy.
 

1. What is gate's torque and why is it important to calculate it during a bull rush?

Gate's torque is the measure of rotational force applied to a gate or door when it is pushed or pulled. It is important to calculate it during a bull rush because it helps determine the force needed to keep the gate closed and prevent a bull from escaping.

2. How is gate's torque calculated?

To calculate gate's torque, you need to know the perpendicular distance from the pivot point of the gate to the point of contact with the bull (lever arm) and the force applied by the bull. The formula for gate's torque is torque = force x lever arm.

3. What is kinetic energy (KE) and how is it related to gate's torque?

Kinetic energy is the energy an object possesses due to its motion. It is related to gate's torque because the force applied by the bull will also determine the KE of the gate as it is pushed open. The greater the force, the more KE the gate will have.

4. Can the angle of the gate affect the calculation of gate's torque during a bull rush?

Yes, the angle of the gate can affect the calculation of gate's torque. If the gate is not perpendicular to the direction of the bull's force, the lever arm will be shorter, resulting in a lower torque calculation. It is important to take the gate's angle into account when calculating gate's torque.

5. How can calculating gate's torque, KE, and angle help prevent a bull from escaping?

By knowing the gate's torque, KE, and angle, you can determine the necessary force needed to keep the gate closed and prevent the bull from escaping. This information can also help in determining the strength and stability of the gate, ensuring it can withstand the force of the bull's rush without breaking or opening.

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