How Do You Calculate the Linear Acceleration and Impact Velocity of a Load?

[brooker2009uk]

Homework Statement

was wondering if anybody here does mech engineering and if so can they point me in the right direction of this question please.


Figure 1 below shows a drum of mass of 50kg and radius 350mm. The drum can be assumed to be a uniform solid cylinder. A rope of negligible mass is wrapped around the drum and is attached to a load of 15kg which is held 2.4m above the ground initially. Determine:
• the linear acceleration of the 15kg load when the brake preventing the drum from rotating is released and
• the velocity with which the 15kg load will impact the ground with.

(Assume the acceleration due to gravity is 9.8 m/s2.)

Homework Equations

q = qo + wo t + (1/2)a t2
w2 = wo
2 + 2 a q

to start, i am not looking the answer and i just want someone to please show me how to get the linear acceleration

thanks

 

[tiny-tim]

welcome to pf!

hi brooker2009uk! welcome to pf!

(btw, this is a fairly standard dynamics problem also, so you'll get answered sooner if you post future questions like this in the physics homework forum )

you'll need F = ma for the load, and τ = Iα for the drum …

(and also the rolling constraint, a = rα)

call the tension "T" …

what do you get? ​

 

[brooker2009uk]

thank you, that is getting the torque but i need an equation to get the linear acceleration of the load when the brake is released

 

[tiny-tim]

thank you, that is getting the torque but i need an equation to get the linear acceleration of the load when the brake is released

yes, that's F = ma !

get on with it! ​

 

[DeeNos]

I am not able to provide specific solutions to homework questions. However, I can guide you in the right direction and provide some general information that may help you solve this problem.

First, it is important to understand the concept of torque, which is the force that causes an object to rotate. In this case, the torque is being applied by the rope wrapped around the drum. The amount of torque applied depends on the force applied by the rope and the distance between the force and the axis of rotation (in this case, the center of the drum).

Next, you will need to apply Newton's second law of motion, which states that the net force applied to an object is equal to its mass multiplied by its acceleration. In this case, the net force is the torque applied by the rope, and the acceleration is the linear acceleration of the load.

To determine the linear acceleration, you will need to use the equation for torque (T = F x r) and equate it to the net force (F = ma). This will allow you to solve for the linear acceleration.

Once you have determined the linear acceleration, you can use the equations provided (q = qo + wo t + (1/2)a t2 and w2 = wo2 + 2 a q) to calculate the velocity of the load when it impacts the ground. Remember to include the acceleration due to gravity in your calculations.

I hope this helps guide you in solving the problem. Remember to always show your work and double check your calculations to ensure accuracy. Good luck!