Finding acceleration of a pulley using forces?

In summary, the problem involves a ramp with a 45-degree angle, a 10kg block on the ramp, and a pulley with a 100kg block hanging from it at the top of the ramp. The pulley itself weighs 50kg and has a radius of 1m. The goal is to find the acceleration of the blocks. Helpful equations include torque=radius x force x sin(theta), torque=inertia of the pulley x angular acceleration, and inertia of the pulley=.5 x mass of the pulley x (radius)^2. However, it is unclear how to find the forces T1 and T2.
  • #1
battosi58
1
0

Homework Statement


alright here is the problem: a ramp that is 45 degrees angle has a block on it with mass 10 kg. then at the top of the inclined plane/ramp, there is a pulley with another block hanging down it. the mass of the hanging block is 100 kg. the mass of the pulley itself is 50kg. the radius of the pulley is 1meter. this is all i know.
i have to find the acceleration of the blocks.

Homework Equations



here are are some helpful equations: Torque=radius x Force x sin(theta)

Torque = Inertia of the pulley x angular acceleration.

inertia of the pulley = .5 x Mass of the pulley x radius^2


The Attempt at a Solution



the basic formula i am using is that R x T1 + R x T2 sin(theta) =Inertia x angular acceleration. i do not know if i am heading in the right direction.
 
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  • #2
for this problem, R would be 1m, theta would be 45 degrees, inertia would be .5 x 50kg x (1m)^2= 25 kg m^2. however, i am not sure how to find T1 and T2. can anyone help me?
 
  • #3


Firstly, it is important to note that the acceleration of the blocks will be the same since they are connected by a string and move together. Therefore, we can focus on finding the acceleration of the hanging block.

To find the acceleration, we can use Newton's second law, which states that the net force on an object is equal to its mass times its acceleration (F=ma).

First, let's consider the forces acting on the hanging block. The weight of the block (100 kg) will be pulling it downwards with a force of 980 N (100 kg x 9.8 m/s^2). The tension in the string will be pulling the block upwards with a force of T.

Next, let's look at the forces acting on the pulley. The weight of the pulley (50 kg) will be pulling it downwards with a force of 490 N (50 kg x 9.8 m/s^2). The tension in the string will also be acting on the pulley, pulling it upwards with a force of T.

Since the pulley is not accelerating (it is rotating at a constant speed), the net force on it must be zero. This means that the tension in the string must be equal to the weight of the pulley (T=490 N).

Now, we can use the fact that the acceleration of the hanging block is equal to the angular acceleration of the pulley multiplied by the radius of the pulley (a=αr). We can also use the equation for torque (τ=rF) to relate the forces acting on the pulley and the hanging block.

Plugging in the values, we get:

980 N - T = 100 kg x a

T = 490 N

r x 490 N + r x 980 N sin(45) = (0.5 x 50 kg x 1 m^2) x α

Solving for a, we get a= 5.9 m/s^2.

Therefore, the acceleration of the blocks is 5.9 m/s^2.
 

1. What is the formula for finding acceleration of a pulley using forces?

The formula for finding acceleration of a pulley using forces is a = (F - T) / m, where a is acceleration, F is the applied force, T is the tension force, and m is the mass of the pulley.

2. How do you determine the applied force in this scenario?

The applied force can be determined by using a force meter or by measuring the weight of the object attached to the pulley. Alternatively, if the system is in equilibrium, the applied force can be calculated by multiplying the mass of the object by the acceleration due to gravity (9.8 m/s²).

3. What is the role of tension force in finding acceleration of a pulley?

The tension force is crucial in determining the acceleration of the pulley because it is the force that is being exerted on the pulley due to the weight of the object attached to it. This force, along with the applied force, affects the acceleration of the pulley.

4. Can the mass of the pulley affect the acceleration?

Yes, the mass of the pulley can affect the acceleration since it is included in the formula. A heavier pulley will require a greater force to accelerate it, resulting in a lower acceleration.

5. What are the units of measurement for acceleration of a pulley?

The units of measurement for acceleration of a pulley are meters per second squared (m/s²). This is the standard unit for acceleration in the International System of Units (SI).

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