# Speed of Block Dropped from 0.41m: Exploring Forces

• MellowOne
In summary, the question involves a 1.3 kg block attached to a string and a pulley with a radius of 7.2 cm. The block is released from rest and the speed of the block after falling through a height of 0.41 m is to be found. Using the third kinematics equation with initial velocity of 0, the speed is calculated to be 2.836 m/s. However, this may not be accurate as the acceleration may be affected by the string and pulley system. The question also asks about the effect of a small lead weight attached to the rim of the pulley on the block's speed.
MellowOne

## Homework Statement

A 1.3 kg block is tied to a string that is wrapped around the rim of a pulley of radius 7.2 cm. The block is released from rest.

(a) Assuming the pulley is a uniform disk with a mass of 0.30 kg, find the speed of the block after it has fallen through a height of 0.41 m.

(b) If a small lead weight is attached near the rim of the pulley and this experiment is repeated, will the speed of the block increase, decrease, or stay the same? Explain.

Kinematics?

## The Attempt at a Solution

Since the block was just falling I assumed you could just use the 3rd kinematics and solve for vf with vi = 0. Substituting the variables I got Vf = sqrt (2 x 9.81m/s^2 x .41m) and the answer came out to be 2.836m/s. Any reason why this wouldn't work?

You can't assume a=9.81 m/s^2, though. If the block is attached to the pulley by a string, don't you think that might change its acceleration?

I would say that your solution is correct. The third kinematics equation, vf^2 = vi^2 + 2ad, is appropriate in this situation since the block is initially at rest and only under the influence of gravity. Your solution correctly takes into account the acceleration due to gravity (9.81m/s^2) and the distance the block has fallen (0.41m).

As for the second part of the question, if a lead weight is attached near the rim of the pulley, the speed of the block will decrease. This is because the added weight will increase the moment of inertia of the pulley, making it harder for the block to rotate the pulley and thus slowing down its descent. This can be explained using the equation for rotational motion, I = mr^2, where I is the moment of inertia, m is the mass, and r is the radius of the pulley. By adding a lead weight, the value of I increases, resulting in a decrease in the angular acceleration of the pulley and a decrease in the speed of the block.

## 1. What is the purpose of exploring the speed of a block dropped from 0.41m?

The purpose of this experiment is to understand the relationship between the forces acting on a block and its resulting speed when dropped from a specific height.

## 2. What materials are needed for this experiment?

The materials needed for this experiment include a block of known mass, a measuring tape or ruler, and a stopwatch or timer.

## 3. How is the speed of the block calculated?

The speed of the block is calculated by dividing the distance the block drops (0.41m) by the time it takes to drop and reach the ground. This is known as the average speed formula, where speed = distance/time.

## 4. How does the force of gravity affect the speed of the block?

The force of gravity is the main force acting on the block when dropped from a height. As the block falls, it accelerates due to the force of gravity, increasing its speed. The greater the force of gravity, the faster the block will fall.

## 5. What other factors may affect the speed of the block?

Other factors that may affect the speed of the block include air resistance and the shape and mass of the block. Air resistance can slow down the block's descent, while a heavier or more streamlined block may fall faster than a lighter or less aerodynamic one.

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