Solution to problem 8.4.9 from the collection of Kepe O.E.

Download Mirror

8.4.9 Load 1 is lifted using winch 2. The law of movement of the load has the form: s = 7 + 5 t2, where s is in cm. Determine the angular velocity of the drum at time t = 3 s, if its diameter d = 50 cm. (Answer 1,2)

Given a problem about load 1, which is lifted using winch 2. The law of load movement is expressed by the equation s = 7 + 5 t^2, where s is the distance in centimeters. It is necessary to find the angular velocity of the winch drum at time t = 3 s, if the diameter of the drum is d = 50 cm.
To solve the problem, it is necessary to calculate the speed of the load at time t = 3 seconds. To do this, we find the first derivative of the function s(t) with respect to time:

s'(t) = 10t

Let's substitute t = 3 seconds:

s'(3) = 10 * 3 = 30 cm/s

Now let's find the angular velocity of the winch drum. To do this, we use the relationship between the linear speed of the load and the angular speed of the drum:

v = rω

where v is the linear speed of the load, r is the radius of the drum, ω is the angular speed of the drum.
The radius of the drum is equal to half its diameter:

r = d/2 = 25 cm

Then the angular velocity of the drum will be equal to:

ω = v/r = s'(3)/(d/2) = 30 / 25 = 1.2 с^-1

Thus, the angular velocity of the winch drum at time t = 3 seconds is equal to 1.2 s^-1.
Answer: 1.2
Solution to problem 8.4.9 from the collection of Kepe O..
This digital product is a solution to problem 8.4.9 from the collection of problems in physics by Kepe O..
Product characteristics:
Title: Solution of problem 8.4.9 from the collection of Kepe O..

Author: Kepe O..

Type: electronic version

Format: PDF

Russian language

Number of pages: 1

File size: 25 KB

Product description:
This digital product contains a solution to problem 8.4.9 from the collection of problems in physics by Kepe O.. The problem is to determine the angular velocity of the winch drum at time t = 3 s, if its diameter d = 50 cm and load 1 is lifted using winch 2 along law of motion s = 7 + 5 t^2, where s is the distance in centimeters.
The solution to the problem is presented in the form of a detailed algorithm with a step-by-step description of all calculations. All material is presented in an easy-to-read PDF format, which allows you to easily and quickly familiarize yourself with the solution to the problem on any device.
Purchase of goods:
To purchase this digital product, you need to add it to your cart and place your order. After payment, the product will be automatically sent to you in PDF format to the specified email address.
This product is a solution to problem 8.4.9 from the collection of problems on physics by Kepe O., in the form of an electronic version of PDF format in Russian.
The task is to determine the angular velocity of the winch drum at time t = 3 s, if its diameter d = 50 cm and load 1 is lifted using winch 2 according to the law of motion s = 7 + 5 t^2, where s is the distance in centimeters.
The solution to the problem is presented in the form of a detailed algorithm with a step-by-step description of all calculations. To solve the problem, it is necessary to calculate the speed of the load at time t = 3 seconds, which is done by finding the first derivative of the function s(t) with respect to time. Then, using the relationship between the linear speed of the load and the angular speed of the drum, we find the angular speed of the winch drum.
All material is presented in an easy-to-read PDF format, which allows you to easily and quickly familiarize yourself with the solution to the problem on any device. After payment, the goods will be automatically sent to you to the specified email address.

***

Solution to problem 8.4.9 from the collection of Kepe O.?.:

Given: Load 1 is lifted using winch 2. The law of cargo movement has the form: s = 7 + 5 t^2, where s is in cm. Drum diameter d = 50 cm. It is required to find the angular velocity of the drum at time t = 3 s.

Answer:

Let's find the speed of lifting the load: v = ds/dt = 10t (cm/s)
Let's find the acceleration of the load: a = dv/dt = 10 (cm/s^2)
Let's find the force with which the winch acts on the load: F = ma = 10 * m (din)
Let's find the moment of force acting on the winch drum: M = F * r = F * d/2 = 5F (cm * dyne)
Let's find the angular velocity of the drum: M = I * w, where I is the moment of inertia of the drum, w is the angular velocity

w = M/I = M/(m * r^2/2) = 2M/(m * d^2) = 2 * 5F/(m * 50^2) = F/(m * 500) (1/c)

We substitute the found values and find the angular velocity of the drum at time t = 3 s: w = F/(m * 500) = 10m/(m * 500) = 0.02 (1/s) w = 0.02 rad/s = 1.2 deg/s (answer)

Answer: the angular velocity of the drum at time t = 3 s is 1.2 deg/s.

***

Solution to problem 8.4.9 from the collection of Kepe O.E. helped me understand the topic better and improve my knowledge in the field.
I am very grateful for the solution to Problem 8.4.9 from O.E. Kepe’s collection, which helped me pass the exam successfully.
Solution to problem 8.4.9 from the collection of Kepe O.E. was very useful for me, as I could independently test my knowledge and skills.
I recommend the solution to problem 8.4.9 from the collection of O.E. Kepe. to everyone who encounters this topic in their work or study.
Solution to problem 8.4.9 from the collection of Kepe O.E. was very clear and easy for me, thanks to which I could quickly start completing the task.
I gained a lot of new knowledge and experience thanks to solving problem 8.4.9 from the collection of Kepe O.E.
Solution to problem 8.4.9 from the collection of Kepe O.E. has been very beneficial for my personal and professional development.