Question

1. При помощи пружинного динамометра с ускорением 6м/с^2, направленным вверх, поднимают груз массой 1кг. Найти удлинение пружины динамометра , если ее жесткость 400H/м 2. мальчик массой 50 кг качается на качелях с длиннной подвеса 3м. С какой силой он давит на сиденье при прохождении среднего положения со скоростью 10 м/с? С ОПИСАНИЕМ !!!!!

Answer 1

Дано а=6 м\с2    k=400 н\м     x- ?

из уравнения динамики kx-mg=ma
x=(g-a)*m\k=1*4\400=0,01 м=1см- ответ

2) дано m=50 кг  L=R=3 м   V=10 м\с    P- ?

так как ускорение направлено вверх   P=m*(g+a)=m*(g+V^2\L)=
=50(9,8+100\3)=2156 Н

Answer 2

Calculation of Spring Extension

To find the extension of the spring in the dynamometer, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. In this case, the force applied is the weight of the mass being lifted.

The weight of an object can be calculated using the formula: weight = mass * acceleration due to gravity.

Given: - Mass of the object (m) = 1 kg - Acceleration (a) = 6 m/s^2 - Spring constant (k) = 400 N/m

To find the extension of the spring, we can use Hooke's law, which states that the force exerted by a spring is directly proportional to the extension of the spring.

Hooke's law can be written as: F = k * x, where F is the force, k is the spring constant, and x is the extension of the spring.

Rearranging the equation, we get: x = F / k.

Using the formula for weight, we can substitute the values into the equation to find the force exerted by the mass: F = m * a.

Let's calculate the extension of the spring:

Step 1: Calculate the weight of the mass: weight = mass * acceleration due to gravity weight = 1 kg * 9.8 m/s^2 weight = 9.8 N

Step 2: Calculate the force exerted by the mass: force = weight force = 9.8 N

Step 3: Calculate the extension of the spring: extension = force / spring constant extension = 9.8 N / 400 N/m extension = 0.0245 m

Therefore, the extension of the spring in the dynamometer is 0.0245 meters.

Calculation of Force on the Swing Seat

To calculate the force exerted on the swing seat by the boy, we can use the concept of centripetal force. When an object moves in a circular path, it experiences a centripetal force directed towards the center of the circle.

Given: - Mass of the boy (m) = 50 kg - Length of the swing's suspension (r) = 3 m - Speed of the swing (v) = 10 m/s

The centripetal force can be calculated using the formula: F = (m * v^2) / r, where F is the centripetal force, m is the mass, v is the velocity, and r is the radius.

Let's calculate the force exerted on the swing seat:

Step 1: Calculate the centripetal force: force = (mass * velocity^2) / radius force = (50 kg * (10 m/s)^2) / 3 m force = 1666.67 N

Therefore, the force exerted on the swing seat by the boy when passing through the middle position with a speed of 10 m/s is approximately 1666.67 Newtons.

Note: The above calculations assume ideal conditions and neglect factors such as air resistance and friction.