Question

Груз массой 20 кг равноускоренно опускают на веревке на высоту 10 м за 4 с. определите работу силы натяжения веревки и работу силы тяжести при этом перемещение груза

Answer 1

A(T) - ?
Aтяж - ?
________________

1) A(T) = T h cos180

по 2з. Ньютона: mg - T = ma,

T = m (g - a).

из кинематики (пусть v0=0): h = a t^2 / 2 => a = 2h / t^2

тогда A(T) = -mh (g - (2h/t^2))

A(T) = -2*10^2 (10 - (20/16)) = - 1750 Дж

2) Aтяж = - ΔEp = - mgΔh = - 2 000 Дж

Answer 2

Calculation of Work Done by Tension Force and Gravity

To determine the work done by the tension force and gravity when a 20 kg mass is uniformly accelerated down a rope to a height of 10 m in 4 seconds, we can use the following formulas:

1. The work done by a force is given by the equation: work = force × displacement × cos(θ), where θ is the angle between the force and the displacement.

2. The work done by gravity is calculated as: work_gravity = m × g × h, where m is the mass, g is the acceleration due to gravity, and h is the height.

3. The work done by the tension force is equal to the negative of the work done by gravity, as the tension force opposes the force of gravity.

Let's calculate the work done by the tension force and gravity step by step.

Calculation Steps:

1. Calculate the work done by gravity: - Mass (m) = 20 kg - Acceleration due to gravity (g) = 9.81 m/s^2 - Height (h) = 10 m

Using the formula work_gravity = m × g × h, we can calculate the work done by gravity: - work_gravity = 20 kg × 9.81 m/s^2 × 10 m = 1962 J

Therefore, the work done by gravity is 1962 Joules.

2. Calculate the work done by the tension force: - Since the tension force opposes the force of gravity, the work done by the tension force is equal to the negative of the work done by gravity. - Therefore, the work done by the tension force is -1962 J.

Therefore, the work done by the tension force is -1962 Joules.

Answer:

The work done by the tension force is -1962 Joules and the work done by the force of gravity is 1962 Joules when a 20 kg mass is uniformly accelerated down a rope to a height of 10 m in 4 seconds.

Please let me know if you need any further clarification.