Question

Груз массой 97 кг перемещают с помощью веревки с постоянной скоростью по горизонтальной поверхности.Угол между веревкой и этой поверхностью равен 30 градусам. Коэффициент трения равен 0,2 Определите работу силы натяжения веревки на пути 100 м

Answer 1

Работа в данном случае будет вычисляться по формуле А=мю(коэффициент трения)F*Scos$\alpha$, в данном случае F=mg, F=97 кг*10 Н/кг=970Н, работа будет равна A=0.2*970 Н*100м*cos30=16878Дж

Answer 2

Problem Analysis

We are given the following information: - Mass of the object: 97 kg - Angle between the rope and the horizontal surface: 30 degrees - Coefficient of friction: 0.2 - Distance traveled: 100 m

We need to determine the work done by the tension force on the object.

Solution

To find the work done by the tension force, we need to calculate the tension force and then multiply it by the distance traveled.

1. Calculate the tension force: - The tension force can be found by resolving the weight of the object into components parallel and perpendicular to the surface. - The component of weight parallel to the surface is given by: F_parallel = m * g * sin(theta), where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and theta is the angle between the rope and the surface. - The component of weight perpendicular to the surface is given by: F_perpendicular = m * g * cos(theta). - The tension force is equal to the sum of the component of weight parallel to the surface and the force of friction: T = F_parallel + F_friction. - The force of friction can be calculated using the equation: F_friction = coefficient_of_friction * F_perpendicular.

2. Calculate the work done by the tension force: - The work done by a force is given by the equation: work = force * distance. - In this case, the force is the tension force and the distance is the distance traveled.

Let's calculate the tension force and the work done.

Calculation

Given: - Mass of the object (m): 97 kg - Angle between the rope and the horizontal surface (theta): 30 degrees - Coefficient of friction (coefficient_of_friction): 0.2 - Distance traveled (distance): 100 m

1. Calculate the tension force: - Calculate the component of weight parallel to the surface: F_parallel = m * g * sin(theta). - Calculate the component of weight perpendicular to the surface: F_perpendicular = m * g * cos(theta). - Calculate the force of friction: F_friction = coefficient_of_friction * F_perpendicular. - Calculate the tension force: T = F_parallel + F_friction.

2. Calculate the work done by the tension force: - Calculate the work done: work = T * distance.

Let's plug in the values and calculate the tension force and the work done.

Calculation

Given: - Mass of the object (m): 97 kg - Angle between the rope and the horizontal surface (theta): 30 degrees - Coefficient of friction (coefficient_of_friction): 0.2 - Distance traveled (distance): 100 m

1. Calculate the tension force: - Calculate the component of weight parallel to the surface: F_parallel = m * g * sin(theta). - Substituting the values: F_parallel = 97 kg * 9.8 m/s^2 * sin(30 degrees). - Calculating: F_parallel ≈ 475.53 N. - Calculate the component of weight perpendicular to the surface: F_perpendicular = m * g * cos(theta). - Substituting the values: F_perpendicular = 97 kg * 9.8 m/s^2 * cos(30 degrees). - Calculating: F_perpendicular ≈ 843.32 N. - Calculate the force of friction: F_friction = coefficient_of_friction * F_perpendicular. - Substituting the values: F_friction = 0.2 * 843.32 N. - Calculating: F_friction ≈ 168.66 N. - Calculate the tension force: T = F_parallel + F_friction. - Substituting the values: T = 475.53 N + 168.66 N. - Calculating: T ≈ 644.19 N.

2. Calculate the work done by the tension force: - Calculate the work done: work = T * distance. - Substituting the values: work = 644.19 N * 100 m. - Calculating: work ≈ 64419 J.

Answer

The work done by the tension force on the object over a distance of 100 m is approximately 64419 J.

Please note that the above calculations are based on the given information and assumptions.