Problem 15.3.3 considers the movement of a material point with a mass of 0.5 kg, thrown from the surface of the Earth with a speed of 20 m/s from the position Mo and reaching a speed of 12 m/s in the position M. It is necessary to determine the work of gravity when moving the point from the position Mo to position M.
To solve the problem, we use the formula for the work of force: W = ∆E = Ek - Eko, where W is the work of force, Ek and Eko are the kinetic energy in the final and initial positions, respectively.
The initial kinetic energy of a material point is Eko = mvо^2/2 = 0.5 * 20^2/2 = 100 J, and the final one is Ek = mv^2/2 = 0.5 * 12^2/2 = 36 J Thus, the work of gravity when moving a point from position Mo to position M is equal to W = ∆E = Ek - Eko = 36 - 100 = -64 J.
Answer: -64.
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Problem 15.3.3 considers the motion of a material point with a mass of 0.5 kg, thrown from the surface of the Earth with a speed of 20 m/s from the position Mo and reaching a speed of 12 m/s at the position M. The solution of the problem includes a detailed analysis and step-by-step solution, which will help you better understand the physical laws underlying this problem.
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A digital product is offered in PDF format, which contains a detailed solution to problem 15.3.3 from the collection of Kepe O.?. The problem considers the movement of a material point with a mass of 0.5 kg, thrown from the surface of the Earth at a speed of 20 m/s and reaching a speed of 12 m/s in position M. It is necessary to determine the work of gravity when moving a point from position Mo to position M. In the solution problem, the formula for the work of force is used: W = ∆E = Ek - Eko, where W is the work of force, Ek and Eko are the kinetic energy in the final and initial positions, respectively. The initial kinetic energy of a material point is Eko = mvо^2/2 = 0.5 * 20^2/2 = 100 J, and the final one is Ek = mv^2/2 = 0.5 * 12^2/2 = 36 J Thus, the work of gravity when moving a point from position Mo to position M is equal to W = ∆E = Ek - Eko = 36 - 100 = -64 J. In addition, the digital product contains a step-by-step solution to the problem, which will help to better understand the physical laws , which are the basis of this task. The solution to the problem is presented in a beautifully designed form and can be downloaded immediately after purchase for easy access to the material at any time.
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Solution to problem 15.3.3 from the collection of Kepe O.?. consists in determining the work of gravity when moving a material point with mass m = 0.5 kg from position Mo with an initial speed vо = 20 m/s to position M with speed v = 12 m/s.
To solve the problem, you need to use the formula for calculating the work of force:
A = F * d * cos(α),
where A is the work done by the force, F is the force, d is the path traveled by the point under the influence of the force, α is the angle between the direction of the force and the direction of movement of the point.
In this problem, the force acting on a material point is the force of gravity, which is directed vertically downward. The angle between the direction of gravity and the direction of movement of the point is 180 degrees, since the point moves in the direction opposite to gravity.
Thus, the work done by gravity when moving a material point from position Mo to position M is equal to:
A = F * d * cos(α) = m * g * h,
where m is the mass of the material point, g is the acceleration of gravity, h is the height to which the point rose.
The initial kinetic energy of a point at the Mo position is:
Ek0 = (m * vо^2) / 2,
and the kinetic energy of the point at position M is equal to:
Ek = (m * v^2) / 2.
Since the work of gravity changed the kinetic energy of the point, then:
A = Ek - Ek0 = (m * v^2) / 2 - (m * vо^2) / 2 = (0,5 * 12^2 - 0,5 * 20^2) / 2 = -64 J.
Answer: the work done by gravity when moving a point from position Mo to position M is equal to -64 J.
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