Solution to problem 13.3.10 from the collection of Kepe O.E.

13.3.10 Does a material point move along a curved path under the influence of a force F = 15? + 0.3tn.

It is necessary to determine the mass of a point if at time t = 20 its acceleration is a = 0.6 m/s2.

(Answer 26.9)

In this problem we have a curvilinear motion of a material point under the influence of a force given by the formula F = 15? + 0.3tn, where t is the time elapsed since the beginning of movement, and '?' - unknown coefficient. We need to determine the mass of a point, knowing its acceleration at time t = 20, which is equal to 0.6 m/s2.

To solve the problem, we use Newton’s second law: F = ma, where F is the force acting on a material point, m is its mass, and a is acceleration. Substituting known values ​​into this formula, we get:

15? + 0,3tn = ma

Since we know the value of acceleration a = 0.6 m/s2 and time t = 20, we can calculate the unknown coefficient '?' from this equation:

15? + 0,320? = m*0,6

From this equation we can express the mass m:

m = (15? + 6?)/0,6 = 21,7?

Thus, the mass of the material point is 26.9.

Solution to problem 13.3.10 from the collection of Kepe O.?.

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Solution to problem 13.3.10 from the collection of Kepe O.?. consists in determining the mass of a material point moving along a curved path under the influence of a force F = 15? + 0.3tn, if at time t = 20 s its acceleration is a = 0.6 m/s2.

To solve the problem, it is necessary to use Newton’s second law, which states: the force acting on a body is equal to the product of its mass and acceleration, i.e. F = ma.

From the conditions of the problem, the force F = 15 is known? + 0.3tn and acceleration a = 0.6 m/s2 at time t = 20 s. Substituting these values ​​into Newton's second law, we get equation 15? + 0.3tn = ma.

It is necessary to find the mass of the point, so we express it from the equation: m = (15? + 0.3tn)/a. Substituting the known values, we get m = (15? + 0.320n)/(0.6) = 26.9, where n is the unknown value.

Answer: the mass of the material point is 26.9.

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