Question

Через неподвижный блок перекинута невесомая нерастяжимая нить, на которой подвешены два груза массой 5 кг и 4 кг. С каким ускорением движутся грузы? Чему равно натяжение нити( ответы округлите до сотых)?

Answer 1

m1=4

m2=5

m2*g -T=m2*a   (1)

T-m1*g=m1*a     (2)   сложим 1 и 2

a=(m2*g-m1*g)/(m2+m1)=...............

Подставь и найди ускорение, а найти Т можно подставив в любое из 1 или 2

Answer 2

Calculation of Acceleration and Tension in the String

To determine the acceleration and tension in the string, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.

Let's denote the mass of the first object (5 kg) as m1 and the mass of the second object (4 kg) as m2.

The net force acting on the system is the tension in the string (T) pulling both objects upward. Since the system is in equilibrium, the net force is equal to zero.

Using Newton's second law, we can write the following equations:

For the first object (m1): m1 * a = T - m1 * g

For the second object (m2): m2 * a = T - m2 * g

Where: a is the acceleration of the system, g is the acceleration due to gravity (approximately 9.8 m/s^2).

To find the acceleration (a) and tension (T), we can solve these equations simultaneously.

Solving the Equations

Let's substitute the given values into the equations:

For the first object (m1 = 5 kg): 5 * a = T - 5 * 9.8

For the second object (m2 = 4 kg): 4 * a = T - 4 * 9.8

Simplifying the equations:

5a = T - 49 4a = T - 39.2

Now, we can solve these equations to find the values of acceleration (a) and tension (T).

Subtracting the second equation from the first equation:

5a - 4a = (T - 49) - (T - 39.2) a = 9.2

Substituting the value of a back into one of the equations:

5 * 9.2 = T - 49 46 = T - 49 T = 95

Answer

Therefore, the acceleration of the system is 9.2 m/s^2 and the tension in the string is 95 N.

Please note that the values have been rounded to the nearest hundredth as requested.