Blocks with masses of 3.0 kg, 4.0 kg, and 5.0 kg are lined up in a row on a frictionless table. All three are pushed forward by a 13 N force applied to the 3.0 kg block. How much force does the 4.0 kg block exert on the 5.0 kg block?

Respuesta :

Answer:

Fc =  5.41 N

Explanation:

Newton's second law:

∑F = m*a Formula (1)

∑F : algebraic sum of the forces in Newton (N)

m : mass s (kg)

a : acceleration  (m/s²)

Newton's second law for the set of the three blocks

F =  13 N

m=3.0 kg+ 4.0 kg+5.0 kg = 12 kg

F = m*a

13 = 12*a

a = 13 / 12

a = 1.083 m/s² : acceleration of the set of the three blocks

Newton's second law for the  5.0 kg block

m= 5.0 kg

a = 1.083 m/s²

Fc: Contact force of the 4 kg block on the 5 kg block

Fc =  5.0 kg * 1.083 m/s²

Fc =  5.41 N

The force that the 4.0 kg block exerts on the 5.0 kg block is 7.581N

According to Newton's second law of motion:

[tex]\sum F = ma[/tex]

If we have blocks with masses of 3.0 kg, 4.0 kg, and 5.0 kg are lined up in a row on a frictionless table, the total mass is expressed as:

Total mass = 3.0 + 4.0 + 5.0

Total mass = 12.0kg

Get the total acceleration "a"

[tex]a=\frac{\sum F}{m}\\a = \frac{13}{12.0} \\a=1.083m/s^2[/tex]

To calculate the force that the 4.0kg block exerts on the 5.0 kg block, we will use the formula above to have;

[tex]F = ma\\ F =(3.0+4.0)(1.083)\\F=7 \times 1.083\\F= 7.581N[/tex]

Hence the force that the 4.0 kg block exerts on the 5.0 kg block is 7.581N

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