Two blocks are stacked on top of each other on the floor of an elevator as shown. The mass of Block 2 (bottom) is 3.0 kg and the mass of Block 1 (upper) is 2.0 kg. The elevator is accelerating upwards at a constant rate of 1.6 m/s2.Find the magnitude of the force that Block 2 exerts on the floor of the elevator.

Two blocks are stacked on top of each other on the floor of an elevator as shown The mass of Block 2 bottom is 30 kg and the mass of Block 1 upper is 20 kg The class=

Respuesta :

The magnitude of the force exerted by Block 2 takes into account the mass of Block 1 because it's above it, so the force must include both masses.

Use Newton's Second Law.

[tex]\Sigma F_y=ma[/tex][tex]\begin{gathered} N-W=(m_1+m_2)a \\ N-(m_1+m_2)g=(m_1+m_2)a_{} \\ N=(m_1+m_2)(g+a) \end{gathered}[/tex]

Use the given magnitudes to find the force N.

[tex]\begin{gathered} N=(2\operatorname{kg}+3\operatorname{kg})(9.8\cdot\frac{m}{s^2}+1.6\cdot\frac{m}{s^2}) \\ N=5\operatorname{kg}\cdot11.4\cdot\frac{m}{s^2} \\ N=57N \end{gathered}[/tex]

Therefore, the force exerted by Block 2 is 57 Newtons.