Question

I need help with #7 I can’t seem to figure it out

Answer 1

Given:

Mass, m1 = 10.0 kg

Mass, m2 = 3.60 kg

θ = 37.0 degrees

Let's solve for the following:

(a) Magnitude of the acceleration of 3.60 kg box.

From Newton's second law, we have:

Fnet = ma

m₁g - T = m₁a................equation 1

Applying Newton's second law along an inclined plane, we have:

T - m₂gsinθ = m₂a.............equation 2

Add both equation 1 and 2:

m₁g - T + T - m₂gsinθ = m₁a + m₂a

m₁g - m₂gsinθ = a(m₁ + m₂)

To find the magnitude of aceleration for m2, rewrite the equation for a:

`\begin{gathered} a=(m_(1)g-m_(2)gsin\theta)/(m_(1)+m_(2)) \\ \\ a=(g(m_1-m_2sin\theta))/(m_1+m_2) \end{gathered}`

Where:

g is acceleration due to gravity = 9.8 m/s²

`\begin{gathered} a=(9.8(10-3.6\sin 37))/(10+3.6) \\ \\ a=5.64m/s^2 \end{gathered}`

The manitude of acceleration of the 3.60 kg box is 5.64 m/s².

(b). What is he tension in the cable?

To find the tension in the cable, apply the formula:

`\begin{gathered} m_1g-T=m_1a \\ \\ T=m_1g-m_1a \\ \\ T=m_1\mleft(g-a\mright) \\ \\ T=10.0(9.8-5.64) \\ \\ T=41.6\text{ N} \end{gathered}`

The tension in the cable is 41.6 N

ANSWER:

(a) 5.64 m/s²

(b) 41.6 N