Question
A mass \(\mathrm{m}_2=1.0 \mathrm{~kg}\), on a \(36.1^{\circ}\) incline, is connected to a mass \(\mathrm{m}_1=6.1 \mathrm{~kg}\), on a horizontal surface. The surfaces and the pulley are frictionless. If \(F=22.5 \mathrm{~N}\), what is the magnitude of the tension in the connecting cord?
▶️Answer/Explanation
Ans:
Applying $F=ma$ for whole system ,
$F-m_2gsin\theta=(m_1+m_2)a_{sys}$
$22.5-1\times 9.8\times sin(36.1^{\circ})=(1+6.1)a_{sys}$
$22.5-5.77=7.1\times a_{sys}$
$a_{sys}=\frac{16.72}{7.1} \Rightarrow 2.355~\rm{m/s^2}$
Now , applying $F=ma$ for $m_1$
$T=m_1(a_{sys})$
$T=6.\times 2.355 \Rightarrow 14.3~\rm{N}$
Question
An object of mass m moving along the x-axis with velocity v is slowed by a force F = -kv, where k is a constant. At time t = 0, the object has velocity vo at position x = 0, as shown above.
a. What is the initial acceleration (magnitude and direction) produced by the resistance force?
b. Derive an equation for the object’s velocity as a function of time t, and sketch this function on the axes below. Let a velocity directed to the right be considered positive.
c. Derive an equation for the distance the object travels as a function of time t and sketch this function on the axes below.
d. Determine the distance the object travels from t = 0 to t = ∞.
Answer/Explanation
Ans:
a. F = ma; F = –kv = ma; a0 = –kv0
b.
c.
d. at t = ∝, 𝑥 = \(\frac{mv_{0}}{k}\)