Question 1:
A force, F acts on a body of mass 5 kg.
(a) If the body accelerates uniformly from 2 m s–1 to 8 m s–1, determine the value of F.
(b) If F = 10 N, determine the displacement of the body 6 seconds after the body starts to move from rest.
Answer:
(a)
$$ \begin{aligned} m & =5 \mathrm{~kg} \\ u & =2 \mathrm{~ms}^{-1} \\ v & =8 \mathrm{~ms}^{-1} \\ t & =2 \mathrm{~s} \end{aligned} $$
$$ \begin{aligned} F & =m a \\ F & =\frac{m(v-u)}{t} \\ & =\frac{5(8-2)}{2} \\ & =\frac{30}{2} \\ & =15 \mathrm{~N} \end{aligned} $$
(b)
$$ \begin{aligned} m & =5 \mathrm{~kg} \\ F & =10 \mathrm{~N} \\ u & =0 \mathrm{~ms}^{-1} \\ t & =6 \mathrm{~s} \\ a & =? \\ s & =? \end{aligned} $$
$$ \begin{aligned} & a=\frac{F}{m}=\frac{10}{5} \\ & \quad a=2 \mathrm{~ms}^{-2} \\ & s=u t+\frac{1}{2} a t^2 \\ & s=0+\frac{1}{2}(2)(6)^2 \\ & =36 \mathrm{~m} \end{aligned} $$
A force, F acts on a body of mass 5 kg.
(a) If the body accelerates uniformly from 2 m s–1 to 8 m s–1, determine the value of F.
(b) If F = 10 N, determine the displacement of the body 6 seconds after the body starts to move from rest.
Answer:
(a)
$$ \begin{aligned} m & =5 \mathrm{~kg} \\ u & =2 \mathrm{~ms}^{-1} \\ v & =8 \mathrm{~ms}^{-1} \\ t & =2 \mathrm{~s} \end{aligned} $$
$$ \begin{aligned} F & =m a \\ F & =\frac{m(v-u)}{t} \\ & =\frac{5(8-2)}{2} \\ & =\frac{30}{2} \\ & =15 \mathrm{~N} \end{aligned} $$
(b)
$$ \begin{aligned} m & =5 \mathrm{~kg} \\ F & =10 \mathrm{~N} \\ u & =0 \mathrm{~ms}^{-1} \\ t & =6 \mathrm{~s} \\ a & =? \\ s & =? \end{aligned} $$
$$ \begin{aligned} & a=\frac{F}{m}=\frac{10}{5} \\ & \quad a=2 \mathrm{~ms}^{-2} \\ & s=u t+\frac{1}{2} a t^2 \\ & s=0+\frac{1}{2}(2)(6)^2 \\ & =36 \mathrm{~m} \end{aligned} $$
Question 2:
A force of 80 N acts on a stationary object for 7 seconds and causes the object to reach a velocity of 35 m s–1. Calculate:
(a) the mass of the object.
(b) the displacement of the object.
Answer:
(a)
$$ \begin{aligned} F & =80 \mathrm{~N} \\ t & =7 \mathrm{~s} \\ u & =0 \mathrm{~ms}^{-1} \\ v & =35 \mathrm{~ms}^{-1} \end{aligned} $$
$$ \begin{aligned} F & =m a \\ F & =\frac{m(v-u)}{t} \\ 80 & =\frac{m(35-0)}{7} \\ m & =\frac{80 \times 7}{35} \\ & =16 \mathrm{~kg} \end{aligned} $$
(b)
$$ \begin{aligned} s & =\frac{1}{2}(u+v) t \\ & =\frac{1}{2}(0+35) 7 \\ & =\frac{245}{2} \\ & =122.5 \mathrm{~m} \end{aligned} $$
A force of 80 N acts on a stationary object for 7 seconds and causes the object to reach a velocity of 35 m s–1. Calculate:
(a) the mass of the object.
(b) the displacement of the object.
Answer:
(a)
$$ \begin{aligned} F & =80 \mathrm{~N} \\ t & =7 \mathrm{~s} \\ u & =0 \mathrm{~ms}^{-1} \\ v & =35 \mathrm{~ms}^{-1} \end{aligned} $$
$$ \begin{aligned} F & =m a \\ F & =\frac{m(v-u)}{t} \\ 80 & =\frac{m(35-0)}{7} \\ m & =\frac{80 \times 7}{35} \\ & =16 \mathrm{~kg} \end{aligned} $$
(b)
$$ \begin{aligned} s & =\frac{1}{2}(u+v) t \\ & =\frac{1}{2}(0+35) 7 \\ & =\frac{245}{2} \\ & =122.5 \mathrm{~m} \end{aligned} $$