Answer:
511.1 J
Explanation:
We are given that
Mass of wood block=m=3 kg
Vertical distance,h=23 m
Horizontal distance =x=30 m
Distance traveled in downward direction y=40 m
Initial velocity,u=0
[tex]y=ut+\frac{1}{2} gt^2[/tex]
Where [tex]g=9.8 m/s^2[/tex]
[tex]40=0+\frac{1}{2}(9.8)t^2=4.9t^2[/tex]
[tex]t^2=\frac{40}{4.9}[/tex]
[tex]t=\sqrt{\frac{40}{4.9}}=2.86 s[/tex]
[tex]x=v_x\times t[/tex]
[tex]30=v_x(2.86)[/tex]
[tex]v=v_x=\frac{30}{2.86}=10.49 m/s[/tex]
By work energy theorem
Change in kinetic energy=Work done= mgh-W
[tex]\frac{1}{2}mv^2-\frac{1}{2}mu^2=3\times 9.8\times 23-W[/tex]
[tex]\frac{1}{2}(3)(10.49)^2-0=676.2-W[/tex]
[tex]W=676.2-\frac{1}{2}(3)(10.49)^2=511.1 J[/tex]
Hence, the work done due to friction on the block as it slides down the ramp=511.1 J
This question involves the concepts of the law of conservation of energy and the equations of motion.
The work done by the friction on the block as it slides down the ramp is "0.51 J".
First, we will find the time taken for the motion using the second equation of motion in the vertical direction:
[tex]h=v_it+\frac{1}{2}gt^2\\[/tex]
where,
h = vertical distance covered by the block = 40 mm = 0.04 m
vi = initial speed in vertical direction = 0 m/s
t = time taken = ?
g = acceleration due to gravity = 9.81 m/s^2
Therefore,
[tex]0.04\ m=(0\ m/s)(t)+\frac{1}{2}(9.81\ m/s^2)(t)^2\\\\t=\sqrt{\frac{2(0.04\ m)}{9.81\ m/s^2}}\\\\t=0.09\ s[/tex]
Now, we will consider the horizontal motion. Since horizontal motion is uniform due to no friction. Therefore,
[tex]s=vt[/tex]
where,
s = horizontal distance covered by the block = 30 mm = 0.03 m
v = final horizontal speed = ?
Therefore,
[tex]v=\frac{0.03\ m}{0.09\ s}[/tex]
v = 0.333 m/s
Now, we apply the law of conservation of energy to this scenario:
[tex]Gain\ in\ K.E + W = Loss\ of\ potential\ energy\\\\\frac{1}{2}mv^2+W=mgh\\\\W=mgh-\frac{1}{2}mv^2\\\\[/tex]
here,
W = work done by friction = ?
h = height of slide = 23 mm = 0.023 m
m = mass of block = 3 kg
Therefore,
[tex]W=(3\ kg)(9.81\ m/s^2)(0.023\ m)-\frac{1}{2}(3\ kg)(0.333\ m/s)^2[/tex]
W = 0.677 J - 0.167 J
W = 0.51 J = 510 mJ
Learn more about the law of conservation of energy here:
brainly.com/question/20971995?referrer=searchResults
The attached picture explains the law of conservation of energy.
