Answer:
1,050 Joules
Explanation:
<u>Step 1:</u> work done in moving the box 30 meters
work done = force X distance
= 25N X 30 = 750 Joules
<u>Step 2: </u>calculate total internal energy
Total internal energy = work done + kinetic energy
= 750 Joules + 300 Joules
= 1,050 Joules = 1.05 KJ
Answer:
165.529454
Explanation:
According to the Pythagorean Theorem for calculating the lengths of a right angle triangle's sides, a^2 + b+2 = c^2, where c is the longest side (and the side opposing the right angle). So in your case it would be 150*150 + 70*70 = 27400. And √ 27400 is your answer.
Answer: ![240\ rad/s^2](https://tex.z-dn.net/?f=240%5C%20rad%2Fs%5E2)
Explanation:
Given
Length of beam ![l=2\ m](https://tex.z-dn.net/?f=l%3D2%5C%20m)
mass of beam ![m=5\ kg](https://tex.z-dn.net/?f=m%3D5%5C%20kg)
Two forces of equal intensity acted in the opposite direction, therefore, they create a torque of magnitude
![\tau =F\times l=200\times 2=400\ N.m](https://tex.z-dn.net/?f=%5Ctau%20%3DF%5Ctimes%20l%3D200%5Ctimes%202%3D400%5C%20N.m)
Also, the beam starts rotating about its center
So, the moment of inertia of the beam is
![I=\dfrac{ml^2}{12}=\dfrac{5\times 2^2}{12}\\\\I=\dfrac{5}{3}\ kg.m^2](https://tex.z-dn.net/?f=I%3D%5Cdfrac%7Bml%5E2%7D%7B12%7D%3D%5Cdfrac%7B5%5Ctimes%202%5E2%7D%7B12%7D%5C%5C%5C%5CI%3D%5Cdfrac%7B5%7D%7B3%7D%5C%20kg.m%5E2)
Torque is the product of moment of inertia and angular acceleration
![\Rightarrow \tau=I\alpha\\\\\Rightarrow 400=\dfrac{5}{3}\times \alpha\\\\\Rightarrow \alpha =240\ rad/s^2](https://tex.z-dn.net/?f=%5CRightarrow%20%5Ctau%3DI%5Calpha%5C%5C%5C%5C%5CRightarrow%20400%3D%5Cdfrac%7B5%7D%7B3%7D%5Ctimes%20%5Calpha%5C%5C%5C%5C%5CRightarrow%20%5Calpha%20%3D240%5C%20rad%2Fs%5E2)
Answer:
12.5 m/s
Explanation:
From the question given above, the following data were obtained:
Initial velocity (u) = 0 m/s
Height (h) = 8 m
Final velocity (v) at 8 m above the lowest point =?
NOTE: Acceleration due to gravity (g) = 9.8 m/s²
The velocity of the roller coaster at 8 m above the lowest point can be obtained as follow:
v² = u² + 2gh
v² = 0² + (2 × 9.8 × 8)
v² = 0 + 156.8
v² = 156.8
Take the square root of both side
v = √156.8
v = 12.5 m/s
Therefore, the velocity of the roller coaster at 8 m above the lowest point is 12.5 m/s.