A uniform rod of length L rests on a frictionless horizontal surface. The rod pivots about a fixed frictionless axis at one end.
1 answer:
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The mass M1 is 7.8 kg
Explanation:
Block M1 is hanging on the string while block M2 is on the frictionless ramp.
We have to write the equations of motion for the two blocks.
- For M1, the only two forces acting on it are the force of gravity (downward) and the tension in the string T (upward). So we can write
where
is the mass of the block
is the acceleration of gravity
is the acceleration of the system
- For M2, the only two forces acting on it are the tension in the string T (acting up along the ramp) and the component of the gravity acting down along the ramp, . So the equation of motion is
where
is the mass of the 2nd block
is the angle of the ramp
In order for the two blocks to be in equilibrium, the acceleration must be zero:
So the two equations become:
Isolating T from the 1st equation,
And substituting into the 2nd equation, we can find the value of the mass :
Learn more about acceleration and forces:
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Answer: The force needed is 140.22 Newtons.
Explanation:
The key assumption in this problem is that the acceleration is constant along the path of the barrel bringing the pellet from velocity 0 to 155 m/s. This means the velocity is linearly increasing in time.
The force exerted on the pellet is
F = m a
In order to calculate the acceleration, given the displacement d,
we will need to determine the time t it took for the pellet to make the distance through the barrel of 0.6m. That time can be determined using the average velocity of the pellet while traveling through the barrel. Since the velocity is a linear function of time, as mentioned above, the average is easy to calculate as:
This value can be used to determine the time for the pellet through the barrel:
Finally, we can use the above to calculate the force: