Answer:
Explanation:
If friction is neglected, the wheel cannot roll and can only slide frictionlessly and will have the same velocity at the bottom of the ramp as if it had been in free fall as it has converted the same amount of potential energy.
mgh = ½mv²
v = √(2gh) = √(2(9.81)(2.00)) = 6.26418... = 6.26 m/s
However if we do not ignore all friction and the wheel rolls without slipping down the slope, the potential energy becomes linear and rotational kinetic energy
mgh = ½mv² + ½Iω²
mgh = ½mv² + ½(½mR²)(v/R)²
2gh = v² + ½v²
2gh = 3v²/2
v = √(4gh/3) =√(4(9.81)(2.00)/3) = 5.11468... = 5.11 m/s
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:

The radioactive decay is shown in the image attached to this answer
Answer:
Alpha
Explanation:
An alpha decay is said to have occurred when the mass number of the daughter nucleus decreases by four units and the atomic number of the daughter nucleus decreases by two units.
If we look at the equation from left to right, we will notice that the mass number of the daughter nucleus decreased by four units and the atomic of the daughter nucleus number by two units compared to that of the parent nucleus leading to the emission of an alpha particle.
<h2>
Answer:</h2>
Workdone = 601.33 Nm
<h2>
Explanation:</h2>
Workdone = Force(F) x horizontal distance(d).
Wordone = F x d
Where F is the horizontal component of the force
Force = 35 pounds
Recall that;
1 pound force = 4.4N
=> 35 pounds = 35 x 4.4N = 154N
=> Force = 154N
But since the rope makes a 10⁰ angle with the ground,
The horizontal component of the force F is Force x cos10⁰
=> F = 154 cos 10⁰
=> F = 154 x 0.9848
=> F = 151.66N
Horizontal distance (d) = 13 feet
Recall that;
1 foot = 0.305m
=> 13 feet = 13 x 0.305m = 3.965m
=> d = 3.965m
=> Substituting the values of F and d into the equation above, we have;
Workdone = F x d
Workdone = 151.66N x 3.965m
Workdone = 601.33Nm