A horizontal force of 210 N is exerted on a 2.0 kg discus as it rotates uniformlyin a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.
is the answer 9.7
centipetal force=holding force.
mass*velocity^2/radius=210
solve for velocity
The question sdoes not make clear whether the force is centripetal, tangential or a combination of both. In an actual discus throw that is well done, the thrower pushes the discus at an increasing speed while spining around in approximatly one complete circle. If the accelerating tangential force is the force they are talking about, then a different speed will be obtained than one would by treating it as a centripetal force problem, for which Force = M V^2/R.
To find the speed of the discus, we need to use the formula for centripetal force.
The centripetal force required to keep an object moving in a circle is given by the formula: F = (mv^2) / r
Where:
F = Centripetal force
m = Mass of the object
v = Velocity or speed of the object
r = Radius of the circle
In this case, the centripetal force is provided by the horizontal force of 210 N.
The mass of the discus is 2.0 kg.
The radius of the circle is 0.90 m.
Plugging in these values into the formula, we can solve for v:
210 = (2.0 * v^2) / 0.9
Rearranging the formula to solve for v:
(2.0 * v^2) / 0.9 = 210
Multiplying both sides of the equation by 0.9 to isolate v:
2.0 * v^2 = 210 * 0.9
2.0 * v^2 = 189
Dividing both sides of the equation by 2.0:
v^2 = 189 / 2.0
v^2 = 94.5
Taking the square root of both sides:
v = √94.5
v ≈ 9.7 m/s
So the speed of the discus is approximately 9.7 m/s. Therefore, your answer is correct.
To calculate the speed of the discus, we can use the formula for centripetal force:
\( F_{c} = \dfrac{mv^2}{r} \)
Where:
\( F_{c} \) is the centripetal force,
\( m \) is the mass of the discus,
\( v \) is the speed of the discus, and
\( r \) is the radius of the circular path.
In this question, we are given:
\( F_{c} = 210 \, \text{N} \) (horizontal force)
\( m = 2.0 \, \text{kg} \) (mass of the discus)
\( r = 0.90 \, \text{m} \) (radius of the circular path)
We can rearrange the formula to solve for \( v \):
\( v = \sqrt{\dfrac{F_{c} \cdot r}{m}} \)
Now, substituting the given values in the equation:
\( v = \sqrt{\dfrac{210 \, \text{N} \cdot 0.90 \, \text{m}}{2.0 \, \text{kg}}} \)
Evaluating this equation gives us:
\( v \approx 9.7 \, \text{m/s} \)
Therefore, the speed of the discus is approximately 9.7 m/s. So, your answer is correct.