A 200 block on a 54 -long string swings in a circle on a horizontal, frictionless table at 90
A) What is the speed of the block?
B) What is the tension in the string?
A) v=ω•R=2•π•n•L
B) T = ma=mv²/L
To find the speed of the block, we can use the formula for centripetal acceleration:
a = v^2 / r
where:
a is the centripetal acceleration,
v is the speed of the block,
and r is the radius of the circular path.
In this case, the radius is given as 54 units. We know that centripetal acceleration is given by:
a = v^2 / r
Since the question mentions that the block is swinging at 90 degrees, we know that the gravitational force is acting as the centripetal force. Therefore, we can use the equation:
a = g = 9.8 m/s^2
By substituting the values into the equation, we get:
9.8 m/s^2 = v^2 / 54
To find v, we can rearrange the equation:
v^2 = 9.8 m/s^2 * 54
v^2 = 529.2 m^2/s^2
Taking the square root of both sides, we find:
v = √529.2 m/s
So, the speed of the block is approximately 22.99 m/s.
Now, let's consider the tension in the string. In a horizontal, frictionless table, the tension in the string provides the centripetal force needed to keep the block moving in a circular path.
The centripetal force can be calculated using the equation:
Fc = m * a
where:
Fc is the centripetal force,
m is the mass of the block,
and a is the centripetal acceleration.
In this case, the mass of the block is not provided, so we cannot find the exact tension. However, we can still solve for the tension in terms of the unknown mass:
Fc = m * a
T = m * a
Given that the centripetal acceleration is 9.8 m/s^2 (from the previous calculation), we can write:
T = m * 9.8 m/s^2
So, the tension in the string is T = 9.8m newtons, where m is the mass of the block in kilograms.