A 3.2 kg block sits on a frictionless table that has a hole cut in the middle of it. The 3.2 kg mass is connected to a string that goes through the hole in the table and attaches to a 4.8 kg mass. The 3.2 kg mass moves in a circle of radius 0.2 m
How fast does it have to be moving so thaf the 4.8kg mass does not fall? Also what is the tension in the string?
Force up = tension in string = 9.8*4.8 = 47 N
so
47 = m v^2/r
47 = 3.2 * v^2 /.2
v = 1.71
To find the speed at which the 3.2 kg mass needs to be moving in order for the 4.8 kg mass not to fall, we can use the concept of centripetal force.
The force required to keep an object moving in a circle is called centripetal force and can be calculated using the formula:
F = m * v^2 / r
Where:
F is the centripetal force
m is the mass of the object
v is the velocity of the object
r is the radius of the circle
In this case, the 3.2 kg mass is moving in a circle of radius 0.2 m. So, we need to find the velocity at which the centripetal force balances the weight of the 4.8 kg mass to prevent it from falling.
The weight of the 4.8 kg mass can be calculated using the formula:
W = m * g
Where:
W is the weight
m is the mass
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Substituting the values, the weight of the 4.8 kg mass is:
W = 4.8 kg * 9.8 m/s^2 = 47.04 N
Now let's set the centripetal force equal to the weight of the 4.8 kg mass:
F = W
m * v^2 / r = W
Solving for v, we have:
v = √(r * W / m)
Substituting the values, we get:
v = √(0.2 m * 47.04 N / 3.2 kg)
v ≈ 2.62 m/s
Therefore, the 3.2 kg mass needs to be moving at approximately 2.62 m/s for the 4.8 kg mass not to fall.
To find the tension in the string, we need to consider the forces acting on the 3.2 kg mass when it's moving in a circle.
The tension in the string provides the centripetal force required to keep the 3.2 kg mass moving in a circle. It can be calculated using the same formula as the centripetal force:
T = m * v^2 / r
Substituting the values, we get:
T = 3.2 kg * (2.62 m/s)^2 / 0.2 m
T ≈ 134.96 N
Therefore, the tension in the string is approximately 134.96 N.