an object tied to the end of a string moves in a circle. the force exerted by the string depends on the mass of the object, its speed, and the radius of the circle what combination of these variables gives the correct dimensions (ML/T2) for the force?
force = m a = M L/T^2
M L/T^2 = M * L/T * L/T * 1/L
but
M is mass
L/T is speed
1/L is 1/R
so
constant times
m v^2 / R
To determine the correct combination of variables that gives the dimensions of force (ML/T2), we can use dimensional analysis.
Starting with the formula for force exerted by the string:
F = m * v2 / r
where:
F is the force exerted by the string,
m is the mass of the object,
v is the speed of the object, and
r is the radius of the circle.
We can break down the dimensions of each variable as follows:
- Mass (m) is measured in kilograms (M).
- Speed (v) is measured in meters per second (L/T).
- Radius (r) is measured in meters (L).
Substituting these dimensions into the formula, we get:
F = m * (L/T)2 / L
Simplifying the equation by rearranging, we have:
F = (m * L2)/(L * T2)
Dividing the equation further, we get:
F = m / (T2)
Thus, the combination of variables that gives the correct dimensions of force (ML/T2) is mass (m) divided by the square of time (T2).