A wrench .9m long lies along the positive y-axis, and grips a bolt at the origin. A force is applied in the direction of (0,1,3) at the end of the wrench. Find the magnitude of the force in newtons needed to supply 100 J of torque to the bolt.
This is the formula i have:
T=|r x F| Can anybody point me in the right direction?
A wrench 0.4 meters long lies along the positive y-axis, and grips a bolt at the origin. A force is applied in the direction of ⟨0,1,5⟩ at the end of the wrench. Find the magnitude of the force in newtons needed to supply 100 newton-meters of torque to the bolt.
To find the magnitude of the force needed to supply a certain amount of torque to the bolt, you can start by using the formula T = |r x F|, where T represents the torque, r represents the position vector, F represents the force vector, and |r x F| represents the cross product of the two vectors.
Given that the wrench is aligned along the positive y-axis and grips the bolt at the origin, the position vector r can be represented as (0, 0.9, 0), since the bolt is at the origin and the wrench is 0.9m long along the y-axis.
The force vector F is given as (0, 1, 3).
To calculate the cross product, you can use the determinant formula:
|r x F| = |i j k|
|0 0.9 0|
|0 1 3|
|r x F| = (0.9 * 3) * i - (0 * 3) * j + (0 * 1 - 0.9 * 0) * k
|r x F| = 2.7 * i - 0 * j + 0 * k
|r x F| = 2.7 * i
Now, you have the cross product magnitude |r x F| = 2.7.
To find the magnitude of the force needed to supply 100 J of torque, you can rearrange the formula T = |r x F| to solve for the magnitude of the force F:
|F| = T / |r x F|
Substituting the given torque value of 100 J and the cross product magnitude of 2.7 into the formula, you get:
|F| = 100 J / 2.7
Thus, the magnitude of the force needed to supply 100 J of torque to the bolt is approximately 37.04 Newtons.
T=100J
r=.9j
F=F (0i+1j+3k)/sq root 1^2+3^2)
Replace the values on the formula and solve for F.