Work is done when a force acts on an object AND the object moves in the direction of the force.
-- <em>Pulling a trailer up a hill. YES. </em> The trailer is moving in the direction of the pulling force.
-- Carrying a box down a corridor. No. The box is not moving in the direction of gravity (down) OR in the direction of your arm (down the corridor).
-- Suspending a heavy weight with a strong chain, No. There's a force (gravity) acting on the weight, but the weight is not moving at all.
-- Pushing against a locked door. No. There's a force (your muscles) acting on the door, but he door is not moving at all.
We will first determine using the given if an aircraft component will fracture with a given stress level (260 MPa), maximum internal crack length (6.0 mm) and fracture toughness (40 MPa m ), given that fracture occurs for the same component using the same alloy for another stress level and internal crack length. First, it is necessary to solve for the parameter Y, using Equation 8.5, for the conditions under which fracture occurred (i.e., σ = 300 MPa and 2 a = 4.0 mm). Therefore,
Y = K(Ic)/ sqrt(π a) = 40 MPa( m ) / (300 MPa) sqrt(( π ) ((4 × 10-3 m)/2)) = 1.68
We will now solve for the product Y σ π a for the other set of conditions, so as to ascertain whether or not this value is greater than the K(Ic) for the alloy. Thus,
Y sqrt(π a) = (1.68)(260 MPa) sqrt (( π )[(6 × 10^-3 m)/ 2])
= 42.4 MPa sqrt (m) (39 ksi in. )
Therefore, fracture will occur since this value ( 42.4 MPa sqrt(m)) is greater than the K(Ic) of the material, 40 MPa sqrt(m).
Answer:
Explanation:
The magnitude of the magnetic force on the proton is given by:
where:
is the proton charge
is the proton velocity
is the magnetic field
is the angle between the direction of v and B
Substituting into the formula, we find
