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Find all vectors that satisfy the equation
where is any real number
Solve the equation where is a nonzero vector with a magnitude of
[T] A mechanic uses a 12-in. wrench to turn a bolt. The wrench makes a angle with the horizontal. If the mechanic applies a vertical force of lb on the wrench handle, what is the magnitude of the torque at point (see the following figure)? Express the answer in foot-pounds rounded to two decimal places.
8.66 ft-lb
[T] A boy applies the brakes on a bicycle by applying a downward force of lb on the pedal when the 6-in. crank makes a angle with the horizontal (see the following figure). Find the torque at point Express your answer in foot-pounds rounded to two decimal places.
[T] Find the magnitude of the force that needs to be applied to the end of a 20-cm wrench located on the positive direction of the y -axis if the force is applied in the direction and it produces a N·m torque to the bolt located at the origin.
250 N
[T] What is the magnitude of the force required to be applied to the end of a 1-ft wrench at an angle of to produce a torque of N·m?
[T] The force vector acting on a proton with an electric charge of (in coulombs) moving in a magnetic field where the velocity vector is given by (here, is expressed in meters per second, is in tesla [T], and is in newtons [N]). Find the force that acts on a proton that moves in the xy -plane at velocity (in meters per second) in a magnetic field given by
[T] The force vector acting on a proton with an electric charge of moving in a magnetic field where the velocity vector v is given by (here, is expressed in meters per second, in and in If the magnitude of force acting on a proton is N and the proton is moving at the speed of 300 m/sec in magnetic field of magnitude 2.4 T, find the angle between velocity vector of the proton and magnetic field Express the answer in degrees rounded to the nearest integer.
[T] Consider the position vector of a particle at time where the components of are expressed in centimeters and time in seconds. Let be the position vector of the particle after sec.
a.
b.
A solar panel is mounted on the roof of a house. The panel may be regarded as positioned at the points of coordinates (in meters) and (see the following figure).
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