A 3030 cmcm wrench is used to loosen a bolt with a force applied 0.30.3 mm from the bolt. It takes 6060 NN to loosen the bolt when the force is applied perpendicular to the wrench. How much force would it take if the force was applied at a 3030 degree angle from perpendicular?A 3030 cmcm wrench is used to loosen a bolt with a force applied 0.30.3 mm from the bolt. It takes 6060 NN to loosen the bolt when the force is applied perpendicular to the wrench. How much force would it take if the force was applied at a 3030 degree angle from perpendicular?

Complete Question

A 30 cmcm wrench is used to loosen a bolt with a force applied 0.30m from the bolt. It takes 60 N to loosen the bolt when the force is applied perpendicular to the wrench. How much force would it take if the force was applied at a 30 degree angle from perpendicular?

The force required is  

Explanation:

From the question we are told that

    The length of the wrench is

    The distance from the bolt is  

      The force it takes to loosen the bolt is

       The angle of application is

Generally the torque required to loosen the bolt is

Now for the bolt to be loosen at the torque at 90° must be the same as that at

So the torque at   is mathematically represented as

substituting values

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s