To tighten a bolt, you push with a force of 72 N at the end of a wrench handle that is 0.26 m from the axis of the bolt.What torque are you exerting?
I GOT THIS PART AS 19N *m unsure of the next two:
If you move your hand inward to be only 0.10 m from the bolt, find the force that you should exert to achieve the same torque.
Do your answers depend on the direction of your push relative to the direction of the wrench handle?
I answered this already. The forces are assume to be applied perpendicular to the wrench handle.
To find the force that you should exert to achieve the same torque when your hand is only 0.10 m from the bolt, we can use the equation for torque:
Torque = Force x Distance
Given that the torque obtained in the previous part is 19 N*m and the new distance is 0.10 m, we can rearrange the equation to solve for the force:
Force = Torque / Distance
Substituting the values, we get:
Force = 19 N*m / 0.10 m
The force exerted when your hand is 0.10 m from the bolt is therefore 190 N.
Regarding the direction of your push relative to the direction of the wrench handle, the magnitude of the torque does not depend on the direction. The torque will be the same whether you push in the clockwise or counterclockwise direction. However, the direction of the force will affect the direction in which the bolt tightens or loosens.
To find the force needed to achieve the same torque when your hand is only 0.10 m from the bolt, we can use the formula for torque:
Torque = force × distance
Given that the initial torque is 19 N⋅m and the initial distance from the bolt is 0.26 m, we can rearrange the formula to solve for the force:
Force = Torque ÷ distance
Substituting the values, we have:
Force = 19 N⋅m ÷ 0.26 m = 73.08 N
Therefore, to achieve the same torque when your hand is only 0.10 m from the bolt, you would need to exert a force of approximately 73.08 N.
Regarding the direction of your push, torque is a vector quantity that depends on both force and the perpendicular distance from the axis of rotation. Therefore, the direction of your push relative to the wrench handle does not affect the torque value. However, it may affect the efficiency or ease with which you tighten the bolt, as well as the overall stability of the wrench.