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Problem 58 Medium Difficulty

A stuntman is being pulled along a rough road at a constant velocity by a cable attached to a moving truck. The cable is parallel to the ground. The mass of the stuntman is 109 kg, and the coefficient of kinetic friction between the road and him is 0.870. Find the tension in the cable.


929 $\mathrm{N}$


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Video Transcript

to calculate detention that cable. We have to apply Newton's second law in two directions. The Y direction on the X direction and these is also the reference fame. I'm using this problem then a plane. Newton's second law, the X Direction Leagues, is the following equation. The Net Force. Next direction Is it close to the mask off the stuntman Times acceleration off that stuntman Dax direction. But the stuntman is being pull it at a constant velocity. The reformed acceleration is equals to zero index direction. Then the X component off the net force is equal to zero. But the net force next direction is composed by two forces the Frictional Force and the pension Force. Therefore, my the tension force which is pointing to the positive X direction miners frictional force, which is pointing to the negative external action, is it goes to zero then the tension force is a close to the frictional force. So too complex detention. Now all we have to do is complete the frictional force. So remember that the frictional force in the situation where the object or the person is already moving is given by the kinetic friction aquisition times the normal force that is acting owned. That object or person than attention force is equals to the kinetic fictional coefficients times the normal force. So the tension force is equal to 0.87 times the normal force. Now, what is the normal force to copulate that we have to use Newton's second law? Apply it on the Y direction. So in the wider action, the Net force is equal to the mass off the stuntman times next generation in the Y direction off that stunt. So the stuntman is on the ground and he's is riding to the right. He is not flying away and he's not filing below the ground. Then here's why. Acceleration is it close to zero. Therefore, the net force and the white interaction is equal to zero troops. But two forces are composing in that force in the Y direction, the normal force and the weight force. So we got the following the normal force, which is pointing to the positive Y direction miners the weight force which is pointing to the negative y direction is it close to zero? Then the normal force is equal to the weight force, then to Catholic the normal force. We have to use this. The equation for the weight force which is the following the weight forced, is equal to the mass off the statement times acceleration of gravity near the surface of the earth which we used as 9.8 meters per second squared approximately then your normal force is equals to 109 kilograms times 9.8 and then we can finally calculate the tension force using our previous equation. So, using that equation, the tension force is equals to 0.87 times 109 times 9.8 and these gives us approximately 929 new cold.

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