Vertical Circles/Work-related Physics

[physixnot4me]

What formula do i apply to the following/theories?

(1) a 0.30 kg mass attached to the end of a string swings in a vertical circle (R=1.6m). At an instant when theta=50 degrees, the tension in the string is 8.0N. what is the magnitude of the resultant force on the mass at this instant?

(2) a 4kg block is lowered down a 37 degree incline a distance of 5m from point A to point B. A horizontal force (F=10N) is applied to the block between A and B. the kinetic energy of the block at A is 10J and at B is 20J. How much work is done on the block by the force of friction between A and B?

(3)A rock attached to a string swings in a vertical circle. Which free body diagram could correctly describe the force(s) on the rock when the string is in one possible horizontal position?

**DIAGRAMS ARE ATTACHED** for all of the above questions.

 

[quantumdude]

You have to show your work to receive help. That is one of the rules you agreed to.

 

[quicknote]

For the first question, the formula that can be applied is the centripetal force equation: Fc = mv^2/r, where Fc is the centripetal force, m is the mass, v is the velocity, and r is the radius of the circle. In this case, the resultant force on the mass can be calculated by subtracting the tension force from the centripetal force.

For the second question, the formula that can be applied is the work-energy theorem: W = ΔKE + ΔPE, where W is work done, ΔKE is the change in kinetic energy, and ΔPE is the change in potential energy. In this case, the work done by the force of friction can be calculated by subtracting the change in kinetic energy from the change in potential energy.

For the third question, the correct free body diagram would show the weight of the rock acting downwards, the tension force acting upwards, and the centripetal force acting towards the center of the circle. This is because when the string is in a horizontal position, the weight and tension forces are balanced, and the centripetal force is the only force causing the rock to move in a circular motion.