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solve this carefully. Only round up values up to 2 decimal places

We are given a problem involving a block with mass \( M = 12.0 \, \text{kg} \), moving to the right with an initial speed \( u = 6.00 \, \text{m/s} \) on a rough horizontal surface. The block is being pulled by a rope exerting a force \( T = 12.0 \, \text{N} \) at an angle \( \alpha = 35^\circ \) above the horizontal. The coefficient of kinetic friction between the block and the surface is \( \mu_k = 0.420 \).

We are asked to solve the following:

### **Part A:** 
When the block has moved 2.50 m from its initial position, what is its speed?

### **Part B:** 
When the block has stopped, how far has it traveled from its initial position?

### **Part C:** 
When the block has stopped, how much work has friction done to the block?

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A block of mass M = 12.0 kg slides to the right with speed u = 6.00 m/s across a rough horizontal surface. A light rope tugs on the block with a force T = 12.0 N oriented α = 35.0° above the horizontal. The coefficient of kinetic friction between the block and the surface is μ_k = 0.420. Solve the following: 

(A) When the block has moved 2.50 m from its initial position, what is the block’s speed? 
(B) When the block has stopped, how far has it traveled from its initial position? 
(C) When the block has stopped, how much work has friction done to the block?

Analyze the motion of a 12.0 kg block on a rough surface with an initial speed of 6.00 m/s, under the influence of a 12.0 N force at a 35° angle. Determine the block's speed after moving 2.50 m, the distance traveled until it stops, and the work done by friction. This problem covers Newton's Second Law, kinematics, and the work-energy theorem. Suitable for undergraduate physics students.

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