How far will it slide before stopping?

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The discussion revolves around various physics problems involving motion, friction, and acceleration. Key questions include calculating the distance a block will slide before stopping under friction, determining the coefficient of friction, and analyzing the time it takes for a block to slide down an inclined plane. Additional problems involve finding the acceleration of blocks on inclined planes and the tension in strings connected to different masses. The conversation highlights the importance of relevant equations and attempts to solve these problems, emphasizing the need for a structured approach to physics questions. Overall, the thread serves as a platform for discussing fundamental concepts in mechanics.
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1. A 400g Block with an initial speed of 80cm/s slides a long a horizontal tabletop against a frictional force of 0.80N.
A) How far will it slide before stopping?
B) What is the coefficient of friction between the block and the tabletop?




2. A 50kg block rests at the top of a smooth plane whose length is 2.0m and whose length is 2.0m and whose length is 0.5m. How long will it take for the block to slide to the bottom of the plane when released?



3. A 6.0lb block rest on a smooth plane inclined at an angle of 20 with the horizontal. The block is pulled up the plane with a force of 30lb parallel to the plane. What is its acceleration?



4. A 2.0 Ton elevator is supported by a cable that can safely support 6400lb. What is the shortest distance in which the elevator can be brought to a stop when it is descending with a speed of 4.0ft/s?



5. A 50kg block is placed a smooth tabletop. A horizontal card attached to the block passes over a light frictioness pulley and is attached to 4.0kg body. Find the acceleation and the tension in the card when the system is released?




6. Two boddies having masses M1=30g and M2= 40g are attached to the ends of a string of negligible mass and suspended from a frictionless pulley. Find the acceleration of the bodies and the tension in the string?




7. Consider the object on a horizontal frictioness plane, acted upon by a single horizontal force.
A) If the mass is 1g and the force is 1dyne, the acceleration is ______?
B) If the mass is 1g and the force is 5dyne the acceleration is________?
C) If the weight is 32lb and the force is 1lb the acceleration is________?
D) If the weight is 320lb and the force is 20lb the acceleration is______?
E) If the mass is 6.0kg and the force is 20N the acceleration is________?
f) If the mass is 1.0K and the force is 9.8N THE ACCELERATION IS ______?

 
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Hm, interesting questions.
I see preciously little filled out under the last two points ("relevant equations" and "the attempt at a solution") however. Surely, you must have some ideas?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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