Energy conservation of ice problem

AI Thread Summary
The discussion focuses on a physics problem involving a block of ice sliding down a curved path, where the goal is to determine the force exerted on the ice by the path at the bottom. The initial energy is calculated using gravitational potential energy and kinetic energy, leading to a final speed of 9.06 m/s. The centripetal force required for circular motion is calculated as 1062 N upwards, while the weight of the block is 431.2 N downwards. A common error is highlighted regarding the interpretation of centripetal force, which is not an applied force but rather a component of the resultant forces. The correct approach emphasizes that the net force should account for the direction of forces acting on the block.
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Homework Statement


https://moodle.telt.unsw.edu.au/pluginfile.php/2296810/question/questiontext/2691158/6/1668509/cart%20track.png
A block of ice (that we shall treat as a particle) slides with negligible friction or air resistance on the curved tpath sketched (black line). The mass of the block is m = 44 kg. Its initial speed is v0 = 1.3 m.s–1. The height h= 4.1 m. At the bottom, the path has a radius of curvature (fine circle) R = 3.4 m. At the bottom of the path, what is the force exerted on the ice by the path?

Homework Equations


K + V = constant

The Attempt at a Solution


Energy before it slides = after it slides:
mgh + 1/2 * m*v0^2 = 1/2 * m*v_final^2 (at the bottom h = 0 -> mgh=0)
44*9.8*4.1 + 1/2*44*1.3^2 = 1/2*44*v_final^2 -> v_final=9.06m/s

Circular motion:
Fc=ma=m*v_f^2/R=44*9.06^2/3.4=1062N upwards
W=mg=44*9.8=431.2N downwards
F_path=1062-431.2=630.8N upwards

Could someone suggest where I did wrong?
Thanks!:smile:
 
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paulxu11 said:
Circular motion:
Fc=ma=m*v_f^2/R=44*9.06^2/3.4=1062N upwards
W=mg=44*9.8=431.2N downwards
F_path=1062-431.2=630.8N upwards

Could someone suggest where I did wrong?
If W and F_path are in opposite directions, the magnitude of the net force is 680.8 N - 431.2 N, no?
 
paulxu11 said:
06^2/3.4=1062N upwards
W=mg=44*9.8=431.2N downwards
F_path=1062-431.2=630.8N upwards
This is a very common error.
Centripetal force is not an applied force. It is that component of the resultant which is perpendicular to the velocity.
So in ΣF=ma, the centripetal force is the ma on the right, and the perpendicular component of each applied force appears in the sum on the left.
 
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