How Do You Calculate Motion and Forces in Physics Problems?

AI Thread Summary
To calculate motion and forces in physics problems, it's essential to apply principles of equilibrium and energy conservation. For the solid sphere rolling down the incline, the speed at the bottom can be derived using gravitational potential energy and rotational kinetic energy equations. In the case of the suspended boom, analyzing the forces and creating a free body diagram (FBD) will help determine the tension in the horizontal cable. Similarly, for the plank, establishing equilibrium conditions and drawing the relevant diagrams is crucial for calculating the tension in the cable. Providing attempts or progress is necessary for further assistance in solving these problems.
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physics circular motion and gravity help please :(

1. a) A solid homogeneous sphere of mass M = 4.80 kg is released from rest at the top of an incline of height H=1.35 m and rolls without slipping to the bottom. The ramp is at an angle of θ = 25.7o to the horizontal. Calculate the speed of the sphere's CM at the bottom of the incline.

b) Determine the rotational kinetic energy of the sphere at the bottom of the incline.

2. A mass M=169 kg is suspended from the end of a uniform boom.The boom (mass=90.0 kg, length=3.60 m) is at an angle θ=68.0 deg from the vertical, and is supported at its mid-point by a horizontal cable and by a pivot at its base. Calculate the tension in the horizontal cable.

3. A plank of length L=1.800 m and mass M=7.00 kg is suspended horizontally by a thin cable at one end and to a pivot on a wall at the other end.The cable is attached at a height H=1.50 m above the pivot and the plank's CM is located a distance d=0.700 m from the pivot. Calculate the tension in the cable.
 
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First show us the attempt.
 
i actually just figured out question one
but i don't even know how to start 2 and 3 :(
 
To start the second one. First draw the Diagram. Then draw the FBD. Show it to us. Same applies for the third one.

Drawing the physical diagram would give you a rough idea of the system.

hint: Both systems are in equlibirium.
 
And one more thing. You must show us your attempt to get any further help. If you can't show the attempt, you have to tell us your progress.
 
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 .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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