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String tension in case of pulley with mass

1. In case of a massless string around a massless pulley , tension on either side of the pulley has to be the same. But when the pulley has mass, we consider tensions to be different on each side. Now i got a solution from someone that since pulley has mass it now needs torque to rotate so the tensions cant be same. but what about the string?? the string is massless so wont it have infinite acceleration?
2. the diagram is in the file attached. this is a question of simple harmonic oscillation in which time period has been asked. It can be easily done by energy conservation but i also wanted to know how t can be done by analysing the forces method. what will be the tension in the string?

Body at incline

1. In first case we have the box with weight, say, 10 Newtons on incline. We calculate two components (perpendicular and parallel)of weight. We calculate normal force and force of friction. The box is at rest.

2. In second case we have ball on incline, made of same material as box from first case. Weight of the ball is the same as in first case, components of weight are the same as in first case. Normal force and friction have the same amount as in the case of box. But,unlike the box, ball is moving – it slides down. How’s that possible? If calculated net force is zero?

It is not true that the ball slides,  but it will roll down.

In the first case, the forces balance each other and there is no motion.

In the second force, the frictional force acting tangentially backwards (up the incline) and the component of weight of the ball acting parallel to the plane and through the centre of the ball constitute a couple and tends to rotate it. Now there is no sliding; it rolls.

(If any further clarification is required please post as comment to this post)

Please refer to http://www.real-world-physics-problems.com/rolling-without-slipping.html for detailed treatment of the Physics of rolling without friction.

A Problem based on Friction

an unloaded bus can be stopped by applying brakes on straight road after covering a distance x. Suppose, the passenger add 50% of its weight as the load and the braking force remains uncharged, how far will the bus go after the application of brakes? (velocity of bus in both case is same)

Weight and inertia on moon

Say True or False; An object on the Moon weights 1/6 of what it weights on the Earth. Therefore, the object has less inertia on the Moon.( Justify your answer)

Inertia depends on mass and not on weight. The weight on moon is less not because of a decrease in mass, but due to the decrease in the acceleration due to gravity on the surface of moon.

Inertia depends on mass and there is no change in mass when a body is taken to moon. Therefore the inertia of a body is same on moon as that on earth or anywhere else in the universe, even in a gravity free space.

Derive an expression for the minimum horizontal velocity to be given to a ball hanging vertically from a point so that it is able to just complete a vertical circular path.

While pushing, we are giving the ball some kinetic energy which will be converted to potential energy as it moves upward. If the whole kinetic energy is converted to potential energy at the top most point, it will fall straight down, resulting in only a semicircle. For the ball to continue the path, it should have a centrifugal force equal to weight of the body when it is at the topmost point.

let V be the initially applied velocity and v be the velocity at the topmost point

mv²/r = mg

v²/r = g

v² = rg

v = √(rg)

Potential Energy at the topmost point , Ep = 2mgr

Ep is the difference in kinetic energy between initial point(Ei) and at topmost point(Et).

Ei – Et =  Ep

½mV² – ½mv² = 2mgr

½m(V²-v²) = 2mgr

V²-v² = 4gr

V² = 4gr + v²

V² = 4gr + rg

V² = 5rg

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Apparent weight in an elevator

You are standing on a bathroom scale in an elevator the is moving upward at constant speed, when suddenly the cable breaks. from just before to just after the cable breaks, the reading on the scale will be?

When the elevator is moving up with constant speed, the bathroom scale (weighing scale) shows the correct weight, because the mechanics involved will be the same if the frame is at rest or moving with a constant velocity.
When the cable breaks, it is a case of freely falling body and the scale reads zero.

Numerical Problems from Pressure, Density and Floatation

1. Ramesh buys 6 bottles of syrup each containing 1litre. Each empty bottle weighs 400g. The density of syrup is 1.2 g/cm3. What weight does Ramesh have to carry home?

2. The volume of 900g of a substance is 1000 cm3. Will the substance sink or float in water if the density of water is 1g/cm3. What will be the mass of water displaced by the substance?

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