1 In the figure, a small, initially stationary block is...

1 In the figure, a small, initially stationary block is released on a frictionless ramp at a height of 3.0 m. Hill heights along the ramp are as shown. The hills have identical circular tops, and the block does not fly off any hill. a). Which hill is the first the block cannot cross? b). On which hilltop is the centripetal acceleration of the block greatest? c). On which hilltop is the normal force on the block least?

Transcript

00:01 Hello everyone, we are going to understand this question.

00:05 Here given in the question, given, initial height of the block is 3 meter.

00:15 Initial height, initial height of the block is equal to 3 meter.

00:30 Let the mass of the block be m.

00:33 Let mass of block be m.

00:43 Now, applying the potential, applying the energy conservation rule, so initial energy of the block, initially, potential energy of the block, potential energy of block, that is mgh.

01:22 Or if we will substitute the value of h, then it will be 3mg.

01:29 And potential energy at hit hill one, potential energy at hill one, that is, 0 .3 .3 .5.

01:47 Mg potential energy at hill 2 it will be 1 .5mg similarly potential energy at the height at the hill 3 potential energy at hill 3 it will be 2 .5mg potential energy at hill 4 it will be 3 .5mg now from the conservation of energy the potential energy at hill 4 is greater than the initial potential energy potential energy or we can say total energy a block initially must be equal to or greater than the block then it will initially total energy of the block if total energy of the block greater than total energy of block at any hill total energy of block at any hill any hill then or we can say potential energy of the block no total potential energy.

04:01 Potential energy a block greater than potential energy a block at any hill then it will cross the hill then it will be able to cross the hill it will be able to cross the hill so here we can see potential energy at hill 4 is greater than potential energy initially means 3 .5mg is greater than 3mg hence we can say hence block will not be able to cross hill 4 hence block will not be able to cross will not be able to cross hill 4 now for part b, we have to find the maximum centipital force at any hill.

05:25 Means at which hill, central frontal force will be maximum.

05:30 So we know that centrifugal acceleration, centripetal acceleration is equal to v square upon height of hill or radius.

05:50 So here, centripetal acceleration is depending on two terms.

05:55 Velocity and height of the hill.

05:58 Velocity are blocked at the peak of hill and velocity and height of the hill.

06:03 So here from the diagram we can see that hill one have the minimum height...

Question

Please give Ace some feedback