(a)
To calculate:
The block's position as a function of time for Oxy axes and the time taken by the block to reach the bottom.
Answer to Problem 1.1P
Position of the block in terms of (x,y) =
Time taken by the block to reach the ground
Explanation of Solution
Given:
A block of mass msliding down on an inclined plane making angle θ with respect to the horizontal surface.
Formula used:
Using equation of motion,
s = distance travelled by the block
u = initial velocity
t = time taken by the block
a = acceleration of the block
Calculation:
Forces on the block along x-axis,
Since the block is moving in x direction therefore, by the equation of motion.
m is the mass of the block
a is the acceleration of the block
by Newton's law of motion,
N = normal force
force of friction is given by
Put the value of N in equation (2)
Put the value of fxin equation (1)
By the equation of motion
Put the value of a from equation (3)
Since there is no motion in vertical direction,
Therefore, y =0
Time taken by the block to reach the ground.
Here, distance covered by the block is l.
Therefore, put
Conclusion:
Therefore, position of the block can be defined in
Time taken by the block to travel distance l,
(b)
To calculate:
The block's position as a function of time for Ox'y' axes and the time taken by the block to reach the bottom.
Answer to Problem 1.1P
Position of the block in terms of
Time taken by the block to reach the ground,
Explanation of Solution
Given:
A block of mass m sliding down on an inclined plane making angle θ with respect to the horizontal surface.
Formula used:
Using equation of motion,
s = distance travelled by the block
u = initial velocity
t = time taken by the block
a = acceleration of the block
Calculation:
Distance travelled in x-direction
Distance travelled in y direction
Position of the block in
Time taken by the block to reach the ground
Adding equation (1) and (2)
It is clear from the solution of part (a) and (b), that time taken by the box is same to travel the distance l.
Taking
Conclusion:
For
For
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Chapter 1 Solutions
Modern Physics for Scientists and Engineers
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- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University