Advertisements
Advertisements
प्रश्न
A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?
Advertisements
उत्तर १
0.86 m/s2; 54.46° with the direction of velocity
Speed of the cyclist, v = 27 km/h = 7.5 m/s
Radius of the circular turn, r = 80 m
Centripetal acceleration is given as:
`a_c = v^2/r`
=(7.5)^2/80 = 0.7 `"m/s"^2`
The situation is shown in the given figure:
Suppose the cyclist begins cycling from point P and moves toward point Q. At point Q, he applies the breaks and decelerates the speed of the bicycle by 0.5 m/s2.
This acceleration is along the tangent at Q and opposite to the direction of motion of the cyclist.
Since the angle between`a_c` and `a_T`is 90°, the resultant acceleration a is given by:
a = `sqrt(a_c^2 + a_T^2)`
=`sqrt((0.7)^2 + (0.5)^2)`
=`sqrt(0.74) = 0.86` `"m/s"^2`
`tan theta = a_c/a_T`
Where `theta` is the angle of the resultant with the direction of velocity
`tan theta = 0.7/0.5 = 1.4`
`theta = tan^(-1)(1.4)`
`=54.46^@`
उत्तर २
Here v = 27 km/h = `27xx5/18` m/s = 7.5 m/s, r = 80 m
and tangential acceleration `a_t = -0.50 "m/s"^2`
:.Centripetal acceleration `a_c = v^2/r = (7.5)^2/80 ms^2` (radially inwards)
Thus as shown in figure two accelerations are mutually perpendicular directions. If `veca` be the resultant acceleration then
|veca| = sqrt(a_t^2+a_c^2) = sqrt((0.5)^2+(0.7)^2) = 0.86 `ms^(-2)`
and tan beta = `a_c/a_t = 0.7/0.5 = 1.4`
`=> beta = tan^(-1) (1.4) = 54.5^@` fromthe direction of negative of the velocity
संबंधित प्रश्न
A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone?
Give an example of motion in which speed remains uniform, but the velocity changes.
| A small pebble tied at one end of a string is placed near the periphery of a circular disc, at the centre of which the other end of the string is tied to a peg. The disc is rotating about an axis passing through its centre. |
- What will be your observation when you are standing outside the disc? Explain.
- What will be your observation when you are standing at the centre of the disc? Explain.
State True or False
The earth moves around the sun with a uniform.
Complete a sentence and explain it.
When an object is in uniform circular motion, its ______ changes at every point.
Which of the following quantity remains constant in a uniform circular motion?
Name the force required for uniform circular motion. State its direction.
What is a conical pendulum?
A uniform rod of length '6L' and mass '8 m' is pivoted at its centre 'C'. Two masses 'm' and ' 2m' with speed 2v, v as shown strikes the rod and stick to the rod. Initially the rod is at rest. Due to impact, if it rotates with angular velocity 'w1' then 'w' will be ________.
A particle goes round a circular path with uniform speed v. After describing half the circle, what is the change in its centripetal acceleration?
A particle of mass m is executing uniform circular motion on a path of radius r. If p is the magnitude of its linear momentum, the radial force acting on the particle is ______.
A string of length `l` is fixed at one end and carries a mass 'm' at the other end. The mass is revolving along a horizontal circle of radius 'r' making 'θ' as the semi-vertical angle of cone and `(1/pi)` revolutions per second around the vertical axis through fixed end. The tension in the string is ______.
The given graph represents motion with ______ speed.
Statement A: Uniform circular motion is a case of accelerated motion
Statement B: In the third equation of motion we do not have the term time
A particle is given an initial speed u inside a smooth spherical shell of radius R = 1 m that it is just able to complete the circle. Acceleration of the particle when its velocity is vertical is ______.
Angular speed of hour hand of a clock in degree per second is ______.
A wheel is Subjected to uniform angular acceleration about its axis. Initially. its angular velocity is zero. In the first 2 s, it rotates through an angle θ1, in the next 2 s, it rotates through an angle θ2. The ratio of `theta_2/theta_1` is ______.
A body of mass m is moving in circle of radius r with a constant speed v. The work done by the centripetal force in moving the body over half the circumference of the circle is ______.
In uniform circular motion, although the speed is constant, why does acceleration occur?
Angular displacement is measured in which unit?
