Mechanics - Motion in a Plane - SS2 Physics Past Questions and Answers - page 2

Explanation: In uniform circular motion, the centripetal force is responsible for keeping the object moving in a circular path. The centripetal force always points towards the centre of the circle, providing the necessary inward force to maintain the circular motion.

Explanation: The magnitude of the centripetal force depends on the mass of the object, the radius of the circular path, and the velocity of the object. The direction of the object's motion does not directly affect the magnitude of the centripetal force, as long as the object is moving in a circular path.

The speed of an object in uniform circular motion is given by the formula: 

speed = (2πr) / T, 

where r is the radius of the circle and T is the time taken to complete one revolution. Plugging in the values, 

we get speed = (2π x 50) / 20 = 5 m/s.

The centripetal acceleration of an object in uniform circular motion is given by the formula: acceleration = (v2) / r, 

where v is the velocity of the object and r is the radius of the circle. Since the stone completes one revolution in 4 seconds, its velocity is given by 

v = (2πr) / T = (2π x 2) / 4 = 2π m/s. 

Plugging in the values, we get acceleration = (2π2) / 2 = 8 m/s2.

The period of an object in orbit around the Earth is given by the formula: 

T = 2π√(r3 / GM), 

where r is the sum of the radius of the Earth and the altitude of the satellite, G is the gravitational constant, and M is the mass of the Earth. 

Plugging in the values, we get 

T = 2π√((6,371 + 400)3 / GM) = 12 hours.

Explanation: In a vertical loop-the-loop, the car experiences maximum acceleration at both the top and bottom of the loop. At the top, the car is moving against gravity, so the net force is the sum of the gravitational force and the normal force, resulting in a higher acceleration. At the bottom, the car is moving with gravity, so the net force is the difference between the gravitational force and the normal force, again resulting in a higher acceleration.

Explanation: The banking angle of a curved track is determined by the speed of the vehicle. The banking angle is designed such that the frictional force between the tires and the road provides the necessary centripetal force to keep the vehicle moving in a curved path. The higher the speed of the vehicle, the greater the banking angle required to provide the appropriate centripetal force.

Explanation: When a car goes around a banked curve with a speed lower than the ideal speed for that curve, it experiences a smaller normal force. The smaller normal force results in a smaller frictional force, which can cause the car to slide or skid off the road. The ideal speed for a banked curve is the speed at which the frictional force provides the necessary centripetal force, allowing the car to safely navigate the curve without sliding.

In vertical circular motion, an object moves in a circular path in a vertical plane. The forces acting on the object in a vertical loop-the-loop are gravity, normal force, and tension (if applicable). At the top of the loop, the object experiences a net force directed towards the centre of the loop, which provides the necessary centripetal force. This net force is the vector sum of the gravitational force and the normal force. The object does not fall off at the top because the normal force is greater than the gravitational force, ensuring a net inward force.

Banking of tracks refers to the incline or tilt of a curved track or road at an angle to the horizontal. The banking angle is determined based on the speed of the vehicle and the radius of the curve. The higher the speed, the greater the banking angle required. The banking angle is determined such that the frictional force between the tires and the road provides the necessary centripetal force to keep the vehicle moving in a curved path. This reduces the reliance on static friction and helps prevent the vehicle from sliding or skidding off the road. Without proper banking, a vehicle may experience a lower frictional force, which can result in loss of control and potential accidents.