(b) At the end of the straight section, the track remains horizontal but bends to the right, as shown in Fig. 2.1.
When the motorcyclist reaches the bend, she travels around the bend in a circular path at a constant speed.
(i) Velocity is a vector quantity.
State how a vector quantity differs from a scalar quantity.
(ii) Describe what happens to the velocity of the motorcyclist as she travels around the bend at constant speed.
(iii) Explain why there must be a resultant force on the motorcyclist as she travels around the bend.
Answer (2)
(i) A vector quantity is different from a scalar quantity in that a vector quantity has both magnitude and direction, while a scalar quantity only has magnitude. For example, velocity is a vector because it describes how fast something is moving and in which direction, whereas speed is a scalar because it only describes how fast something is moving regardless of its direction.
(ii) As the motorcyclist travels around the bend at a constant speed, her velocity changes despite the speed remaining constant. This is because velocity, being a vector, includes both speed and direction. As she goes around the bend, the direction of her motion continually changes, which means her velocity is also changing, even though her speed (magnitude of velocity) remains the same.
(iii) There must be a resultant force on the motorcyclist as she travels around the bend because any change in velocity implies an acceleration, according to Newton's Second Law. Since acceleration is a change in the velocity of an object (which includes changes in direction as well as speed), and since the motorcyclist is changing direction continually as she goes around the bend, there must be an acceleration towards the center of the circular path. This acceleration is called centripetal acceleration, and it requires a centripetal force. Therefore, a resultant force is necessary to cause this change in direction, allowing the motorcyclist to navigate the curve.
Vector quantities possess both magnitude and direction, while scalar quantities have only magnitude. The motorcyclist's velocity changes as she navigates a bend at constant speed due to a continual change in direction. A resultant force is required to account for the acceleration experienced while the motorcyclist changes direction around the bend.
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