This page covers the following topics:
1. Terminal velocity
2. Velocity-time graphs for terminal velocity
Any object dropped near the surface of the Earth will accelerate downwards due to the force of gravity. As the speed of the object increases, the frictional forces (drag/air resistance) increase too. When the frictional forces increase enough to match the weight of the object, the resultant force on the object will be 0. Since there is no resultant force, the object will no longer be accelerating and will be travelling at a constant velocity called the terminal velocity.
In the case of a skydiver, when the parachute is opened, the air resistance suddenly increases due to the great surface area of the parachute, causing the skydiver to slow down. As the speed of the skydiver decreases, the air resistance force decreases too, until a new terminal velocity is reached when the weight of the skydiver and the air resistance become equal again.
The motion of a falling object that reaches terminal velocity can be modelled by the given velocity-time graph. The beginning of the graph shows the acceleration of the object downwards due to its weight. The slope then starts to decrease as the resistive forces start to increase with increasing speed. Eventually, the graph flattens out as the object reaches its constant terminal velocity.
Use Newton's second law to explain terminal velocity.
An object is said to reach terminal velocity when its weight and the air resistance acting on it are equal. This results in there being no resultant force acting on the object. According to Newton's second law, the object will have no acceleration and thus will be falling at a consant velocity called the terminal velocity.
no resultant force → no acceleration → constant (terminal) velocity
A pebble is dropped into a cylinder filled with water. Given that the mass of the pebble is 100 g, what is the drag force that will act on the pebble at terminal velocity? Use g = 9.8 m/s².
At terminal velocity, the drag force acting on the pebble will be equal to its weight.
Using w = mg, w = 0.1 kg × 9.8 m/s² = 0.98 N.
Therefore, the drag that will act at terminal velocity is 0.98 N upwards.
0.98 N upwards
Explain what happens when a skydiver opens their parachute after having reached terminal velocity.
Before the parachute is opened, the skydiver is falling at terminal velocity, therefore their weight and the air resistance are equal. When the parachute is opened, the increase in surface area will cause a sudden increase in air resistance acting on the skydiver, therefore there will now be an upwards resultant force, which will cause the skydiver to decelerate and slow down. As the speed of the skydiver decreases, the air resistance also decreases, until the weight and air resistance become equal again. Then, the skydiver will again have a resultant force of 0 acting on them, and thus will continue to fall at a new, lower terminal velocity.
higher surface area → higher air resistance → deceleration → no resultant force → terminal velocity
Draw the velocity-time graph for a skydiver who first reaches a terminal velocity of 60 m/s after 35 seconds of falling, opens their parachute 25 seconds after that and it reaches a second terminal velocity of 10 m/s 12 second after that, at which they travel for a further 8 seconds.
At the beginning of the motion, the graph is a positive straight line, since the skydiver is accelerating due to the fact that the only force acting on them is their weight. As their velocity increases, the air resistance acting on them also increases and their acceleration starts to decrease, as the slope of the graph is also decreasing. At t = 35 s, the skydiver reaches their terminal velocity of 60 m/s and travels at this velocity for a further 25 seconds. At t = 60 s, the skydiver opens their parachute as they experience a great deceleration, seen by the negative slope of the graph. As the speed of the skydiver decreases, the air resistance acting on them also decreases and the deceleration of the skydiver decreases, as the slope becomes less negative. At t = 72 s, the skyidver reaches their second lower terminal velocity of 10 m/s. They travel at this terminal velocity for a further 8 seconds and then they land.
Define terminal velocity.
Terminal velocity is the velocity at which a falling object experiences when the frictional forces acting on it are equal to its weight.
velocity at zero resultant force
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