An object with cross section A is shot horizontally across frictionless ice. Its initial velocity is at . Air resistance is not negligible.
a. Show that the velocity at time t is given by the expression
b. A -wide, -high, car with a drag coefficient of hits a very slick patch of ice while going . If friction is neglected, how long will it take until the car’s speed drops to ? To ?
c. Assess whether or not it is reasonable to neglect kinetic friction.
a. derivation of the velocity at time
b. time taken for car to drop its speed is
c. Its absurd. so that kinetic friction were neglected.
cross section of the object
Initial velocity at
velocity at time
Coefficient of drag
density of air
mass of the object
From Newton's second law
The drag force is
Consider the negative sign for drag force as it acts opposite to the net force and equal the drag force.
Therefore, we get
On integrating the above equation, we get
Conclusion: The expression for velocity at time has been derived.
length of the car
height of the car
mass of the car
density of air
The velocity expression at time is given by
Plugging all the values in the above equation, we get
The time taken for the car to drop its speed
If we consider an object that moves by inertia with the drag or frictional force, the net force is not zero and the motion will be decelerated (non-uniform), and we will have to introduce new forces to make it uniform, which is absurd. That is why we neglect the mentioned forces.
In an electricity experiment, a plastic ball is suspended on a -cm-long string and given an electric charge. A charged rod brought near the ball exerts a horizontal electrical force on it, causing the ball to swing out to a angle and remain there.
a. What is the magnitude of ?
b. What is the tension in the string
94% of StudySmarter users get better grades.Sign up for free