A 0.5 kg glass falls with an initial velocity of -1.5 m/s and lands on the hard floor. The same type of glass falls with the same initial velocity and lands on the carpet. Which glass experiences a greater contact force with the floor?
hint: which one is more likely to break?
same change of momentum over greater stopping time on carpet.
F = d momentum / dt
To determine which glass experiences a greater contact force with the floor, we need to consider the concept of impulse. Impulse is the change in momentum of an object and is equal to the force applied multiplied by the time over which it is applied.
When the glass falls and lands on the hard floor, the time of impact is relatively short compared to the landing on the carpet. As a result, the impulse during impact will be greater on the hard floor due to the shorter time of contact. Since impulse is directly proportional to force, the glass that lands on the hard floor will experience a greater contact force.
Therefore, the glass that falls and lands on the hard floor will experience a greater contact force with the floor compared to the glass that lands on the carpet.
To determine which glass experiences a greater contact force with the floor, we need to consider the concept of momentum and the interaction between the glass and the floor.
The momentum of an object is given by the product of its mass and velocity: momentum = mass × velocity. In this case, both glasses have the same initial velocity of -1.5 m/s.
To find the momentum, we can use the formula: momentum = mass × velocity.
For the glass falling on the hard floor:
Mass = 0.5 kg
Velocity = -1.5 m/s
Momentum = (0.5 kg) × (-1.5 m/s) = -0.75 kg·m/s
For the glass falling on the carpet:
Mass = 0.5 kg
Velocity = -1.5 m/s
Momentum = (0.5 kg) × (-1.5 m/s) = -0.75 kg·m/s
As we can see, both glasses have the same momentum.
Now, let's consider the contact force between an object and a surface. When the glass lands on the hard floor, the interaction results in a larger contact force compared to landing on the carpet. This is because the hard floor does not deform as much as the carpet, causing a higher force and a shorter duration of contact.
Therefore, the glass falling on the hard floor experiences a greater contact force with the floor compared to the glass falling on the carpet.