A ball whose mass is 0.2kg hits the floor with a speed of 8m/s and rebounds upward with a speed of 7 m/s. The ball was in contact with the floor for 0.5 ms.
(a) What was the average magnitude of the force exerted on the ball by the floor?
(b) Calculate the magnitude of the gravitational force that the Earth exerts on the ball.
(c) In a collision for a brief time, there are forces between the colliding objects that are much greater than external forces.
You know the third law, right?
Net force = rate of change of momentum = m a
so find the change of momentum P
Pdown = .2 * -.8
Pup = .2 * .7
dP = change in P = .2 (.7 - -.8) = .2 * 1.5 = .3 kg m/s
dT = .5 * 10^-3 s
so
F = dP/dt = (.3/.5)10^3 = 600 N
gravity force = m g = .3 * 9.81 N, about 3 N, much less
I mean second law !
To find the average magnitude of the force exerted on the ball by the floor, we can use Newton's second law of motion:
Force = Change in momentum / Time
(a) Calculating the change in momentum:
Initial momentum = mass * initial velocity = 0.2 kg * 8 m/s = 1.6 kg·m/s
Final momentum = mass * final velocity = 0.2 kg * (-7 m/s) = -1.4 kg·m/s
Change in momentum = Final momentum - Initial momentum
= -1.4 kg·m/s - 1.6 kg·m/s
= -3 kg·m/s
Average magnitude of the force = |Change in momentum / Time|
Given that the ball was in contact with the floor for 0.5 ms, we need to convert the time to seconds:
0.5 ms = 0.5 * 10^(-3) s
Average magnitude of the force = |-3 kg·m/s / (0.5 * 10^(-3) s)|
= |(-3 kg·m/s) / (0.0005 s)|
= |-6000 N|
= 6000 N
Therefore, the average magnitude of the force exerted on the ball by the floor is 6000 N.
(b) The magnitude of the gravitational force that the Earth exerts on the ball can be found using the formula:
Gravitational force = mass * acceleration due to gravity
Given that the mass of the ball is 0.2 kg, and the acceleration due to gravity is approximately 9.8 m/s^2:
Gravitational force = 0.2 kg * 9.8 m/s^2
= 1.96 N
Therefore, the magnitude of the gravitational force that the Earth exerts on the ball is 1.96 N.
(c) In a collision, there are internal forces between the colliding objects that are greater than external forces. This is because during a collision, the objects involved exert forces on each other due to their interaction. These internal forces can cause deformation, acceleration, or changes in momentum of the objects. External forces, on the other hand, are exerted by the environment or bodies outside the collision and may have lesser impact compared to the internal forces involved in the collision.
To find the answers to these questions, we need to apply the laws of motion and physics. Here's how you can calculate each value:
(a) Average magnitude of the force exerted on the ball by the floor:
To find the average magnitude of the force, we can use the impulse-momentum theorem. The impulse experienced by an object is equal to the change in momentum.
Impulse = Δp = mass × change in velocity
The change in momentum can be calculated as the final momentum minus the initial momentum:
Δp = (mass × final velocity) - (mass × initial velocity)
Δp = m(vf - vi)
Plugging in the given values:
mass = 0.2 kg
initial velocity (vi) = 8 m/s
final velocity (vf) = -7 m/s (negative sign indicates the opposite direction)
Δp = 0.2 kg × (-7 m/s - 8 m/s)
Now, calculate Δp to find the impulse experienced by the ball.
(b) Magnitude of the gravitational force that the Earth exerts on the ball:
The magnitude of the gravitational force between two objects can be calculated using the formula:
F = G × (m1 × m2) / r^2
Here, G is the gravitational constant (approximately 6.67 × 10^-11 N·m^2/kg^2), m1 is the mass of the first object (in this case, Earth), m2 is the mass of the second object (the ball), and r is the distance between the centers of the two objects (in this case, the radius of Earth).
Given:
mass of the ball (m2) = 0.2 kg
radius of Earth = 6,371,000 m
Substitute these values into the formula to find the gravitational force.
(c) Forces in a collision:
In a collision, the forces between the colliding objects can be categorized into internal forces and external forces. Internal forces act between the objects involved in the collision, while external forces act on the entire system of objects.
The internal forces during a collision are much greater than the external forces. This is because internal forces are responsible for causing changes in the object's momentum, while external forces, such as friction or air resistance, can be relatively small in comparison.
Therefore, the magnitude of internal forces during a collision is typically much greater than the magnitude of external forces.
Remember that during a collision, momentum is conserved, and the change in momentum of an object is equal to the impulse experienced by that object.
I hope this explanation helps you understand how to find the answers to these questions.