A 10-m-long glider with a mass of 680 kg (including the passengers) is gliding horizontally through the air at 26 m/s when a 60
1 answer:
You might be interested in
Answer:
E. Zero Maximum
Explanation:
At the point of maximum displacement, the speed is zero while the restoring force is maximum. In fact:
- The restoring force is given by , where k is the spring constant and x is the displacement - at the point of maximum displacement, x is maximum, so F is maximum as well
- the total energy of the system is sum of kinetic energy and elastic potential energy:
where m is the mass of the system and v is the speed. Since E (the total energy) is constant due to the law of conservation of energy, we have that when K increases, U decreases, and viceversa. As a result, when x increases, v decreases, and viceversa. At the point of maximum displacement, x is maximum, so v will have its minimum value (which is zero, since the system is changing direction of motion).
A) 6.64 m/s downward
B) 0.026 s
C) -40.9 N
Explanation:
A)
We can solve this problem by using the law of conservation of energy.
In fact, since the total mechanical energy of the ball must be conserved, this means that the initial gravitational potential energy of the ball before the fall is entirely converted into kinetic energy just before it reaches the floor.
So we can write:
where
m = 0.160 kg is the mass of the ball
is the acceleration due to gravity
h = 2.25 m is the initial height of the ball
v is the final velocity of the ball before hitting the ground
Solving for v, we find:
And the direction of the velocity is downward.
B)
The motion of the ballduring the collision is a uniformly accelerated motion (= with constant acceleration), so the time of impact can be found by using a suvat equation:
where:
v is the final velocity
u is the initial velocity
s is the displacement of the ball during the impact
t is the time
Here we have:
u = 6.64 m/s is the velocity of the ball before the impact
v = 0 m/s is the final velocity after the impact (assuming it comes to a stop)
s = 0.087 m is the displacement, as the ball compresses by 0.087 m
Therefore, the time of the impact is:
C)
The force exerted by the floor on the ball can be found using the equation:
where
is the change in momentum of the ball
t is the time of the impact
The change in momentum can be written as
So the equation can be rewritten as
Here we have:
m = 0.160 kg is the mass of the ball
v = 0 is the final velocity
u = 6.64 m/s is the initial velocity
t = 0.026 s is the time of impact
Substituting, we find the force:
And the sign indicates that the direction of the force is opposite to the direction of motion of the ball.