An initially electrically neutral conducting sphere is placed on an insulating stand. A negatively-charged glass rod is brought
1 answer:
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Answer: 0.5 seconds or 2.625 seconds
Explanation:
At t = 0, The ball is 4 ft above the ground.
The height of the football varies with time in the following way:
s(t) = -16 t² + 50 t + 4
we need to find the time in which the height would of the football would be 25 ft:
⇒25 = -16 t² + 50 t + 4
we need to solve the quadratic equation:
⇒ 16 t² - 50 t + 21 = 0
⇒ t = 0.5 s or 2.625 s
Therefore, at t = 0.5 s or 2.625 s, the football would be 25 ft above the ground.
Answer:
1. True
2. False
3. True
Explanation:
Newton's 2nd law states that the net force exerted on an object is equal to the product between the mass of the object and its acceleration:
(1)
where
is the net force on the object
m is its mass
a is the acceleration
Furthermore, we know that acceleration is defined as the rate of change of velocity:
So let's now analyize the three statements:
1. A net force causes velocity to change: TRUE. Net force (means non-zero) causes a non-zero acceleration, which means that the velocity of the object must change.
2. If an object has a velocity, then we can conclude that there is a net force on the object: FALSE. The fact that the object has a velocity does not imply anything about its acceleration: in fact, if its velocity is constant, then its acceleration is zero, which would mean that the net force on the object is zero. So this statement is not necessarly true.
3. Accelerations are caused by the presence of a net force: TRUE. This is directly implied by eq.(1): the presence of the net force results in the object having a non-zero acceleration.
Answer:
a) The work done by the applied force is 1500 joules.
b) The kinetic energy of the block after 10 seconds is 1200 joules.
c) The magnitude of the force of friction is 3 newtons and its direction is against motion.
d) 300 joules of energy are lost during motion.
Explanation:
a) Since the object has a constant mass, on which a constant horizontal force is exerted. The work done by the force (), measured in joules, is defined by the following expression:
(1)
Where:
- Force, measured in newtons.
- Distance, measured in meters.
If we know that and
, then the work done by the force exerted on the object is:
The work done by the applied force is 1500 joules.
b) At first we need to calculate the net acceleration of the object (), measured in meters per square second. By assuming a constant acceleration, we use the following kinematic formula:
(2)
Where is the initial velocity of the object, measured in meters per second.
We clear the acceleration within the equation above:
If we know that ,
and
, then the net acceleration experimented by the object is:
By the 2nd Newton's Law, we construct the following equation of equilibrium under the consideration of a friction force acting against the motion of the object:
(3)
Where:
- External force exerted on the object, measured in newtons.
- Kinetic friction force, measured in newtons.
If we know that ,
and
, the kinetic friction force is:
The work done by friction (), measured in joules, is:
(4)
And the net work experimented by the object is:
By the Work-Energy Theorem we understand that change in translational kinetic energy (), measured in joules, is equal to the change in net work. That is:
(5)
If we know that , then the change in translational kinetic energy is:
The kinetic energy of the block after 10 seconds is 1200 joules.
c) The magnitude of the force of friction is 3 newtons and its direction is against motion.
d) The energy lost by the object is equal to the work done by the force of friction. Therefore, 300 joules of energy are lost during motion.