A 0.50-kg croquet ball is initially at rest on the grass. When the ball is struck by a mallet, the average force exerted on it i
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Answer:
46.48m/s
Explanation:
The problem is a combination of the principle of conservation of linear momentum and projectile motion.
The principle of conservation of linear momentum states that in a closed system, the total momentum of colliding bodies before impact is equal to the total momentum after impact. The masses stated in the problem experienced an inelastic collision. In an inelastic collision, the bodies involved stick together after the collision and move with a common velocity.
For two bodies of masses and
moving with velocities
and
before impact, if they experience inelastic collision, the conservation of their momenta is as stated in equation (1);
were v is their common velocity after impact. If the second mass was at rest before the impact, then its initial velocity
. therefore
. Equation (1) then becomes;
In the problem stated, the second mass taken as the mass of the wooden block was at rest before the impact and the collision was inelastic since both the wood and the dart stuck together and moved with a common velocity after the impact. Therefore we can use equation (2) for the problem.
Given;
Substituting these values into (2), we get the following;
Their common v velocity after impact now makes both the wooden block and the dart (as a single body) to fall vertically through a height h of 1.5m over a range R of 3.5m as stated by the problem; hence by the principle of projectile motion for a body projected horizontally, the following relationship holds;
were t is the time taken to fall through the height h. To obtain t we use the second equation of free fall under gravity;
were g is acceleration due to gravity taken as . Therefore;
We then substitute R and t into equation (4) to obtain v.
We now further substitute this value of v into (3) to obtain ;
Answer:
Explanation:
The capacitance of a parallel plate capacitor is given by:
(1)
where
is the vacuum permittivity
A is the area of the plates
d is the separation between the plates
The charge stored on the capacitor is given by
(2)
where C is the capacitance and V is the voltage across the capacitor.
The displacement current in the capacitor is given by
(3)
where t is the time elapsed
Substituting (1) and (2) into (3), we find an expression for the displacement current:
where we have
Substituting into the equation, we find