a waterwheel built in Hamah, Syria, has a radius of 20 m . If the tangential velocity at the wheels edge is 7.85 m/s , what is t
1 answer:
Answer:
3.08m/s²
Explanation:
Given parameters:
Radius = 20m
Tangential velocity = 7.85m/s
Unknown:
Centripetal acceleration = ?
Solution:
Centripetal acceleration is the acceleration of a body along a circular path.
it is mathematically given as;
a =
v is the tangential velocity
r is the radius
a = = 3.08m/s²
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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: v = 0.6 m/s
Explanation: <u>Momentum</u> <u>Conservation</u> <u>Principle</u> states that for a collision between two objects in an isolated system, the total momentum of the objects before the collision is equal to the total momentum of the objects after the collision.
Momentum is calculated as Q = m.v
For the piñata problem:
Before the collision, the piñata is not moving, so .
After the collision, the stick stops, so .
Rearraging, we have:
Substituting:
0.6
Immediately after being cracked by the stick, the piñata has a swing speed of 0.6 m/s.