a 0.0780 kg lemming runs off a 5.36 m high cliff at 4.84 m/s. what is its total mechanical energy(ME)PLEASE HELP
2 answers:
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- The length of the cross product of two vectors
- The scalar triple product of the vectors a, b, and c
- The volume of the parallelepiped determined by the vectors a, b, and c is the magnitude of their scalar triple product.
<u>Explanation</u>:
- The length of the cross product of two vectors is
| a
b | = |a| |b| sin θ
- The length of the cross product of two vectors is equal to the area of the parallelogram determined by the two vectors (see figure below).
- Anticommutativity:
| a b | = - | b
a |
- Multiplication by scalars:
(ca) b = c (a
b) = a
(cb)
- Distributivity:
a (b + c) = (a
b) + (a
c)
- The scalar triple product of the vectors a, b, and c:
a . (b c) = (a
b) . c
- The magnitude of the scalar triple product is the volume of the parallelepiped of the vectors a, b, and c.
- The vector triple product of the vectors a, b, and c is given as
a (b
c) = (a.c) b - (a.b)
c
Answer:
a) 24 J
b) Gravitational Force
c) 45 J
d) 0
e) 6.782m/s
Explanation:
a) m = 3kg
v = 4m/s
h = 1.5m
KE = ?
0.5 * 3 * 16 = 24J
b) Gravitational force
c) F = ma = 3 * 10 = 30N
Work done = Force * distance = 30 * 1.5 = 45J
d) Final Kinetic Energy of the ball is zero because the ball eventually stops moving
e) velocity of ball as it strikes the ground = v
where
v is the velocity as it strikes the ground
u is the initial velocity
a is acceleration
s is the distance
Now since the ball is thrown downwards, a is positive because the velocity of the ball is increasing as the gravitational force acts on it
u = 4m/s
a = 10
s = 1.5
=>
=
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