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1. Vector v has a magnitude of 76 m and vector u has a magnitude of 77 m. The angle
between v and u is 150°. What is v•u ? Answer in m^2
v i u = v u cosϕ = ( 76 ) ( 77 ) cos150º = −5,067.98
2. A net force of 1.6×〖10〗^(-15) N acts on an electron over a displacement of 5.0 cm, in
the same direction as the net force.
(a) What is the change in kinetic energy of the electron in Joules?
The change in kinetic energy is equal to the work done in moving the electron:
ΔKE = W = Fx = (1.6 × 10 −15 N ) ( 0.05m ) = 8.0 × 10 −17 J
(b) If the electron was initially at rest, what is the speed of the electron in m/s? An
electron has a mass of 9.1×〖10〗^(-31) kg.
KE =
1 2
mv
2
8.0 × 10 −17 =
v =
2
1
9.1× 10 −31 ) v 2
(
2
2 ( 8.0 × 10 −17 )
9.1× 10 −31
v = 1.33 × 10 7 m / s
3. An applied force accelerates a 50-kg crate along a frictionless floor from rest to 5 m/s.
The work performed by this force is most nearly (choose the correct answer):
125 J
250 J
500 J
625 J
1,250 J
Work = change in kinetic energy
= ½(m)(5 m/s)2 – ½(m)(0 m/s)2 = ½(50 kg)(5 m/s)2 = 625 J
4. During the collision of two galaxies, two of their stars, having equal masses and
speeds, make a head-on collision and merge into a single star. Choose the correct
statement.
A. The total energy of the system, mechanical and otherwise, is conserved in the
collision.
B. The collision conserves the kinetic energy of the system.
C. The merged star moves in the direction of motion of the larger galaxy.
D. Conservation of momentum is not applicable in such a situation.
E. Both momentum and kinetic energy are conserved in the collision.
5. A motor lifts a 70.0 kg box off the ground, starting from rest. In 8.00 seconds it lifts
the box to a height of 20.0 m. At that time, the box is moving upward with a velocity of
5.00 m/s. What is the average power of the motor during this time interval?
Average power =
work done
time
Work done = change in potential energy + change in kinetic energy
1
Work done = mgh + mv 2
2
Work done = ( 70 kg ) ( 9.8 m / s 2 ) ( 20 m ) +
Work done = 14,595 J
Average power =
14,595 J
= 1,824.4W
8s
1
2
70 kg ) ( 5 m / s )
(
2