If you walk 1.2 km north and then 1.6 km east, what are the magnitude and direction of your resultant displacement?
1 answer:
B
Assume north and east as two sides of a right angled triangle. magnitude of the distance is then given by the length of the hypotenuse which is
where a = 1.2 km north
and b = 1.6 km east
magnitude = 2 km
Direction is given by the angle between them, that is atan(a/b) = 36.86 deg north of east = 53.1 deg east of north.
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Answer:
1.54 kg
Explanation:
mass of first block (m) = 0.76 kg
acceleration due to gravity (g) = 9.8 m/s
what is the mass (m) of the second block
- force = kx ⇒ mg = kx
mg = kx
where m is the mass, g is the acceleration due to gravity, k is the
spring constant and x is the extension
0.76 x 9.8 = kx
7.5 = kx
k = 7.5/x ... equation 1
- when a second block is attached to the first one the amount of stretch triples (this means that extension (x) = 3x)
therefore the new mass becomes m + 0.76 and the extension
becomes 3x
with the new mass and extension, mg = kx now becomes
(m+0.76)g = k(3x) ... equation 2
Recall that k = 7.5/x from equation 1, substituting this value of k into
equation 2 we have
(m+0.76)g = × (3x)
(m+0.76)g = 7.5 × 3
substituting the value of g = 9.8 m/s^{2}
(m + 0.76) x 9.8 = 7.5 x 3
m + 0.76 = 22.5 ÷ 9.8
m + 0.76 = 2.3
m = 2.3 - 0.76 = 1.54 kg