A box with mass\' m = 43.kg slides down a Ar = 10 m ramp with incline 6 = 24\".
ID: 1485480 • Letter: A
Question
A box with mass' m = 43.kg slides down a Ar = 10 m ramp with incline 6 = 24". Find the work done by gravity. A cart on a roller coaster moves at 29_m/s when 59.m above the ground. Assuming all of the energy is mechanical, find the speed of the cart when it is 22_m above the ground. A toy train engine (2.5 kg) is moving 0.25 m/s when it collides with a car (1.6 kg) moving 0.15 m/s in the same direction, and they stick together. Find the speed of the engine-car combination as they move off together. Let A = - 5.7i + 0.56j + 2.2k and B = 3.7i + 6.4j + 4.5k. Then find C = A x B.Explanation / Answer
17) workdone by gravitational force = F * displacement
W= mgsin(theta)* delta r = 43*9.8sin(24degree)*10= 1714 J
OPTION 'e'
18) according to mechanical energy conservation
mgh1 + (mv^2)/2 = mgh2 + (m(v')^2)/2
where v is initial velocity and v' is final velocity
=> 9.8*59+ (29^2)/2 = 9.8*22 + (v')^2/2
=> v' = 39.58 m/s
OPTION 'b'
19) according to momentum conservation
m1v1+m2v2 = (m1+m2)Veq
2.5*0.25 + 1.6*0.15 =(2.5+1.6)Veq
=> Veq = 0.2110 m/s
OPTION 'f'
20,21,22) A = -5.7i+ 0.56j+2.2k
B = 3.7i+6.4j+4.5k
C =A X B = (-5.7i+ 0.56j+2.2k ) X (3.7i+6.4j+4.5k) = -36.48k+25.65j-2.072k+2.52i+8.14j-14.08i
C = -11.56i+33.79j-38.55k
20) Cx= -11.56 OPTION 'a'
Cy = 33.79 OPTION 'd'
Cz = -38.55 OPTION 'a'
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