Question

1) a 130 pound block slides up a 22.6'' en dine with coefficient of friction of 0.1 and initial velocity of 30 ft/sec. how far will the block slide up the incline before coming to rest?

a)18ft

b)29ft

c)42ft

d)57ft

2) Luio Freight cars weighing 5000 kg each roll toward each other and couple. The left car has a velocity of 1.5 m/s and the right car has a velocity of 1.2 m/s prior to impact. What is the velocity of the two cars coupled together after the impact?

a)0.013 m/s

b)0.26m/s

c)1.4 m/s

d) 16 m/s

3) A point travels in a circle according to to w=6t^2-10t . where t is in second. Determine the angular displacement between t=1s and t=3s.

a)6rad

b)10rad

c)12rad

d)15rad

Answer 1

1)

Here,

according to question,

theta = 22.6^o

So, along vertical direction with respect to the inclined surface :

N = m * g * cos(22.6)

Also,

along horizontal direction with respect to the inclined surface:

F_net = frictional force + m * g * sin(22.6)

So,

a_net = 15.32 ft sec^-2

Now,

using motion equations:

a_net will be negative because it is in opposite direction of motion of block

v = final velocity = 0 ft/sec

u = initial velocity = 30 ft/sec

s = distance travelled by block

s = 29.37 ft

So, Answer : B) 29 ft

2)

M₁ = 5000 kg = M₂

V₁ = 1.5 m/s

V₂ = -1.2 m/s (Since, both cars are rolling towards each other)

Let V be the velocity with which both cars move after impact

So, by conservation of momentum:

initial momentum = final momentum

V = 0.15 m/s

So, Answer : B) 0.26 m/s (nearly equal. Since all other options have large deviations)

C)

We know

where, theta = angular displacement

omega = angular speed

So,

On solving,

theta = 12 radians

So, Answer: C) 12 radians

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