Please show every step of the solutions. Many thanks in advance! A 5 kg block is
ID: 1282311 • Letter: P
Question
Please show every step of the solutions. Many thanks in advance!
A 5 kg block is moving at v0 = 6 m/s along a frictionless, horizontal surface toward a spring with force constant k = 500 N/m that is attached to a wall, (a) Find the maximum distance that the spring will be compressed, (b) If the spring is to be compressed no more than 0.15 m, what is the maximum value of v0. How many joules of energy does a 100 Watt light bulb use per hour? How fast would a 70 kg person have to run to have the same amount of kinetic energy? A ski tow operates on a ski slope that is 300 in long at an angle of 15degree. The rope moves at 12 km/hr and can move a total of 50 skiers. Assuming the average mass of the skiers is 70 kg, determine the power required to operate the tow. You may treat the slope as frictionless. The engine of a car with mass m supplies a constant power P to the wheels to accelerate the car. You can ignore rolling friction and air resistance. The car is initially at rest, (a) Find the speed of the car as a function of time t in terms of m, P and t. (b) Find the acceleration as a function of the same variables.Explanation / Answer
1) a) Ei = Ef
1/2 mv^2 = 1/2 kx^2
5*6^2 = 500*x^2
x=0.6 m
b)
1/2 mv^2 = 1/2 kx^2
5*v^2 = 500*0.15^2
v=1.5 m/s
2)
P = W/t
W = 100*60*60=3.6E5 J
b) 3.6E5 = 0.5*70*v^2
v=101 m/s
3)
so add forces up the slope
F - m g sin theta = 0
F = 50*70*9.81*sin(15 degrees)
12 km/hr = 3.33 m/s
P = F v = 50*70*9.81*sin(15 degrees)*3.33= 2.96E5 W
4) a) W = 1/2 mv^2
W = P t
so P t = 1/2 mv^2
v = sqrt( 2 P t/m)
b) P = F v and F = m a
P = m a v
P = m a sqrt( 2 P t/m) = a sqrt( 2 m P t)
a = sqrt( P/( 2 m t))
c) v = sqrt( 2 P/m) t^(1/2)
v = dx/dt
so dx = sqrt( 2 P/m) t^(1/2) dt
integrate both sides
x = sqrt( 2 P/m) 2/3* t^(3/2)
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