Calculate the energy dissipated from the brakes of a 1500 kg car when it deceler

Question

Calculate the energy dissipated from the brakes of a 1500 kg car when it decelerates from 80 km/h to a stop (370.4 kJ) The stiffness of a spring is 88 N/mm of axial compression. Calculate th compression from 50 mm to 80 mm (171.61) The tractive resistance of a vehicle of 2000 kg mass is 0.18 N/kg. If a total pull of 1 kN is applied to the vehicle find a) The acceleration (0.32 m/s) b) The speed after travelling for one minute from rest (19.2 m/s) c) The work done during the one minute (576 kl) d) The energy lost to friction (207.36 kJ) A hammer head moving at a velocity of 10 m/s strikes a board and is brought to rest in 3 milliseconds while exerting an average force of 2000N. Find the mass of the hammer head (0.6 kg) 1) 2) 3) e work to increase the 4) 5) For each of the following collisions E Ekmnut Ex mv i) Find the final common velocity if the objects remain stuck together (inelastic) i) Find the loss of kinetic energy U) for the inelastic collision ii) Find the final velocities of each after an elastic collision. a) A 12 kg mass is moving right at 2 m/s and collides with a 4 kg mass moving left at 8 m/s (-0.5 m/s, 150 J, -3 m/s, 7 m/s) A 200 gram mass moving up at 45 m/s collides with a 1.2 kg mass moving down at 12 m/s (-3.86 m/s, 278.47 J, -52.72 m/s, 4.29 m/s) A group of 12 rail cars is moving north with an initial velocity of 3 m/s.It collides, and remai connected to a group of 15 cars moving south on the same track. After the collision, the group of 27 cars is heading north at 1 m/s. The mass of each car is 8 tonne. Find the initial velocity of th southbound group of cars (0.6 m/s) lCave values in tonn s ns 6) bullet with a mass of 40 g is fired at a stationary block of mass 2.2kg. After collision, the block has a velocity of 1.95 m/s. Determine the initial velocity of the bullet if: a) The bullet becomes embedded in the block (109.2 m/s) b) The bullet passes through the block and exits with a velocity of 45 m/s (152.2 A bullet of mass 30 grams is fired into a freely suspended block of oak. The initial velocity of the bullet is 600 m/s. Immediately after the collision, the velocity of the block with the emb is 2 m/s. Find a) The mass of the block (8.97 kg) b) The change in total kinetic energy (before and after the collision (5382 J c) The maximum height reached by the block as it swings up (0.204 m 7) A 5 m/s) 8) edded b

Explanation / Answer

1) mass of car m = 1500 kg

deceleration is a = -80 kmph

energy dissipated is u = 0.5*m*v^2

= 0.5*1500(80*5/18)^2 J

= 370370.370 J

= 370.370 j = 370.4 kJ

2)

given stiff ness of a spring k = 88 N/mm = 88000 N/m

work done in increasing the compression from 50 mm to 80 mm is = change in elastic potential energy

W = 0.5*k(x2^2-x1^2)

W = 0.5*88000(0.08^2 - 0.05^2) J

W = 171.6 J

3) tractve resistance is a = 0.18 N/kg

a) mass m = 2000 kg

force applied is F = 1000 N

the acceleration is , a = (1000 - 0.18*2000)/2000 = 0.32 m/s2

b)

speed after one minute from rest is  

v = u+at

v = 0 +0.32*60 m/s

v = 19.2 m/s

c) work done during one minute is W = 0.5*mv^2 = 0.5*2000*19.2^2 J = 368640 J

work done due to friction is 368640 J

the energy lost is 576000 - 368640 = 207360 J

4)

v = 10 m/s, t= 3*10^-3 s,

F = 2000 N

m = ?

we know that rate of momentum = force

m(v2-v1)/t = F

m = F*t/(v2-v1)

m = 2000*3*10^-3/(0-10) kg

m= 0.6 kg

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