Suppose the cart has mass m = 766 g, and it strikes the clay at speed v o = 3.56

Question

Suppose the cart has mass m = 766 g, and it strikes the clay at speed vo = 3.56 m/s and comes to a dead stop. Assume the track is frictionless, and the clay is crushed inward by 1.71 cm.

a) Find the magnitude of the impulse exerted by the clay on the cart.  
J = __ N-s

b) Find the magnitude of the average force exerted by the clay on the cart.
HINT: Use kinematics, assuming the force is constant during the impulse!
Favg = __ N

c) Find the time it took for the cart to come to rest while in contact with the clay.
t = __ s

Explanation / Answer

a)

initial momentum of the cart = Pi = m Vo = 0.766 x 3.56 = 2.73 m/s

final momentum of cart = Pf = 0

Impulse = change in momentum = Pf - Pi = 0 - 2.73 = - 2.73 kgm/s

impulse magnitude = 2.73

b)

Vi = initial speed = 3.56 m/s

Vf = final speed = 0

a = acceleration

d = distance travelled = 1.71 cm = 0.0171 m

using the equation

Vf2 = Vi2 + 2 a d

02 = 3.562 + 2 a (0.0171)

a = - 370.6 m/s2

force is given as

F = ma = 0.766 x 370.6 = 283.88 N

c)

Impulse = F t

2.73 = 283.88 t

t = 0.00962 sec

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