This question refers to procedure 1. Two carts sit on a horizontal, frictionless
ID: 1453680 • Letter: T
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This question refers to procedure 1. Two carts sit on a horizontal, frictionless track; the spring between them is compressed. The small cart has mass m, and the mass of the larger cart is M = 5.04m. Every velocity needs magnitude and direction (given by the sign). Suppose the carts are initially at rest, and after the "explosion" the smaller cart is moving at velocity v = + 3.48 m/s. - Find the velocity of the larger cart. V = m/s - Assume now that the mass of the smaller cart is m = 7.44 kg. Assuming there is no loss of energy: find the energy stored in the spring before the explosion. W_k = J - If the spring has spring constant k = 863 N/m: find x, the distance the spring was compressed before the "explosion". Suppose the carts are initially moving together, with the spring compressed between them, at constant velocity v_0 = +7.97 m/s. After the "explosion", the smaller cart is moving at velocity v = +3.48 m/s. Find the velocity of the larger cart. V = 1 m/s Suppose now that the small cart (mass m) is Initially moving at velocity v_0 = +3.68 m/s. At what velocity would the large cart (mass 5.04m) have to be moving so, when they collide and stick together, they remain at rest?Explanation / Answer
A pair of cart sits on a frictionless track. Assume the mass of the larger cart is 5.04 times the mass of the
small cart, In this system, however, there is a spring between the carts which can "explode", pushing on the two carts at once..
let mass of small cart = m
mass of larger cart = 5.04*m
a) Suppose the carts are initially at rest, and after the "explosion" the smaller cart is moving at velocity +3.48 m/s.
Momentum is always conserved!
Initial momentum = 0, since both carts are at rest
Final momentum = (m * 3.48) + (5.04 * m * v)
Final momentum = Initial momentum
(m * 3.48) + (5.04 * m * v) = 0
(m * 3.48) = -(5.04 * m * v)
v = -0.69 m/s
The velocity of the larger cart = 0.69 m/s in the opposite direction of smaller cart.
- If the mass of the smaller cart is 7.44 kg, find the energy supplied by the spring to the carts.
The energy supplied by the spring is transferred to the carts.
Total KE of carts = energy supplied by the spring
KE = ½ * mass * velocity^2
Mass of larger car = 5.04 * 7.44 = 37.5 kg
Total KE = ½ * 7.44 * 3.48^2 + ½ * 37.5 * 0.69^2
The energy supplied by the spring = ½ * 7.44 * 3.48^2 + ½ * 37.5 * 0.69^2 = 53.98 J
Spring potential energy = ½ * k * distance^2
½ *863* distance^2 = 53.98
distance = 0.354 m
b) Suppose the carts are initially moving together at constant velocity +7.97 m/s. After the "explosion", the smaller cart is moving at velocity +3.48 m/s. Find the velocity of the larger cart.
Total Initial momentum = (7.44 + 37.5) * 7.97
Total Final momentum = (7.44 * 3.48) + (37.5 * vf)
(7.44 * 3.48) + (37.5 * vf) = (7.44 + 37.5) * 7.97
vf = 8.86 m/s
c) Total Initial momentum = m*3.68 + 5.04m*v
Total Final momentum = 0
m*3.68 + 5.04m*v = 0 =======> v = -0.73 m/s
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