In the figure at right, a 3.00kg block is accelerated from rest by a compressed
ID: 1454512 • Letter: I
Question
In the figure at right, a 3.00kg block is accelerated from rest by a compressed spring. The spring's initial compression distance is Deltax = 0.500m; the spring constant is 600N/m. The block leaves the spring at the spring's relaxed length at A and then travels up a functionless 30degree incline before coming to a stop at C. (a) Calculate the initial potential energy of the compressed spring. (b) Calculate the total mechanical energy of the earth-block-spring system. (Assume that the block has gravitational potential energy of zero at Position A) (c) Calculate the kinetic energy of the block at the instant that it leaves the spring. (d) Use conservation of mechanical energy to calculate the height, h to which the block slides along the incline before coming to a stop at C. (e) Using mechanical energy conservation, calculate the speed of the block after it has slid 2.00m up the incline (Position B).Explanation / Answer
Given mass m= 3kg
initial compression x = 0.5 m
K = 600 N/m
a)
initial potential energy is
U = 1/2 * k * x^2
U = 0.5 * 600 * 0.5^2
u = 75 J
b)
total mechanical energy
E = 75 J
c)
The knetic energy of the block at the instant it leaves the spring
is K.E = 75 J
d)
from conservation of energy
mgh = K.E
3 * 9.8 * h = 75
h = 2.55 m
e)
at position B
1/2 m * v^2 + mgh = E
1/2 * 3 * v^2 + (3*9.8*2* sin(30)) = 75
v = 5.51 m/s