a) The energy stored in the spring is 0.32 J.
b) The change in kinetic energy from the moment the object is released until it stops is -0.078 J.
c) The energy lost to friction as the object rises is 0.32 J.
How the Energy calculations with incline was done
a. To calculate the energy stored in the spring, we can use the formula for potential energy of a spring:
U = (1/2) k x^2
where U is the potential energy stored in the spring, k is the spring constant, and x is the distance the spring is compressed.
Plugging in the given values, we get:
U = (1/2) * 100 N/m * (0.08 m)^2
U = 0.32 J
Therefore, the energy stored in the spring is 0.32 J.
b. The initial potential energy stored in the spring is converted to kinetic energy as the object is released and moves up the incline. At the top of the incline, all of the kinetic energy is converted back to potential energy. At this point, the object comes to a stop.
To calculate the change in kinetic energy from the moment the object is released until it stops, we can use the conservation of energy:
K1 + U1 + Wnc = K2 + U2
Since K1 = K2 = 0, and U1 = 0.32 J (from part a), we have:
Wnc = U1 - U2
Wnc = 0.32 J - mgh
Plugging in the given values, we get:
Wnc = 0.32 J - 0.05 kg * 9.8 m/s^2 * 1 m
Wnc = -0.078 J
Therefore, the change in kinetic energy from the moment the object is released until it stops is -0.078 J.
c. To calculate the energy lost to friction as the object rises, we can use the same equation as in part b:
Wnc = U1 - U2
Plugging in the values from part a and the final potential energy at the maximum height (which is 0), we get:
Wnc = 0.32 J - 0
Wnc = 0.32 J
Therefore, the energy lost to friction as the object rises is 0.32 J.
d. we can use the equation for the work done by friction:
Wf = f * d * cos(theta)
At the top , so the work done by friction is equal to the initial potential energy stored in the spring (from part a):
Wf = U1
Plugging in the given values and solving for f, we get:
U1 = f * d * cos(theta)
0.32 J = f * 1 m * cos(30°)
f = 0.64 N
The normal force on the object is equal to its weight, which is mg, where g is the acceleration due to gravity (9.8 m/s^2):
N = mg
N = 0.05 kg * 9.8 m/s^2
N = 0