How high does the 35g ball go if the ball leaves the spring at the point shown in image? K=953 N/m and Xa=0 and Xb=0.120m
(b)? What is the velocity of the ball when it leaves the spring?
A figure is needed to make sense of this.
To determine the maximum height that the ball reaches and its velocity when it leaves the spring, we can use the principle of conservation of mechanical energy.
1. Calculate the potential energy at point A:
- Potential energy at point A is given by the equation Ua = (1/2) * k * Xa^2, where "k" is the spring constant and "Xa" is the displacement from the equilibrium position.
- In this case, Xa = 0, so the potential energy at point A is zero: Ua = 0.
2. Calculate the total mechanical energy at point B:
- The total mechanical energy at point B is given by the equation Eb = (1/2) * k * Xb^2 + (1/2) * m * Vb^2, where "m" is the mass of the ball, "Xb" is the displacement from the equilibrium position, and "Vb" is the velocity at point B.
- In this case, Xb = 0.120m and m = 35g = 0.035kg.
3. Calculate the velocity at point B:
- To find the velocity at point B, we need to find the total mechanical energy at point B first.
- Since the potential energy at point A is zero, the total mechanical energy at point B is equal to the potential energy at point B: Eb = (1/2) * k * Xb^2.
- Plugging in the given values: Eb = (1/2) * (953 N/m) * (0.120m)^2.
4. Determine the maximum height:
- At the maximum height, the kinetic energy is zero, so the total mechanical energy is equal to the potential energy.
- Since the kinetic energy at the maximum height is zero, the potential energy at the maximum height is equal to the total mechanical energy at point B: Umax = (1/2) * k * Xb^2.
- Plugging in the given values: Umax = (1/2) * (953 N/m) * (0.120m)^2.
5. Calculate the maximum height:
- The maximum height can be calculated using the equation Umax = m * g * h, where "g" is the acceleration due to gravity and "h" is the maximum height.
- Rearranging the equation: h = Umax / (m * g).
- Plugging in the given values: h = (Umax) / (0.035kg * 9.8 m/s^2).
6. Calculate the velocity at point B:
- To find the velocity at point B, we need to use the equation v = sqrt((2 * (Eb - Umax)) / m), where "v" is the velocity at point B.
- Plugging in the given values: v = sqrt((2 * ((1/2) * (953 N/m) * (0.120m)^2 - Umax)) / 0.035kg).
By following these steps, you can find both the maximum height the ball reaches and its velocity when it leaves the spring.