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Explain Bot To calculate the gravitational energy (potential energy) of the 20 kg ball at its apex 2 m above the trampoline, you can use the formula:
Gravitational Energy = mass * gravitational acceleration * height
a) The gravitational acceleration is approximately 9.8 m/s^2 (standard value). Plugging in the values:
Gravitational Energy = 20 kg * 9.8 m/s^2 * 2 m
Gravitational Energy = 392 J
Therefore, the gravitational energy of the 20 kg ball at its apex is 392 Joules.
To calculate the kinetic energy of the ball just before impacting the trampoline, you can use the formula:
Kinetic Energy = (1/2) * mass * velocity^2
First, you need to find the velocity of the ball just before impact. Since no other information is provided, we'll assume the ball is dropped from rest.
Using the equation:
velocity = sqrt(2 * gravitational acceleration * height)
where the height is 2 m and gravitational acceleration is 9.8 m/s^2:
velocity = sqrt(2 * 9.8 m/s^2 * 2 m) = sqrt(39.2) m/s ≈ 6.26 m/s
b) Plugging in the values:
Kinetic Energy = 0.5 * 20 kg * (6.26 m/s)^2
Kinetic Energy = 0.5 * 20 kg * 39.12 m^2/s^2
Kinetic Energy = 392.4 J
Therefore, the kinetic energy of the ball just before impacting the trampoline is approximately 392.4 Joules.
To find the k-value of the trampoline, you can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement of the spring from its equilibrium position. The equation for Hooke's Law is:
Force = -k * displacement
c) In this case, the displacement is given as 0.35 m. The negative sign indicates that the force is acting in the opposite direction of the displacement.
The force acting on the ball, just before impact, is the weight of the ball (mg) and can be calculated using:
Force = mass * gravitational acceleration
Force = 20 kg * 9.8 m/s^2 = 196 N
Since the trampoline stretches below its unstretched surface, it exerts an upward force on the ball equal in magnitude to the weight of the ball. So, the force exerted by the trampoline is also 196 N.
Using Hooke's Law, we can equate the force exerted by the trampoline to the k-value multiplied by the displacement:
Force = -k * displacement
196 N = -k * 0.35 m
Solving for k:
k = -196 N / 0.35 m ≈ -560 N/m
Therefore, the k-value of the trampoline is approximately 560 N/m. Note that the negative sign indicates a restoring force acting in the opposite direction of the displacement.